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}
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@article{8050604b-681f-354b-ab48-39957b0409a7,
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@article{b12b2451-33d8-353d-ad23-1608f2964126,
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@Inbook{Kossovsky2020,
author={{Kossovsky, A. E.}},
title="The Bitter Dispute with Leibniz over Calculus Priority",
bookTitle="The Birth of Science",
year="2020",
publisher="Springer International Publishing",
address="Cham",
pages="161--161",
abstract="Newton invented the calculus in the mid to late 1660s, almost a decade before Leibniz did so independently and ultimately more influentially. Newton later became involved in a long and very bitter dispute with Leibniz over priority in the development of calculus (a.k.a `the Leibniz--Newton Calculus Controversy'). Most modern historians believe that Newton and Leibniz developed calculus independently, although with very different notations.",
isbn="978-3-030-51744-1",
doi="10.1007/978-3-030-51744-1_33",
url="https://doi.org/10.1007/978-3-030-51744-1_33"
}
@article{koyama2005,
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 author = {{Koyama, S. -J., & Kurokawa, N.}},
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 pages = {1257--1265},
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 title = {Euler's Integrals and Multiple Sine Functions},
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}
@inbook{anglin1995,
author={{Anglin, W. S., Lambek, J.}},
title={Mathematics in the Renaissance},
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year={1995},
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pages={125--131},
isbn={978-1-4612-0803-7},
doi={10.1007/978-1-4612-0803-7_25}
}
@book{gregory1668geometriae,     url={https://archive.org/details/gregory_universalis/page/n144/mode/1up},
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    author={{Gregory, J.}},
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    publisher={Typis Heredum Pauli Frambotti},
    address={Patavii},
    language={lat}
}
@book{gregory1668exercitationes,
  title={Exercitationes geometricae},
  author={{Gregory, J.}},
  url={https://books.google.at/books?id=ZtRYqgyD5YsC},
  year={1668},
  publisher={{Typis Guilielmi Godbid, & Impensis Mosis Pitt Bibliopolae, in vico vulgo vocato Little Britain}},
  address={Londini},
  language={lat}
}
@article{Divakaran2007,
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 journal = {Journal of Indian Philosophy},
 number = {5/6},
 pages = {417--443},
 publisher = {Springer},
 title = {{The First Textbook of Calculus: "Yuktibhāṣā"}},
 volume = {35},
 year = {2007}
}
@book{Jyesthadeva1530,
  title={{Ganita-Yukti-Bhasa (Rationales in Mathematical Astronomy)}},
  author={{Jyesthadeva}},    url={https://archive.org/details/raswhishNA-124/page/n1/mode/1up},
  year={1530},
  publisher={Kerala school of astronomy and mathematics},
  address={Kingdom of Cochin}
}
@article{whish1834,
    author={{Whish, C. M.}},
    title={{XXXIII. On the Hindú Quadrature of the Circle, and the infinite Series of the proportion of the circumference to the diameter exhibited in the four S'ástras, the Tantra Sangraham, Yucti Bháshá, Carana Padhati, and Sadratnamála}},
    journal={Transactions of the Royal Asiatic Society of Great Britain and Ireland},
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   number={3},
   year={1834},
   pages={509--523},
   doi={10.1017/S0950473700001221},
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abstract={A'ryab'hatta, who flourished in the beginning of the thirty-seventh century of the Cáli Yuga, of which four thousand nine hundred and twenty years have passed, has in his work, the Aryab'hatiyam, in which he mentions the period of his birth, exhibited the proportion of the diameter to the circumference of the circle as 20000 to 62832, in the following verse:

Chaturadhicam ṣatamashṭaguṇandwáshashṭistathá sahasráṇám Ayutadwaya vishcambhasyásannó vritta pariṇáhah.}
}
@article{GUPTA1974287,
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    year = {1974},
    issn = {0315-0860},
    doi = {10.1016/0315-0860(74)90067-6},
    url = {https://www.sciencedirect.com/science/article/pii/0315086074900676},
    author = {{Gupta, R. C.}},
    abstract = {The paper describes an approximation formula for sine (x + h) that differs from the first four terms of the Taylor expansion only by having 4 in place of 6 in the denominator of the fourth term. It appears in Sanskrit stanzas quoted in a work of about the fifteenth century and given here with translation and explanation.}
}
@book{gregory1939james,
  title={James Gregory: Tercentenary Memorial Volume, Containing His Correspondence with John Collins and His Hither to Unpublished Mathematical Manuscripts, Together with Addresses and Essays Communicated to the Royal Society of Edinburgh, July 4, 1938},
  author={{Gregory, J., & Collins, J.}},
  editor={{Turnbull, H. W.}},
  lccn={40013492},
  url={https://books.google.at/books?id=\_eruAAAAMAAJ},
  year={1939},
  publisher={Royal Society of Edinburgh},
  address={Edinburgh}
}
@misc{Collins1671,
    author={{Collins, J.}},
    year={1671},
    month={02},
    day={15},
    title={{Extracts from a letter from James Gregory to John Collins, 15 February 1671}},
    publisher={University Library},
    address={{Cambridge}},
url={https://archivesearch.lib.cam.ac.uk/repositories/2/archival_objects/566767}
}
@book{taylor1715methodus,
  title={{Methodus incrementorum directa & inversa. Auctore Brook Taylor, LL. D. & Regiae Societatis Secretario}},
  author={{Taylor, B.}},
  url={https://books.google.com/books?id=iXN1xgEACAAJ},
  year={1715},
  publisher={Typis Pearsonianis: Prostant apud Gul. Innys ad Insignia Principis in Coemeterio Paulino MDCCXV},
  address={Londini}
}
@book{taylor1717methodus,
  title={{Methodus incrementorum directa & inversa. Auctore Brook Taylor, LL. D. & Regiae Societatis Secretario}},
  author={{Taylor, B.}},
  url={https://books.google.com/books?id=r-Gq9YyZYXYC},
  year={1717},
  publisher={Impensis Gulielmi Innys ad Insignia Principis in Coemetrio D. Pauli. MDCCXVII},
  address={Londini}
}
@article{17c5d199-da2b-3c2c-90b5-0f8b612544b7,
 ISSN = {00031224},
 URL = {http://www.jstor.org/stable/2090408},
 abstract = {A pair of asymmetric coefficients is introduced which are appropriate for measuring the association in ordered contingency tables. Earlier statistical methods are reviewed, and the new coefficients are shown to be closely related to both Kendall's tau-b and to Goodman and Kruskal's gamma, as well as the commonly used "percentage-difference." They are also shown to have a operational interpretation (in the Goodman-Kruskal sense). Their utility in both square and non-square contingency tables is discussed, as well as the way they may be interpreted as ordinal analogues of the traditional regression coefficients.},
 author = {{Somers, R. H.}},
 journal = {American Sociological Review},
 number = {6},
 pages = {799--811},
 publisher = {[American Sociological Association, Sage Publications, Inc.]},
 title = {A New Asymmetric Measure of Association for Ordinal Variables},
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}
@article{665905b2-6123-3642-832e-05dbc1f48979,
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 author = {{Kendall, M. G.}},
 journal = {Biometrika},
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 pages = {81--93},
 publisher = {[Oxford University Press, Biometrika Trust]},
 title = {A New Measure of Rank Correlation},
 urldate = {2025-01-27},
 volume = {30},
 year = {1938}
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@article{ca468a70-0be4-389a-b0b9-5dd1ff52b33f,
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 publisher = {University of Illinois Press},
 title = {The Proof and Measurement of Association between Two Things},
 urldate = {2025-01-27},
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 year = {1904}
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@book{Meyberg2001b,
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title={{Höhere Mathematik 2: Differentialgleichungen, Funktionentheorie, Fourier-Analysis, Variationsrechnung}},
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@book{Burckel2021,
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abstract="The history of some subjects often makes exciting reading, especially when there is a dispute over dates or prior art. Clarifying who did something before someone else is the work of historians, who can help unravel who should be blamed for an event, and who should take the credit. Untangling events from journals, books and private letters, and placing them in an unbiased, temporal sequence requires subject knowledge, tenacity and objective analysis.",
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doi="10.1007/978-1-4471-7509-4_4",
url="https://doi.org/10.1007/978-1-4471-7509-4_4"
}
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author = {{Pearson, K.}},
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    address={Department of Applied Mathematics. University College, University of London},
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url={https://openlibrary.org/books/OL24168960M}
}
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    author={{Pearson, K.}},
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    title={{Mathematical contributions to the theory of evolution. XIV. On the general theory of skew correlation and non-linear regression}},
    series={{Drapers' Company research memoirs. Biometric Series, II}},
    address={Department of Applied Mathematics. University College, University of London},
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url={https://openlibrary.org/books/OL6555066M}
}
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}
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@article{10.1214/aoms/1177730491,
author = {{Mann, H. B., & Whitney, D. R.}},
title = {{On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other}},
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journal = {The Annals of Mathematical Statistics},
number = {1},
publisher = {Institute of Mathematical Statistics},
pages = {50 -- 60},
year = {1947},
doi = {10.1214/aoms/1177730491},
URL = {https://doi.org/10.1214/aoms/1177730491}
}
@article{Lüroth1876,
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@article{Pearson1895,
   author={{Pearson, K.}},
    year={1895},
    title={Contributions to the Mathematical Theory of Evolution. II. Skew Variation in Homogeneous Material},
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 ISSN = {00063444},
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 author = {{Fisher, R. A.}},
 journal = {Biometrika},
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 title = {Frequency Distribution of the Values of the Correlation Coefficient in Samples from an Indefinitely Large Population},
 volume = {10},
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author = {{Olkin, I., & Pratt, J. W.}},
title = {{Unbiased Estimation of Certain Correlation Coefficients}},
volume = {29},
journal = {The Annals of Mathematical Statistics},
number = {1},
publisher = {Institute of Mathematical Statistics},
pages = {201 -- 211},
abstract = {This paper deals with the unbiased estimation of the correlation of two variates having a bivariate normal distribution (Sec. 2), and of the intraclass correlation, i.e., the common correlation coefficient of a $p$-variate normal distribution with equal variances and equal covariances (Sec. 3). In both cases, the estimator has the following properties. It is a function of a complete sufficient statistic and is therefore the unique (except for probability zero) minimum variance unbiased estimator. Its range is the region of possible values of the estimated quantity. It is a strictly increasing function of the usual estimator differing from it only by terms of order $1/n$ and consequently having the same asymptotic distribution. Since the unbiased estimators are cumbersome in form in that they are expressed as series or integrals, tables are included giving the unbiased estimators as functions of the usual estimators. In Sec. 4 we give an unbiased estimator of the squared multiple correlation. It has the properties mentioned in the second paragraph except that it may be negative, which the squared multiple correlation cannot. In each case the estimator is obtained by inverting a Laplace transform. We are grateful to W. H. Kruskal and L. J. Savage for very helpful comments and suggestions, and to R. R. Blough for his able computations.},
year = {1958},
doi = {10.1214/aoms/1177706717},
URL = {https://doi.org/10.1214/aoms/1177706717}
}
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    url={https://doi.org/10.2307/2340521}
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    publisher = {Institute of Mathematical Statistics},
    pages = {131--153},
    keywords = {categorical data, Chi-squared tests, computational algorithms, conditional inference, Fisher's exact test, logistic regression, loglinear models, Odds ratios, sufficient statistics},
    year = {1992},
    doi = {10.1214/ss/1177011454},
    URL = {https://doi.org/10.1214/ss/1177011454}
}
@book{Cohen1977,
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}
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}
@article{Quenouille1949,
    author = {{Quenouille, M. H.}},
    title = {Approximate Tests of Correlation in Time-Series},
    journal = {Journal of the Royal Statistical Society B},
    series={Methodological},
    volume = {11},
    number = {1},
    pages = {68--84},
    doi = {10.1111/j.2517-6161.1949.tb00023.x},
    url = {https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/j.2517-6161.1949.tb00023.x},
    year = {1949}
}
@article{Efron1979,
    author = {{Efron, B.}},
    title = {{Bootstrap Methods: Another Look at the Jackknife}},
    volume = {7},
    journal = {The Annals of Statistics},
    number = {1},
    publisher = {Institute of Mathematical Statistics},
    pages = {1--26},
    year = {1979},
    doi = {10.1214/aos/1176344552},
    URL = {https://doi.org/10.1214/aos/117634455}
}
@article{Efron1981,
    author = {{Efron, B.}},
    title = {Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods},
    journal = {Biometrika},
    volume = {68},
    number = {3},
    pages = {589--599},
    year = {1981},
    month = {12},
    abstract = {We discuss several nonparametric methods for attaching a standard error to a point estimate: the jackknife, the bootstrap, half-sampling, subsampling, balanced repeated replications, the infinitesimal jackknife, influence function techniques and the delta method. The last three methods are shown to be identical. All the methods derive from the same basic idea, which is also the idea underlying the common parametric methods. Extended numerical comparisons are made for the special case of the correlation coefficient.},
    issn = {0006-3444},
    doi = {10.1093/biomet/68.3.589},
    url = {https://doi.org/10.1093/biomet/68.3.589}
}
@book{Efron1982,
    author = {{Efron, B.}},
    title = {The Jackknife, the Bootstrap and Other Resampling Plans},
    publisher = {{SIAM, Society for Industrial and Applied Mathematics}},
    year = {1982},
    doi = {10.1137/1.9781611970319},
    address = {Philadelphia},
    series   = {CBMS-NSF Regional Conference Series in Applied Mathematics, Monograph 38},
    URL = {https://epubs.siam.org/doi/abs/10.1137/1.9781611970319}
}
@article{Pearson14786440009463897,
    author = {{Pearson,  K.}},
    title = {{X. On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling}},
    journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science},
    volume = {50},
    number = {302},
    pages = {157--175},
    year  = {1900},
    publisher = {Taylor & Francis},
    doi = {10.1080/14786440009463897},
    URL = {https://doi.org/10.1080/14786440009463897},
    eprint = {https://doi.org/10.1080/14786440009463897}
}
@article{Helmert1876,
    author={{Helmert, F. R.}},
    year={1876},
    title={Ueber die Wahrscheinlichkeit der Potenzsummen der Beobachtungsfehler und über einige damit im Zusammenhange stehende Fragen},
    journal={Zeitschrift für Mathematik und Physik},
    volume={21},
    pages={192--219},
    url={https://gdz.sub.uni-goettingen.de/id/PPN599415665_0021}
}
@article{Plackett1983,
    author={{Plackett, R. L.}},
    year={1983},
    title={Karl Pearson and the Chi-Squared Test},
    journal={International Statistical Review / Revue Internationale de Statistique},
    volume={51},
    number={1},
    pages={59--72},
    url={https://doi.org/10.2307/1402731}
}
@article{Elderton1902,
    author={{Elderton, W. P.}},
    year={1902},
    title={Tables for Testing the Goodness of Fit of Theory to Observation},
    journal={Biometrika},
    volume={1},
    number={2},
    pages={155--163},
    doi={10.1093/biomet/1.2.155},
    url={https://doi.org/10.1093/biomet/1.2.155}
}
@article{Pearson1914,
    author={{Pearson, K.}},
    year={1914},
    title={On the probability that two independent distributions of frequency are really samples of the same population, with special reference to recent work on the identity of Trypanosome strains},
    journal={Biometrika}, 
    volume={10},
    pages={85--154},
    doi={10.1093/biomet/10.1.85},
    url={https://doi.org/10.1093/biomet/10.1.85}
}
@article{Fisher1924,
    author={{Fisher, R. A.}},
    year={1924},
    title={On a distribution yielding the error functions of several well-known statistics},
    journal={Proceedings International Mathematical Congress, Toronto},
    volume={2},
    pages={805--813},     url={https://repository.rothamsted.ac.uk/item/8w2q9/on-a-distribution-yielding-the-error-functions-of-several-well-known-statistics}
}
@book{Snedecor1934,
    author={{Snedecor, G. W.}},
    year={1934},
    title={Calculation and interpretation of analysis of variance and covariance},
    publisher={Collegiate Press},
    address={Ames, Iowa},
    url={https://doi.org/10.1037/13308-000}
}
@book{Scheffe1959,
    author={{Scheffé,  H.}},
    year={1959},
    title={The analysis of variance},
    publisher={Wiley},
    address={New York},
    url={https://psycnet.apa.org/record/1961-00074-000}
}
@book{Gauße-rara-2857,
    doi = {10.3931/e-rara-2857},
    URL = {https://doi.org/10.3931/e-rara-2857},
    title={Theoria combinationis observationum erroribus minimis obnoxiae},
    author={{Gauß, C. F.}},
    year={1823},
    publisher={{apud Henricum Dieterich}},
    address={Göttingen},
    language={lat},
    pages= {58}
}
@book{Gauß1809,
    author={{Gauß, C. F.}},
    year={1809},
    title={{Theoria motvs corporvm coelestivm in sectionibvs conicis Solem ambientivm}},
    address={Hambvrgi},
    publisher={{Svmtibvs F. Perthes et I. H. Besser}},      url={https://archive.org/details/theoriamotuscor00gausgoog/page/n1/mode/1up}
}
@book{DeMoivre1738,
  title={{The Doctrine of Chances: Or, A Method of Calculating the Probability of Events in Play}},
  edition={2},
  author={{de Moivre, A.}},
  url={https://books.google.com/books?id=PII\_AAAAcAAJ},
  year={1738},
  address={London},
  publisher={H. Woodfall}
}
@book{jahnke1909,
    title={Funktionentafeln mit Formeln und Kurven},
    author={{Jahnke, E., & Emde, F.}},
    lccn={09029241},
    series={Mathematisch-physikalische Schriften f{\"u}r Ingenieure und Studierende},
    edition={1},
    url={https://books.google.com/books?id=BVRzvgAACAAJ},
    year={1909},
    address={Leipzig},
    publisher={B. G. Teubner}
}
@article{Euler1738,
    author={{Euler, L.}},
    year={1738},
    title={{De progressionibus transcendentibus seu quarum termini generales algebraice dari nequeunt}},
    journal={{Commentarii academiae scientiarum Petropolitanae}},
    volume={5},
    pages={36--57},
    url={https://scholarlycommons.pacific.edu/euler-works/19/}
}
@incollection{SCHNEIDER200588,
    title = {{Chapter 6 - Jakob Bernoulli, Ars conjectandi (1713)}},
    editor = {{Grattan-Guinness, I., Cooke, R., Corry, L., Crépel, P., & Guicciardini, N.}},
    booktitle = {{Landmark Writings in Western Mathematics 1640-1940}},
    publisher = {Elsevier Science},
    address = {Amsterdam},
    pages = {88--104},
    year = {2005},
    isbn = {978-0-444-50871-3},
    doi = {10.1016/B978-044450871-3/50087-5},
    url = {https://www.sciencedirect.com/science/article/pii/B9780444508713500875},
    author = {{Schneider, I.}}
}
@book{Bernoulli1713,
    author={{Bernoulli, J.}},
    year={1713},
    title={{Ars conjectandi, opus posthumum. Accedit Tractatus de seriebus infinitis, et epistola gallicé scripta de ludo pilae reticularis}},
    address={Basileae},
    publisher={Impensis Thurnisiorum, Fratrum},
    url={https://www.e-rara.ch/zut/doi/10.3931/e-rara-9001}
}
@misc{Bernoulli1729,
    author={{Bernoulli, D.}},
    year={1729},
    month={10},
    title={{Lettre XLVII. D. Bernoulli a Goldbach}},
    address={{St.-Petersbourg ce 6. octobre 1729}},
    url={https://commons.m.wikimedia.org/wiki/File:DanielBernoulliLetterToGoldbach-1729-10-06.jpg}
}
@article{Fisher1926,
    author={{Fisher, R. A.}},
    year={1926},
    title={The arrangement of field experiments},
    journal={Journal of the Ministry of Agriculture},
    volume={33},
    pages={503--515},         
    abstract={Author's note. From about 1923 onwards the Statistical Department at Rothamsted had been much concerned with the precision of field experiments in agriculture, and with modifications in their design, having the dual aim of increasing the precision and of providing a valid estimate of error. These two desiderata had been somewhat confused in the minds of the experimenters, and the present paper was the author's first attempt at setting out the rational principles on which he might proceed. The paper is a precursor to the book on the Design of Experiments published nine years later.},
    issn={0368-3087},
    url={https://doi.org/10.23637/rothamsted.8v61q}
}
@book{Fisher1935,
    author={{Fisher, R. A.}},
    year={1935},
    title={The design of experiments},
    edition={1},
    publisher={Oliver & Boyd},        
    address={Edinburgh},  
    abstract={Different types of experimentation are considered with reference to their logical structure, to show that valid conclusions may be drawn from them without using the disputed theory of inductive inferences, i.e., of arguing from observation to explanatory theory. This is possible if a null hypothesis is explicitly formulated when the experiment is designed; this hypothesis can never be proved, but may be disproved with whatever probability one will accept as demonstrating a positive result. Chapters II, III, and IV illustrate simple applications of the principles involved in sensitiveness, significance, tests of wider hypotheses, validity, and estimation and elimination of error. More elaborate structures are treated in later chapters. Chapter titles are: (V) the Latin square; (VI) factorial design in experimentation; (VII) confounding; (VIII) special cases of partial confounding; (IX) increase of precision by concomitant measurements: statistical control; (X) generalization of null hypotheses: fiducial probability; (XI) measurement of amount of information in general.},
    url={https://psycnet.apa.org/record/1939-04964-000}
}
@book{Fisher1966,
    author={{Fisher, R. A.}},
    year={1966},
    title={The design of experiments},
    edition={8},
    publisher={Hafner},        
    address={Edinburgh},  
    abstract={Are scientific disciplines really different? This question often crystallizes into the old debate: Are Physics and Biology different? If Physics and Biology worked on highly different entities (objects), or if they had highly different methods, it would be straightforward to close the debate by a negative answer. However, if we cannot identify any differences, we should explore more deeply the status of the laws found in Physics and questioned in Biology. By slightly modifying the definition of what is a law, I argue here that both disciplines possess some laws exhibiting various “degrees of confirmation”. I finally propose explanations for why P and B give the illusion differing radically, although they both belong to the same continuum of a unified scientific domain.},
    url={https://scirp.org/reference/referencespapers.aspx?referenceid=895747}
}
@book{Fisher1971,
    author={{Fisher, R. A.}},
    year={1971},
    title={The design of experiments},
    edition={9},
    publisher={Hafner Press},        
    address={New York},  
    abstract={The Ninth Edition, 1971, is the same as the eighth, except for additions and clarifications (mostly in Chapter X), introduced from notes written for this purpose by Sir Ronald Fisher some time before his death.},
    url={https://home.iitk.ac.in/~shalab/anova/DOE-RAF.pdf}
}
@article{Pitman1937a,
 ISSN = {14666162},
 URL = {http://www.jstor.org/stable/2984124},
 author = {{Pitman, E. J. G.}},
 journal = {Supplement to the Journal of the Royal Statistical Society},
 number = {1},
 pages = {119--130},
 publisher = {[Wiley, Royal Statistical Society]},
 title = {Significance Tests Which May be Applied to Samples From any Populations},
 volume = {4},
 year = {1937}
}
@article{Pitman1937b,
 ISSN = {14666162},
 URL = {http://www.jstor.org/stable/2983647},
 author = {{Pitman, E. J. G.}},
 journal = {Supplement to the Journal of the Royal Statistical Society},
 number = {2},
 pages = {225--232},
 publisher = {[Wiley, Royal Statistical Society]},
 title = {Significance Tests Which May be Applied to Samples from any Populations. II. The Correlation Coefficient Test},
 volume = {4},
 year = {1937}
}
@article{Pitman1938,
 ISSN = {00063444},
 URL = {http://www.jstor.org/stable/2332008},
 author = {{Pitman, E. J. G.}},
 journal = {Biometrika},
 number = {3/4},
 pages = {322--335},
 publisher = {[Oxford University Press, Biometrika Trust]},
 title = {Significance Tests which May be Applied to Samples from any Populations: III. The Analysis of Variance Test},
 volume = {29},
 year = {1938}
}
@book{Good2006,
    author={{Good, P.}},
    year={2006},
    title={Resampling Methods},
    edition={3},
    publisher={{Birkhäuser}},        
    address={Basel},  
    abstract={This thoroughly revised and expanded third edition is a practical guide to data analysis using the bootstrap, cross-validation, and permutation tests. Only requiring minimal mathematics beyond algebra, it provides a table-free introduction to data analysis utilizing numerous exercises, practical data sets, and freely available statistical shareware.},
    isbn={978-0817643867},     url={https://www.amazon.com/Resampling-Methods-Practical-Guide-Analysis/dp/0817643869}
}
@inbook{Edgington2011,
author={{Edgington, E. S.}},
editor={{Lovric, M.}},
title="Randomization Tests",
bookTitle="International Encyclopedia of Statistical Science",
year="2011",
publisher="Springer",
address="Berlin, Heidelberg",
pages="1182--1183",
isbn="978-3-642-04898-2",
doi="10.1007/978-3-642-04898-2_56",
url="https://doi.org/10.1007/978-3-642-04898-2_56"
}
@article{Edgington1964,
 author = {{Edgington, E. S.}},
 year = {1964},
 title = {Randomization tests},
 journal = {The Journal of Psychology: Interdisciplinary and Applied},
 volume = {57},
 number = {2},
 pages = {445--449},
 doi={10.1080/00223980.1964.9916711}
}
@article{Edgington1987,
 author = {{Edgington, E. S.}},
 year = {1987},
 title = {Randomized single-subject experiments and statistical tests},
 journal = {Journal of Counseling Psychology},
 volume = {34},
 number = {4},
 pages = {437--442},
 doi={10.1037/0022-0167.34.4.437}
}
@article{Edgington1980,
 author = {{Edgington, E. S.}},
 year = {1980},
 title = {Validity of randomization tests for one-subject experiments},
 journal = {Journal of Educational Statistics},
 volume = {5},
 number = {3},
 pages = {235--251},
 doi={10.2307/1164966}
}
@book{Edgington2007,
    author={{Edgington, E. S., & Onghena, P.}},
    year={2007},
    title={Randomization Tests},
    edition={4},
    publisher={{Chapman and Hall/CRC}},        
    address={New York},  
    abstract={},
    isbn={9780367577711},       
    url={https://doi.org/10.1201/9781420011814}
}
@incollection{Beasley2009,
    author={{Beasley, W. H., & Rodgers, J. L.}},
    year={2009},
    title={Resampling methods},
    editor={{Millsap, R. E., & Maydeu-Olivares,  A.}},
    booktitle={The Sage handbook of quantitative methods in psychology},
    publisher={{Sage Publications Ltd.}},        
    address={Thousand Oaks, California},  
    pages={362--386},  
    url={https://psycnet.apa.org/doi/10.4135/9780857020994.n16}
}
@article{Argand1813,
author={{Argand, R.}},
title={{Essai sur une manière de représenter les quantités imaginaires dans les constructions géométriques}},
journal={Annales de mathématiques pures et appliquées},
volume={4},
pages={133--147},
year={1813},
url={https://fr.wikisource.org/wiki/Annales_de_math%C3%A9matiques_pures_et_appliqu%C3%A9es/Tome_04/Philosophie_math%C3%A9matique,_article_4}
}
@book{Argand1874,
author={{Argand, R.}},
title={{Essai sur une manière de représenter les quantités imaginaires dans les constructions géométriques}},
subtitle={{Précédée d'une préface par M. J. Hoüel, et suivie d'un appendice contenant des extraits des "Annales de Gergonne", relatifs à la question des imaginaires}},
journal={Annales de mathématiques pures et appliquées},
edition={2},
address={Paris},
publisher={Gauthier-Villars},
year={1874},
url={http://catalogue.bnf.fr/ark:/12148/cb300261909}
}
@book{descartes2012geometry,
    title={The Geometry of Ren{\'e} Descartes: with a Facsimile of the First Edition},
    author={{Descartes, R.}},
    isbn={9780486158174},
    series={Dover Books on Mathematics},
    url={https://books.google.com/books?id=MB7F32p0y5MC},
    year={2012},
    address={New York},
    publisher={Dover Publications}
}
@book{Descartes1664geometry,
    author={{Descartes, R.}},
    year={1664},
    title={{La Géométrie}},
    address={A Paris},
    publisher={{Chez Charles Angot, Libraire Iuré, ruë S. Iacques, au Lion d’Or. M. DC. LXIV. Avec Privilege du Roy}},
    url={https://books.google.com/books?id=VtFcAAAAcAAJ}
}
@book{Gauss1828,
    doi={10.3931/e-rara-61066},
    url={https://doi.org/10.3931/e-rara-61066},
    title={{Theoria residuorum biquadraticorum: commentatio prima}},
    author={{Gauß, C. F.}},
    year={1828},
    publisher={typis Dieterichianis},
    address={Gottingae}
}
@book{Gauss1832,
    doi={10.3931/e-rara-61067},
    url={https://doi.org/10.3931/e-rara-61067},
    title={{Theoria residuorum biquadraticorum: commentatio secunda}},
    author={{Gauß, C. F.}},
    year={1832},
    publisher={typis Dieterichianis},
    address={Gottingae}
}
@article{Wirtinger1927,
    url = {https://doi.org/10.1007/BF01447872},
    title = {{Zur formalen Theorie der Funktionen von mehr komplexen Veränderlichen}},
    author = {{Wirtinger, W.}},
    journal={Mathematische Annalen},
    pages = {357--374},
    volume = {97},
    doi = {10.1007/BF01447872},
    year = {1927}
}
@article{McNemar1947, 
title={Note on the Sampling Error of the Difference Between Correlated Proportions or Percentages}, 
volume={12}, 
DOI={10.1007/BF02295996}, 
number={2}, 
journal={Psychometrika}, 
author={{McNemar, Q.}}, 
year={1947}, 
pages={153–-157}
} 
@article{yates1934,
 ISSN = {14666162},
 URL = {http://www.jstor.org/stable/2983604},
 author = {{Yates, F.}},
 journal = {Supplement to the Journal of the Royal Statistical Society},
 number = {2},
 pages = {217--235},
 publisher = {[Oxford University Press, Royal Statistical Society]},
 title = {Contingency Tables Involving Small Numbers and the χ2 Test},
 volume = {1},
 year = {1934}
}
@article{Siegel01061942,
author = {{Siegel, I. H.}},
title = {Index-Number Differences: Geometric Means},
journal = {Journal of the American Statistical Association},
volume = {37},
number = {218},
pages = {271--274},
year = {1942},
doi = {10.1080/01621459.1942.10500636}
}
@book{weierstrass1894,
author={{Weierstraß, K.}},
year={1894},
title={Mathematische Werke},
volume={1},
address={Berlin},
publisher={Mayer & Müller},
url={https://quod.lib.umich.edu/u/umhistmath/AAN8481.0001.001}
}
@inproceedings{SchrausserRG.2.2.14805.91369,
    doi = {10.13140/RG.2.2.14805.91369},
    url = {http://dx.doi.org/10.13140/RG.2.2.14805.91369},
    author = {{Schrausser, D. G.}},
    language = {de},
    title = {{Exakte Verfahren oder Asymptotische Approximation?}},
    bookTitle = {{3. Tagung der österreichischen Gesellschaft für Psychologie (ÖGP)}},
    publisher = {{Universität Salzburg}},
    address={Salzburg, Österreich},
    year = {1997},
    month={12}
} 
@inproceedings{SchrausserRG.2.2.19532.69768,
    doi = {10.13140/RG.2.2.19532.69768},
    url = {http://dx.doi.org/10.13140/RG.2.2.19532.69768},
    author = {{Schrausser, D. G.}},
    language = {de},
    title = {{Die Permutationsmethode: Voraussetzungsfrei testen}},
     bookTitle = {{41. Kongreß der Deutschen Gesellschaft für Psychologie}},
    publisher = {{Technische Universität Dresden}},
    address={Dresden, Deutschland},
    year = {1998},
    month={09}
} 
@software{schrausser_2024_14280500,
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  added-at = {2025-01-22T19:54:42.000+0100},
  author = {{Schrausser, D. G.}},
  biburl = {https://www.bibsonomy.org/bibtex/24c3740faa802ad82ca7a8d3429f23349/schrausser},
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  month = jun,
  publisher = {Zenodo},
  timestamp = {2025-01-22T19:55:07.000+0100},
  title = {{Schrausser/HP_Prime_MATH: 3.0}},
  url = {https://doi.org/10.5281/zenodo.14721085},
  version = {v3.0.0},
  year = 2025
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@article{Fisher1926,
    author={{Fisher, R. A.}},
    year={1926},
    title={The arrangement of field experiments},
    journal={Journal of the Ministry of Agriculture},
    volume={33},
    pages={503--515},         
    abstract={Author's note. From about 1923 onwards the Statistical Department at Rothamsted had been much concerned with the precision of field experiments in agriculture, and with modifications in their design, having the dual aim of increasing the precision and of providing a valid estimate of error. These two desiderata had been somewhat confused in the minds of the experimenters, and the present paper was the author's first attempt at setting out the rational principles on which he might proceed. The paper is a precursor to the book on the Design of Experiments published nine years later.},
    issn={0368-3087},
    url={https://doi.org/10.23637/rothamsted.8v61q}
}
@book{Fisher1935,
    author={{Fisher, R. A.}},
    year={1935},
    title={The design of experiments},
    edition={1},
    publisher={Oliver & Boyd},        
    address={Edinburgh},  
    abstract={Different types of experimentation are considered with reference to their logical structure, to show that valid conclusions may be drawn from them without using the disputed theory of inductive inferences, i.e., of arguing from observation to explanatory theory. This is possible if a null hypothesis is explicitly formulated when the experiment is designed; this hypothesis can never be proved, but may be disproved with whatever probability one will accept as demonstrating a positive result. Chapters II, III, and IV illustrate simple applications of the principles involved in sensitiveness, significance, tests of wider hypotheses, validity, and estimation and elimination of error. More elaborate structures are treated in later chapters. Chapter titles are: (V) the Latin square; (VI) factorial design in experimentation; (VII) confounding; (VIII) special cases of partial confounding; (IX) increase of precision by concomitant measurements: statistical control; (X) generalization of null hypotheses: fiducial probability; (XI) measurement of amount of information in general.},
    url={https://psycnet.apa.org/record/1939-04964-000}
}
@book{Fisher1966,
    author={{Fisher, R. A.}},
    year={1966},
    title={The design of experiments},
    edition={8},
    publisher={Hafner},        
    address={Edinburgh},  
    abstract={Are scientific disciplines really different? This question often crystallizes into the old debate: Are Physics and Biology different? If Physics and Biology worked on highly different entities (objects), or if they had highly different methods, it would be straightforward to close the debate by a negative answer. However, if we cannot identify any differences, we should explore more deeply the status of the laws found in Physics and questioned in Biology. By slightly modifying the definition of what is a law, I argue here that both disciplines possess some laws exhibiting various “degrees of confirmation”. I finally propose explanations for why P and B give the illusion differing radically, although they both belong to the same continuum of a unified scientific domain.},
    url={https://scirp.org/reference/referencespapers.aspx?referenceid=895747}
}
@book{Fisher1971,
    author={{Fisher, R. A.}},
    year={1971},
    title={The design of experiments},
    edition={9},
    publisher={Hafner Press},        
    address={New York},  
    abstract={The Ninth Edition, 1971, is the same as the eighth, except for additions and clarifications (mostly in Chapter X), introduced from notes written for this purpose by Sir Ronald Fisher some time before his death.},
    url={https://home.iitk.ac.in/~shalab/anova/DOE-RAF.pdf}
}
@article{Pitman1937a,
 ISSN = {14666162},
 URL = {http://www.jstor.org/stable/2984124},
 author = {{Pitman, E. J. G.}},
 journal = {Supplement to the Journal of the Royal Statistical Society},
 number = {1},
 pages = {119--130},
 publisher = {[Wiley, Royal Statistical Society]},
 title = {Significance Tests Which May be Applied to Samples From any Populations},
 volume = {4},
 year = {1937}
}
@article{Pitman1937b,
 ISSN = {14666162},
 URL = {http://www.jstor.org/stable/2983647},
 author = {{Pitman, E. J. G.}},
 journal = {Supplement to the Journal of the Royal Statistical Society},
 number = {2},
 pages = {225--232},
 publisher = {[Wiley, Royal Statistical Society]},
 title = {Significance Tests Which May be Applied to Samples from any Populations. II. The Correlation Coefficient Test},
 volume = {4},
 year = {1937}
}
@article{Pitman1938,
 ISSN = {00063444},
 URL = {http://www.jstor.org/stable/2332008},
 author = {{Pitman, E. J. G.}},
 journal = {Biometrika},
 number = {3/4},
 pages = {322--335},
 publisher = {[Oxford University Press, Biometrika Trust]},
 title = {Significance Tests which May be Applied to Samples from any Populations: III. The Analysis of Variance Test},
 volume = {29},
 year = {1938}
}
@book{Edgington2007,
    author={{Edgington, E. S., & Onghena, P.}},
    year={2007},
    title={Randomization Tests},
    edition={4},
    publisher={{Chapman and Hall/CRC}},        
    address={New York},  
    abstract={},
    isbn={9780367577711},       
    url={https://doi.org/10.1201/9781420011814}
}
@mastersthesis{SchrausserThesis,
    author = {{Schrausser, D. G.}},
    year = {1996},
    month = {07},
    language = {de},
    title = {{Permutationstests: Theoretische und praktische Arbeitsweise von Permutationsverfahren beim unverbundenen 2 Stichprobenproblem}},
    type = {Mag.rer.nat.},
    school = {Naturwissenschaftliche Fakultät},
    address = {Universität Graz},
    doi = {10.13140/RG.2.2.24500.32640/1},
    url = {https://rgdoi.net/10.13140/RG.2.2.24500.32640/1}
} 
@incollection{Schrausser75975252,
    author = {{Schrausser, D. G.}},
    year = {1998},
    title = {{Exakte Verfahren oder Asymptotische Approximation?}},
   editor={{Glück, J., Jirasco, M., & Rollett, B.}},
    bookTitle = {Perspektiven psychologischer Forschung in Österreich},
    volume = {2},
    publisher = {WUV-Univ.-Verl., Wien},
    isbn = {9783851144413, 3851144414},
    url = {https://www.worldcat.org/de/title/75975252},
    doi={10.5281/zenodo.11673333}
} 
@misc{Schrausser94993376,
    author = {{Scambor, C., & Schrausser, D. G.}},
    title = {{Introduction (part II, permutation tests for repeated measurement designs)}},
    year = {2023},
    month = {01},
    journal = {Thesis Chapters},
    publisher = {Academia},
    note={translation},
    language = {en},
    url = {https://www.academia.edu/94993376}
} 
@misc{Schrausser82224369,
    author = {{Schrausser, D. G.}},
    title = {{Thesis chapter 1: Introduction}},
    year = {2022},
    month = {07},
    journal = {Thesis Chapters},
    publisher = {Academia},
    note={translation},
    language = {en},
    url = {https://www.academia.edu/82224369}
} 
@book{cox1974,
title={Theoretical Statistics},
author={{Cox, D. R., & Hinkley, D. V.}},
year={1974},
address={New York},
edition={1},
publisher={Chapman and Hall/CRC},
isbn={9780429170218},
doi={10.1201/b14832}
}
@software{Schrausser7651660,
  author       ={{Schrausser, D. G.}},
  title        = {{Schrausser/FunktionWin: Windows Interface for 
                   distribution functions}},
  month        = feb,
  year         = 2023,
  publisher    = {Zenodo},
  version      = {{v1.0.0}},
  doi          = {10.5281/zenodo.7651660},
  url          = {https://doi.org/10.5281/zenodo.7651660}
}
@software{Schrausser7659263,
  author       ={{Schrausser, D. G.}},
  title        = {{Schrausser/ThetaWin: Distribution simulator}},
  month        = feb,
  year         = 2023,
  publisher    = {Zenodo},
  version      = {v1.0.0},
  doi          = {10.5281/zenodo.7659263},
  url          = {https://doi.org/10.5281/zenodo.7659263}
}
@software{Schrausser7664141,
  author       ={{Schrausser, D. G.}},
  title        = {{Schrausser/ConsoleApp\_DistributionFunctions: 
                   Console applications for distribution functions}},
  month        = feb,
  year         = 2023,
  publisher    = {Zenodo},
  version      = {v1.0.0},
  doi          = {10.5281/zenodo.7664141},
  url          = {https://doi.org/10.5281/zenodo.7664141}
}
@software{Schrausser7655056,
  author       ={{Schrausser, D. G.}},
  title        = {{Schrausser/ConsoleApp\_Integral: Console 
                   applications for integral and interpolation}},
  month        = feb,
  year         = 2023,
  publisher    = {Zenodo},
  version      = {v1.0.0},
  doi          = {10.5281/zenodo.7655056},
  url          = {https://doi.org/10.5281/zenodo.7655056}
}
@misc{SchrausserRG.2.2.28314.52164,
    url = {https://www.academia.edu/81395688},
    author = {{Schrausser, D. G.}},
    language = {de},
    title = {{Mathematical-Statistical Algorithm Interpreter, SCHRAUSSER-MAT: Function Index, Manual}},
    journal = {Handbooks},
    publisher = {Academia},
    year = {2022},
    month={}
} 
@mastersthesis{ScamborThesis,
    author = {{Scambor, C.}},
    year = {1997},
    month = {apr},
    language = {de},
    title = {{Permutationsverfahren in Einzelfallstudien: Grundlagen, Anwendungen und Teststärke}},
    type = {Mag.rer.nat.},
    school = {Naturwissenschaftliche Fakultät},
    address = {Universität Graz},
    doi = {10.13140/RG.2.2.28632.06405}
} 
@article{Neyman1923,
    author = {{Neyman, J.}},
    year = {1923},
    title={{Sur les applications de la theorie des probabilites aux experience agricoles: Essay de principes}},
    journal={Roczniki Nank Polniczek},
    volume = {10},
    pages={1--51},     url={https://link.springer.com/chapter/10.1007/978-94-015-8816-4_10}
}
@article{Neyman1937,
    author={{Neyman, J.}},
    year={1937},
    title={Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability},
    journal={Philosophical Transactions of the Royal Society of London A},
    series={Mathematical and Physical Sciences},
    volume={236},
    number={767},
    pages={333--380},
    abstract={We shall distinguish two aspects of the problems of estimation . (i) the practical and (ii) the theoretical. The practical aspect may be described as follows: (ia) The statistician is concerned with a population, π, which for some reason or other cannot be studied exhaustively. It is only possible to draw a sample from this population which may be studied in detail and used to form an opinion the values of certain constants describing the properties of the population π. For example, it may be desired to calculate approximately the mean of a certain character possessed by the individuals forming the population π, etc.},
    url={https://doi.org/10.1098/rsta.1937.0005}
}
@article{Neyman1933,
    author={{Neyman, J., & Pearson, E. S.}},
    year={1933},
    title={{On the problem of the most efficient tests of statistical hypotheses}},
    journal={Phil. Trans. R. Soc. Lond. A.},
    volume={231},
    number={{694--706}},
    pages={289--337},
    doi={10.1098/rsta.1933.0009},
    url={https//:doi.org10.1098/rsta.1933.0009},
    ISSN={0264-3952}
}
@article{Lehmann1993,
    author={{Lehmann, E. L.}},
    year={1993},
    title={{The Fisher, Neyman-Pearson Theories of Testing Hypotheses: One Theory or Two?}},
    journal={Journal of the American Statistical Association},
    volume={88},
    number={424},
    pages={1242--1249},
    DOI={10.1080/01621459.1993.10476404},
    url={http//:doi.org/10.1080/01621459.1993.10476404}
}
@book{Pascal1665,
    author={Pascal, B.},
    year={1665},
    title={{Traite´ du triangle arithmetique : auec quelques autres petits traitez sur la mesme matie`re}},
    publisher={{Chez Guillaume Desprez, rue Saint Jacques, a Saint Prosper}},
    address={A Paris},
    url={https://gallica.bnf.fr/ark:/12148/btv1b86262012.image#}
}
@book{Ettingshausen1826,
    author={{Ettingshausen, A.}},
    year={1826},
    title={{Die combinatorische Analysis: als Vorbereitungslehre zum Studium der theoretischen höhern Mathematik}},
    address={Wien},
    publisher={Wallishausser},     url={https://archive.org/details/diecombinatoris00ettigoog/page/n70/mode/1up?view=theater}
}
@book{Sylvester1904,
    author={{Sylvester, J. J.}},
    year={1904},
    editor={{Baker, H. F.}},
    title={The Collected Mathematical Papers of James Joseph Sylvester},
    volume={1},
    publisher={University Press},
    address={Cambridge},
    ISBN={978-0-8218-3654-5},
    url={https://archive.org/details/collectedmathem01sylvrich/page/n7/mode/1up}
}
@book{Sylvester1908,
    author={{Sylvester, J. J.}},
    year={1908},
    editor={{Baker, H. F.}},
    title={The Collected Mathematical Papers of James Joseph Sylvester},
    volume={2},
    publisher={University Press},
    address={Cambridge},
    ISBN={978-0-8218-4719-0},
    url={https://archive.org/details/SylvesterCollected2/page/n3/mode/1up}
}
@book{Sylvester1909,
    author={{Sylvester, J. J.}},
    year={1909},
    editor={{Baker, H. F.}},
    title={The Collected Mathematical Papers of James Joseph Sylvester},
    volume={3},
    publisher={University Press},
    address={Cambridge},
    ISBN={978-0-8218-4720-6},
    url={https://archive.org/details/TheCollectedMathematicalPapersOfJamesJosephSylvesterVolumeIii/page/n3/mode/1up}
}
@book{Sylvester1912,
    author={{Sylvester, J. J.}},
    year={1912},
    editor={{Baker, H. F.}},
    title={The Collected Mathematical Papers of James Joseph Sylvester},
    volume={4},
    publisher={University Press},
    address={Cambridge},
    ISBN={978-0-8218-4238-6},
    url={https://archive.org/details/collectedmathema04sylvuoft/page/n8/mode/1up}
}
@book{MacMohan1915,
    author={{MacMohan, P. A.}},
    year={1915},
    title={Combinatory Analysis},
    volume={1},
    publisher={University Press},
    address={Cambridge}, url={https://openlibrary.org/works/OL1109964W/Combinatory_analysis}
}
@book{MacMohan1916,
    author={{MacMohan, P. A.}},
    year={1916},
    title={Combinatory Analysis},
    volume={2},
    publisher={University Press},
    address={Cambridge},
    lccn={a16000325}, url={https://books.google.com/books/about/Combinatory_Analysis.html?id=A_PuAAAAMAAJ&redir_esc=y}
}
@article{Euler1753,
    author={{Euler, L.}},
    year={1753},
    title={{Calcul de la probabilité dans le jeu de rencontre}},
    volume={7},
    pages={255--270},
    journal={Mémoires de l'académie des sciences de Berlin},
    url={https://scholarlycommons.pacific.edu/euler-works/201/}
}
@article{Leibnitz1684,
    author={{Leibniz, G. W.}},
    year={1684},
    title={{Nova methodus pro maximis et minimis itemque tangentibus, quae nec fractas nec irrationales quantitates moratur, et singulare pro illis calculi genus, per G.G.L.}},
    journal={{Acta eruditorum anno MDCLXXXIV}},
    pages={467--473},
    address={Lipsae}, 
    url={https://gdz.sub.uni-goettingen.de/id/PPN788262599}
}
@article{Leibnitz1686,
    author={{Leibniz, G. W.}},
    year={1686},
    title={{De geometria recondita et analysi indivisibilium atque infinitorum}},
    journal={{Acta eruditorum anno MDCLXXXVI}},
    pages={292--300},
    address={Lipsae}, 
    url={https://gdz.sub.uni-goettingen.de/id/PPN788262947}
}
@article{Leibnitz1693,
    author={{Leibniz, G. W.}},
    year={1693},
    title={{Supplementum geometriae dimensoriae, seu generalissima omnium tetragonismorum effectio per motum: similiterque multiplex constructio lineae ex data tangentium conditione}},
    journal={{Acta eruditorum anno MDCLXCIII}},
    pages={385--392},
    address={Lipsae},      
    url={https://archive.org/details/s1id13206590}
}
@book{Gerhardt1848,
    author={{Gerhardt, C. I.}},
    year={1848},
    title={{Die Entdeckung der Differentialrechnung durch Leibniz mit Benutzung der Leibnizischen Manuscripte auf der Königlichen Bibliothek zu Hannover}},
    publisher={H. W. Schmidt},
    address={Halle},
    url={https://doi.org/10.3931/e-rara-4272}
}
@incollection{ROERO200546,
    title = {Chapter 4 - Gottfried Wilhelm Leibniz, first three papers on the calculus (1684, 1686, 1693)},
    editor = {{Grattan-Guinness, I., Cooke, R., Corry, L., Crépel, P., & Guicciardini, N.}},
    booktitle = {Landmark Writings in Western Mathematics 1640-1940},
    publisher = {Elsevier Science},
    address = {Amsterdam},
    pages = {46--58},
    year = {2005},
    isbn = {978-0-444-50871-3},
    doi = {https://doi.org/10.1016/B978-044450871-3/50085-1},
    url = {https://www.sciencedirect.com/science/article/pii/B9780444508713500851},
    author = {{Roero, C. S.}},
    abstract = {Publisher Summary The invention of the differential and integral calculus is one of the most important and revolutionary developments in mathematics. Leibniz and Newton share out the glory of the invention of the infinitesimal calculus that they found independently. The priority of publication is because of Leibniz, who had the fortune to be followed by mathematicians of first rank who collaborated on the diffusion of his methods. The first public presentation of differential calculus appeared in October 1684 in the journal Acta Eruditorum, established in Leipzig, in only six and an half pages, written in a disorganized manner with numerous typographical errors. The first papers on integral calculus was the book by John Craig on quadratures, Methodus figurarum lineis rectis et curvis comprehensarum quadraturas determinandi, published in London in 1685, that stimulated Leibniz to draft his first exposition of the integral calculus. Craig attributed to him the paper on figures, published in the Acta Eruditorum. Leibniz's followers, especially Johann Bernoulli, reacted strongly against this slander, with the result that the mathematical community became polarized.}
}
@book{Newton1687,
    author={{Newton,  I.}},
    year={1687},
    title={{Philosophiae naturalis principia mathematica}},
    edition={1},
    address={Londini},
    publisher={{Jussu Societatis Regiae ac typis Josephi Streater, prostant venales apud Sam. Smith}},     url={https://books.google.com/books?id=XJwx0lnKvOgC&pg=PP2&redir_esc=y#v=onepage&q&f=false}
}
@book{Newton1713,
    author={{Newton,  I.}},
    year={1713},
    title={{Philosophiae naturalis principia mathematica}},
    edition={2},
    address={Cantabrigiae},
    publisher={{Newton, I.}},    
    url={https://digital.onb.ac.at/OnbViewer/viewer.faces?doc=ABO_%2BZ180810706&order=7&view=SINGLE}
}
@book{Newton1726,
    author={{Newton,  I.}},
    year={1726},
    title={{Philosophiae naturalis principia mathematica}},
    edition={3},
    address={Londini},
    publisher={{Apud Guil. & Joh. Innys}},     
    url={https://gdz.sub.uni-goettingen.de/id/PPN512261393}
}
@book{craig1685,
   title={{Methodus figurarum lineis rectis et curvis comprehensarum quadraturas determinandi}},
   author={{Craig, J.}},
   url={https://books.google.com/books?id=tD4PAAAAQAAJ},
   year={1685},
   address={Londini},
   publisher={impensis Mosis Pitt, ad insigne Angeli in Coemeterio D. Paulo}
}
@article{Craig10.1098/rstl.1686.0031,
    author = {{Craig, J.}},
    title = {{An account of a book. Methodus Figurarum lineis rectis \& curvis comprehensarum quadraturas determinandi authore J. Craige. 4to. Londini 1685}},
    journal = {Philosophical Transactions of the Royal Society of London},
    volume = {16},
    number = {183},
    pages = {185--190},
    year = {1686},
    doi = {10.1098/rstl.1686.0031},
    URL = {https://royalsocietypublishing.org/doi/abs/10.1098/rstl.1686.0031},
    eprint = {https://royalsocietypublishing.org/doi/pdf/10.1098/rstl.1686.0031},
    abstract = { The great use of drawing the tangents of curve lines, has made the most famous amongst the modern mathematicians endeavour to find out general methods of finding the tangents of curve lines }
}
@article{Metropolis1949,
    author = {{Metropolis, N., & Ulam, S.}},
    title = {The Monte Carlo Method},
    journal = {Journal of the American Statistical Association},
    volume = {44},
    number = {247},
    pages = {335--341},
    year  = {1949},
    publisher = {Taylor & Francis},
    doi = {10.1080/01621459.1949.10483310},
    note ={PMID: 18139350},
    URL={https://www.tandfonline.com/doi/abs/10.1080/01621459.1949.10483310},
    abstract = {Abstract We shall present here the motivation and a general description of a method dealing with a class of problems in mathematical physics. The method is, essentially, a statistical approach to the study of differential equations, or more generally, of integro-differential equations that occur in various branches of the natural sciences.}
}
@article{DALLAL19889,
title = {PITMAN: A FORTRAN program for exact randomization tests},
journal = {Computers and Biomedical Research},
volume = {21},
number = {1},
pages = {9-15},
year = {1988},
issn = {0010-4809},
doi = {https://doi.org/10.1016/0010-4809(88)90037-7},
url = {https://www.sciencedirect.com/science/article/pii/0010480988900377},
author = {{Dallal, G. E.}},
abstract = {PITMAN performs exact randomization tests. It also performs Wilcoxon signed-rank tests and Wilcoxon-Mann-Whitney U tests in the presence of an arbitrary number of ties in the data. PITMAN requires an IBM PC with 256K of memory. The source code is available for those who wish to compile smaller or larger versions or wish to move PITMAN to another computer.}
}
@article{e58060c9-2bc9-3b21-996e-d2928eb4f067,
 ISSN = {00031305},
 URL = {http://www.jstor.org/stable/2684555},
 author = {{Dallal, G. E.}},
 journal = {The American Statistician},
 number = {3},
 pages = {236--236},
 publisher = {[American Statistical Association, Taylor & Francis, Ltd.]},
 title = {STATOOLS: Statistical Utility Programs},
 urldate = {2024-11-08},
 volume = {40},
 year = {1986}
}
@inproceedings{solomon1982,
author = {{Solomon, S. L.}},
title = {Simstat a simple statistical package to support simulation},
year = {1982},
publisher = {Winter Simulation Conference},
booktitle = {Proceedings of the 14th Conference on Winter Simulation - Volume 1},
pages = {307--311},
numpages = {5},
location = {San Diego, California},
series = {WSC '82},
doi={10.5555/1035853.1035900}
}
@Article{woof1994,
  author={{Wooff, D., & Peladeau, N.}},
  title={{Simstat: Simulation and Statistics for Ibm Personal Computers or Compatibles, Version 2.0}},
  journal={Journal of the Royal Statistical Society Series C},
  year={1994},
  volume={43},
  number={2},
  pages={417--422},
  month={June},
  keywords={},
  doi={10.2307/2986032}
}
@inbook{mehta2014,
author = {{Mehta, C. R., Patel, N. R., Senchaudhuri, P., & Corcoran, C. D.}},
publisher = {John Wiley & Sons, Ltd},
isbn = {9781118445112},
title = {StatXact},
booktitle = {Wiley StatsRef: Statistics Reference Online},
doi = {10.1002/9781118445112.stat04892},
year = {2014}
}
@article{simstat1993,
  author={{Peladeau, N.}},
  title={{SIMSTAT: Bootstrap computer simulation and statistical program for IBM personal computers}},
  journal={Behavior Research Methods, Instruments, & Computers},
  year={1993},
  volume={25},
  number={3},
  pages={410--413},
  doi={10.3758/BF03204533}
}
@article{DeMoivre1711,
    author={{de Moivre, A.}},
    title = {{De mensura sortis, seu, de probabilitate eventuum in ludis a casu fortuito pendentibus}},
    journal = {Philosophical Transactions of the Royal Society of London},
    volume = {27},
    number = {329},
    pages = {213--264},
    year = {1711},
    doi = {10.1098/rstl.1710.0018},
    URL = {https://royalsocietypublishing.org/doi/abs/10.1098/rstl.1710.0018},
    eprint = {https://royalsocietypublishing.org/doi/pdf/10.1098/rstl.1710.0018},
    abstract = {Si p sit numerus casuum quibus eventus aliquis contingere possit, \& q numerus casuum quibus possit non-contingere; }
}
@book{DeMoivre1718,
  title={{The Doctrine of Chances: Or, A Method of Calculating the Probability of Events in Play}},
  edition={1},
  author={{de Moivre, A.}},
  isbn={9780598843753},
  lccn={30014721},
  url={https://books.google.com/books?id=3EPac6QpbuMC},
  year={1718},
  address={London},
  publisher={W. Pearson}
}
@book{DeMoivre1756,
  title={{The Doctrine of Chances: Or, A Method of Calculating the Probability of Events in Play}},
  edition={3},
  author={{de Moivre, A.}},
 url={https://archive.org/details/doctrineofchance00moiv/page/n2/mode/1up},
  year={1756},
  address={London},
  publisher={A. Millar}
}
@article{Bayes1763,
 ISSN = {02607085},
 URL = {http://www.jstor.org/stable/105741},
 author = {{Bayes, T., & Price, R.}},
 journal = {Philosophical Transactions (1683-1775)},
 pages = {370--418},
 publisher = {The Royal Society},
 title = {An Essay towards Solving a Problem in the Doctrine of Chances. By the Late Rev. Mr. Bayes, F. R. S. Communicated by Mr. Price, in a Letter to John Canton, A. M. F. R. S.},
 volume = {53},
 year = {1763}
}
@book{Arnauld1662,
    author={{Arnauld, A., & Nicole, P.}},
    year={1662},
    title={{La logique ou L'art de penser}},
    address={A Paris},
    publisher={{Chez Charles Savreux, au pied de la Tour de Nostre Dame}},
     edition={1},
    note= {Many later editions. Reprinted by Flammarion, Paris, 1970. Translated as The art olthinking by J. Dickoff and P. James, 1964, Bobbs-Merrill, Indianapolis.},     url={https://gallica.bnf.fr/ark:/12148/bpt6k574432.image}
}
@book{Stigler1986,
    author={{Stigler, S. M.}},
    year={1986},
    title={{The history of statistics: the measurement of uncertainty before 1900}},
    address={Cambridge, MA},
    publisher={Belknap Press of Harvard University Press},
    ISBN={978-0-674-40340-6},     url={https://www.scirp.org/(S(351jmbntvnsjt1aadkposzje))/reference/ReferencesPapers.aspx?ReferenceID=1973131}
}
@article{Bayes1763,
 ISSN = {02607085},
 URL = {http://www.jstor.org/stable/105741},
 author = {{Bayes, T., & Price, R.}},
 journal = {Philosophical Transactions (1683-1775)},
 pages = {370--418},
 publisher = {The Royal Society},
 title = {An Essay towards Solving a Problem in the Doctrine of Chances. By the Late Rev. Mr. Bayes, F. R. S. Communicated by Mr. Price, in a Letter to John Canton, A. M. F. R. S.},
 volume = {53},
 year = {1763}
}
@book{Hald1998,
    author={{Hald, A.}},
    year={1998},
    title={{A History of Mathematical Statistics from 1750 to 1930}},
    address={New York},
    publisher={Wiley},
 ISBN={0-471-17912-4}, url={https://www.abebooks.com/History-Mathematical-Statistics-1750-1930-Wiley/31042381048/bd}
}
@book{Hald2003,
    author={{Hald, A.}},
    year={2003},
    title={{A History of Probability and Statistics and Their Applications before 1750}},
    address={Hoboken, NJ},
    publisher={Wiley-Interscience},
    ISBN={0-471-47129-1},
    url={https://www.wiley.com/en-us/A+History+of+Probability+and+Statistics+and+Their+Applications+before+1750-p-9780471725176}
}
@book{Hald2007,
    author={{Hald, A.}},
    year={2007},
    title={{A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713–1935}},
    address={New York},
    publisher={Springer},
    ISBN={978-0-387-46408-4},
url={https://link.springer.com/book/10.1007/978-0-387-46409-1#bibliographic-information}
}
@book{Hald1990,
    author={{Hald, A.}},
    year={1990},
    title={{History of Probability and Statistics and Their Applications before 1750}},
    address={New York},
    publisher={Wiley Series in Probability and Statistics, Wiley-Interscience},     url={https://onlinelibrary.wiley.com/doi/book/10.1002/0471725161}
}
@book{Ewald1996,
    title = {{From Kant to Hilbert: A Source Book in the Foundations of Mathematics}},
	 author = {{Ewald, W. B.}},
volume={1},
	 year = {1996},
    address={Oxford},
	 publisher = {Oxford University Press OUP},
    ISBN={9780198505358},
    url={https://philpapers.org/rec/BRAFKT}
}
@book{Ewald1996II,
    title = {{From Kant to Hilbert: A Source Book in the Foundations of Mathematics}},
	 author = {{Ewald, W. B.}},
volume={2},
	 year = {1996},
    address={Oxford},
	 publisher = {Oxford University Press OUP},
    ISBN={9780198505365},
    url={https://philpapers.org/rec/EWAFKT-4}
}
@book{Boyer2011,
    author={{Merzbach, U. C., & Boyer, C. B.}},
    title={A History of Mathematics},
    year={2011},
    edition={3},
    publisher = {John Wiley & Sons, Inc.},
    address={Hoboken, New Jersey},
    url={https://books.google.com/books/about/A_History_of_Mathematics.html?id=bR9HAAAAQBAJ&redir_esc=y},
    note={https://atiekubaidillah.files.wordpress.com/2013/03/a-history-of-mathematics-3rded.pdf}
}
@book{Arnauld1662,
    author={{Arnauld, A., & Nicole, P.}},
    year={1662},
    title={{La logique ou L'art de penser}},
    address={A Paris},
    publisher={{Chez Charles Savreux, au pied de la Tour de Nostre Dame}},
     edition={1},
    note= {Many later editions. Reprinted by Flammarion, Paris, 1970. Translated as The art olthinking by J. Dickoff and P. James, 1964, Bobbs-Merrill, Indianapolis.},     url={https://gallica.bnf.fr/ark:/12148/bpt6k574432.image}
}
@book{Arnauld1693,
	author = {{Arnauld, A., & Nicole, P.}},
	edition = {2},
   address={London},
	publisher = {Printed by T. B. for John Taylor at the Ship at St. Paul's Church Yard},
	title = {Logic: Or, The Art of Thinking: In which Besides the Common, are Contain'd Many Excellent New Rules, Very Profitable for Directing of Reason, and Acquiring of Judgment, in Things as Well Relating to the Instruction of a Man's Self, as of Others. In Four Parts. I. Consistin of Reflections Upon Ideas, Or Upon the First Operation of the Mind, which is Called Apprehension, \&c. II. Of Considerations of Men about Proper Judgments, \&c. III. Of the Nature and Various Kinds of Reasoning, \&c. IV. Treats of the Most Profitable Method for Demonstrating Or Illustrating Any Truth To which is Added an Index to the Whole Book. For the Excellency of the Matter, Printed Many Times in French and Latin, and Now for Publick Good Translated Into English by Several Hands},
	year = {1693},
   language={english},
    url={https://archive.org/details/logicorartofthin00arnaiala}
}
@book{arnauld1682,
  title={Logica Sive Ars Cogitandi: In qua praeter Vulgares Regulas Plura Nova Habentur Ad Rationem dirigendam utilia},
  author={{Arnauld, A., & Nicole, P.}},
  edition={Editio optima & ultima},
  language={lat},
  url={https://books.google.com/books?id=XQVaAAAAcAAJ},
  year={1682},
  address={Lugduni Batavorum},
  publisher={Apud Jacobum Gaal}
}
@book{Newton1687,
    author={{Newton,  I.}},
    year={1687},
    title={{Philosophiae naturalis principia mathematica}},
    edition={1},
    address={Londini},
    publisher={{Jussu Societatis Regiae ac typis Josephi Streater, prostant venales apud Sam. Smith}},     url={https://books.google.com/books?id=XJwx0lnKvOgC&pg=PP2&redir_esc=y#v=onepage&q&f=false}
}
@book{Newton1713,
    author={{Newton,  I.}},
    year={1713},
    title={{Philosophiae naturalis principia mathematica}},
    edition={2},
    address={Cantabrigiae},
    publisher={{Newton, I.}},    
    url={https://digital.onb.ac.at/OnbViewer/viewer.faces?doc=ABO_%2BZ180810706&order=7&view=SINGLE}
}
@book{Newton1726,
    author={{Newton,  I.}},
    year={1726},
    title={{Philosophiae naturalis principia mathematica}},
    edition={3},
    address={Londini},
    publisher={{Apud Guil. & Joh. Innys}},     
    url={https://gdz.sub.uni-goettingen.de/id/PPN512261393}
}
@article{everitt1912,
 ISSN = {00063444},
 URL = {http://www.jstor.org/stable/2331587},
 author = {{Everitt, P. F.}},
 journal = {Biometrika},
 number = {3/4},
 pages = {385--395},
 publisher = {[Oxford University Press, Biometrika Trust]},
 title = {Supplementary Tables for Finding the Correlation Coefficient from Tetrachoric Groupings},
 volume = {8},
 year = {1912}
}
@article{everitt1910,
    author = {{Everitt, P. F.}},
    title = {Tables of the Tetrachoric Functions for Fourfold Correlation Tables},
    journal = {Biometrika},
    volume = {7},
    number = {4},
    pages = {437-451},
    year = {1910},
    month = {11},
    issn = {0006-3444},
    doi = {10.1093/biomet/7.4.437},
    url = {https://doi.org/10.1093/biomet/7.4.437}
}
@article{brown1977,
 ISSN = {00359254, 14679876},
 URL = {http://www.jstor.org/stable/2346985},
 author = {{Brown, M. B.}},
 journal = {Journal of the Royal Statistical Society. Series C (Applied Statistics)},
 number = {3},
 pages = {343--351},
 publisher = {[Royal Statistical Society, Oxford University Press]},
 title = {Algorithm AS 116: The Tetrachoric Correlation and its Asymptotic Standard Error},
 volume = {26},
 year = {1977}
}
@article{digby1983,
 ISSN = {0006341X, 15410420},
 URL = {http://www.jstor.org/stable/2531104},
 abstract = {This communication describes two approximating functions for the tetrachoric correlation coefficient. The values of both functions can be calculated easily and should be sufficiently accurate for many applications.},
 author = {{Digby, P. G. N.}},
 journal = {Biometrics},
 number = {3},
 pages = {753--757},
 publisher = {International Biometric Society},
 title = {Approximating the Tetrachoric Correlation Coefficient},
 volume = {39},
 year = {1983}
}
@article{long2009,
author = {{Long, M. A., Berry, K. J., & Mielke, P. W.}},
title ={Tetrachoric Correlation: A Permutation Alternative},
journal = {Educational and Psychological Measurement},
volume = {69},
number = {3},
pages = {429-437},
year = {2009},
doi = {10.1177/0013164408324463},
    abstract = { An exact permutation test is provided for the tetrachoric correlation coefficient. Comparisons with the conventional test employing Student's t distribution demonstrate the necessity of using the permutation approach for small sample sizes and/or disproportionate marginal frequency totals. }
}
@article{bonett2005,
 ISSN = {10769986, 19351054},
 URL = {http://www.jstor.org/stable/3701350},
 author = {{Bonett, D. G., & Price, R. M.}},
 journal = {Journal of Educational and Behavioral Statistics},
 number = {2},
 pages = {213--225},
 publisher = {[American Educational Research Association, Sage Publications, Inc., American Statistical Association]},
 title = {Inferential Methods for the Tetrachoric Correlation Coefficient},
 volume = {30},
 year = {2005}
}
@book{lehmann2008,
  title={Testing Statistical Hypotheses},
  author={{Lehmann, E. L., & Romano, J. P.}},
  isbn={9780387988641},
  lccn={2004051464},
  series={Springer Texts in Statistics},
  edition={3},
  url={https://books.google.com/books?id=IlJE_9_e8UEC},
  year={2008},
  address={New York},
  publisher={Springer}
}
@inbook{Howie2001,
author={{Howie, J. M.}},
title="The Logarithmic and Exponential Functions",
bookTitle="Real Analysis",
year="2001",
publisher="Springer",
address="London",
pages="165--179",
abstract="It is convenient at this stage to introduce two of the most important functions in mathematics. In a huge range of applications, from the discharge of a capacitor to the population growth of bacteria, the exponential function plays a crucial role, and ``log-log'' graphs are a crucial part of the methodology over a wide area of experimental science",
doi="10.1007/978-1-4471-0341-7_6"
}
@Inbook{Marsden1985,
author={{Marsden, J., & Weinstein, A.}},
title="Exponentials and Logarithms",
bookTitle="Calculus I",
year="1985",
publisher="Springer",
address="New York, NY",
pages="307--335",
abstract="In our work so far, we have studied integer powers (bn) and rational powers (bm/n) as functions of a variable base, i.e., y = xmor y = xm/n. In this chapter, we will study powers as functions of a variable exponent, i.e., y = bx: To do this, we must first define bxwhen x is not a rational number. This we do in Section 6.1; the rest of the chapter is devoted to the differential and integral calculus of the exponential functions y = bxand their inverses, the logarithms. The special value b = e = 2.7182818285... leads to especially simple formulas",
doi="10.1007/978-1-4612-5024-1_9"
}
@Inbook{Sobot2021,
author={{Sobot, R.}},
title="Exponential and Logarithmic Functions",
bookTitle="Engineering Mathematics by Example",
year="2021",
publisher="Springer International Publishing",
address="Cham",
pages="51--66",
doi="10.1007/978-3-030-79545-0_4"
}
@article{Allbright1991,
author = {{Allbright, G. S.}},
title = {Emulsion Speed Rating Systems},
journal = {The Journal of Photographic Science},
volume = {39},
number = {2},
pages = {95--99},
year = {1991},
address={Oxfordshire, UK},
publisher = {{Taylor and Francis}},
doi = {10.1080/00223638.1991.11737126}
}
@book{Hacking1975,
	year = {1975},
	author = {{Hacking, I.}},
	publisher = {Cambridge University Press},
	title = {{The Emergence of Probability: A Philosophical Study of Early Ideas About Probability, Induction and Statistical Inference}},
    url={https://philpapers.org/rec/HACTEO-8}
}
@book{Cardano1545,
    author={Cardano, G.},
    year={1545},
title={{ARTIS MAGNAE, SIVE DE REGVLIS ALGEBRAICIS, LIBER VNVS}},
    publisher={ANDREAE OSIANDRO viro eruditiss},
    address={S. P. D},     url={https://web.archive.org/web/20220201093634/http://www.filosofia.unimi.it/cardano/testi/operaomnia/vol_4_s_4.pdf}
}
@book{Cardano1993,
    author={Cardano, G.},
    year={1545},
    title={{Ars magna or The Rules of Algebra}},
    publisher={{Dover (published 1993)}},
    address={New York},
    isbn={0-486-67811-3},     url={https://archive.org/details/arsmagnaorruleso0000card/page/n3/mode/1up}
}
@Inbook{Remmert1998,
author={{Remmert, R.}},
title="The Gamma Function",
bookTitle="Classical Topics in Complex Function Theory",
year="1998",
publisher="Springer",
address="New York, NY",
pages="33--72",
abstract="The problem of extending the function n! to real arguments and finding the simplest possible ``factorial function'' with value n! at n ∈ ℕ led Euler in 1729 to the Г-function. He gave the infinite product {\$}{\$}{\backslash}Gamma {\backslash}left( {\{}z + 1{\}} {\backslash}right): = {\backslash}frac{\{}{\{}1 {\backslash}cdot {\{}2^z{\}}{\}}{\}}{\{}{\{}1 + z{\}}{\}} {\backslash}cdot {\backslash}frac{\{}{\{}{\{}2^{\{}1 - z{\}}{\}}{\{}3^z{\}}{\}}{\}}{\{}{\{}2 + z{\}}{\}} {\backslash}cdot {\backslash}frac{\{}{\{}{\{}3^{\{}1 - z{\}}{\}}{\{}4^z{\}}{\}}{\}}{\{}{\{}3 + z{\}}{\}} {\backslash}cdot{\backslash}ldots= {\backslash}prod{\backslash}limits{\_}{\{}{\backslash}nu= 1{\}}^{\backslash}infty{\{}{\{}{\{}{\backslash}left( {\{}1 + {\backslash}frac{\{}1{\}}{\{}{\backslash}nu {\}}{\}} {\backslash}right){\}}^z{\}}{\{}{\{}{\backslash}left( {\{}1 + {\backslash}frac{\{}z{\}}{\{}{\backslash}nu {\}}{\}} {\backslash}right){\}}^{\{} - 1{\}}{\}}{\}} {\$}{\$}as a solution.l Euler considered only real arguments; Gauss, in 1811, admitted complex numbers as well. On 21 November 1811, he wrote to Bessel (1784--1846), who was also concerned with the problem of general factorials, ``Will man sich aber nicht... zahllosen Paralogismen und Paradoxen und Widerspr{\"u}chen blossstellen, so muss 1∙2∙3.... x nicht als Definition von Пx gebraucht werden, da eine solche nur, wenn x eine ganze Zahl ist, einen bestimmten Sinn hat, sondern man muss von einer h{\"o}heren allgemein, selbst auf imagin{\"a}re Werthe von x anwendbaren, Definition ausgehen, wovon... jene als specieller Fall erscheint. Ich habe folgenden gew{\"a}hlt {\$}{\$}{\backslash}prod x = {\backslash}frac{\{}{\{}1.2.3 {\backslash}ldots k.k^x {\}}{\}}{\{}{\{}x + 1.x + 2.x + 3 {\backslash}ldots x + k'{\}}{\}}{\$}{\$}wenn k unendlich wird.'' (But if one doesn't want... countless fallacies and paradoxes and contradictions to be exposed, 1∙2∙3... x must not be used as the definition of Пx, since such a definition has a precise meaning only when x is an integer; rather, one must start with a definition of greater generality, applicable even to imaginary values of x, of which that one occurs as a special case. I have chosen the following... when k becomes infinite.) (Cf. [G1], pp. 362--363.) We will understand in {\textsection}2.1 why, in fact, Gauss had no other choice.",
isbn="978-1-4757-2956-6",
doi="10.1007/978-1-4757-2956-6_2",
url="https://doi.org/10.1007/978-1-4757-2956-6_2"
}
@book{gersonides1450,
author={{Abraham Bar Hiyya Savasorda, & et al.}},
year={1450},
title={{Ma'aseh Hoshev}},
publisher={Retrieved from the Library of Congress}, url={https://www.loc.gov/item/2021667539/}
}
@article{rabinovitch1970,
 ISSN = {00039519, 14320657},
 URL = {http://www.jstor.org/stable/41133303},
 author = {{Rabinovitch, N. L.}},
 journal = {Archive for History of Exact Sciences},
 number = {3},
 pages = {237--248},
 publisher = {Springer},
 title = {Rabbi Levi Ben Gershon and the Origins of Mathematical Induction},
 year = {1970}
}
@article{Fisher1918,
    author={{Fisher, R. A.}},
    year={1918},
    title={The Correlation Between Relatives on the Supposition of Mendelian Inheritance},
    journal={Philosophical Transactions of the Royal Society of Edinburgh},
    volume={52},
    pages={399--433},
    url={https://hdl.handle.net/2440/15097}
}
@article{Fisher1921,
    author={{Fisher, R. A.}},
    year={1921},
    title={On the "Probable Error" of a Coefficient of Correlation Deduced from a Small Sample},
    journal={Metron},
    volume={1},
    pages={3--32},
    url={https://hdl.handle.net/2440/15169}
}
@book{Fisher1925,
    author={{Fisher, R. A.}},
    year={1925},
    title={Statistical Methods for Research Workers},
    publisher={Oliver and Boyd},
    address={Edinburgh},
    isbn={},
    edition={1}, url={https://www.scirp.org/(S(i43dyn45teexjx455qlt3d2q))/reference/ReferencesPapers.aspx?ReferenceID=2056938}
}
@book{Fisher1973,
    author={{Fisher, R. A.}},
    year={1973},
    title={Statistical Methods for Research Workers},
    publisher={‎Hafner Publishing Company},
    address={New York},
    isbn={0050021702},
    edition={14}, url={https://www.amazon.com/Statistical-methods-research-workers-Fourteenth/dp/0050021702}
}
@book{Fisher2017,
    author={{Fisher, R. A.}},
    year={2017},
    title={Statistical Methods for Research Workers},
    publisher={‎‎Gyan Books},
    address={New Delhi},
    isbn={9351286584},
    edition={14th rev. ed}, url={https://www.amazon.com/Statistical-Methods-Research-Workers-Fisher/dp/9351286584}
}
@book{Fisher1954,
    author={{Fisher, R. A.}},
    year={1954},
    title={Statistical Methods for Research Workers},
    publisher={Oliver and Boyd},
    address={Edinburgh},
    isbn={0-05-002170-2},
    edition={12}, url={https://www.worldcat.org/de/title/statistical-methods-for-research-workers/oclc/312138}
}
@article{Thurstone1931,
    author={{Thurstone, L. L.}},
    year = {1931},
    title={Multiple factor analysis},
    journal={Psychological Review},
    volume={38},
    number={5},
    pages={406--427},
    doi={10.1037/h0069792},
    url={https://psycnet.apa.org/doiLanding?doi=10.1037%2Fh0069792}
}
@article{Thurstone1934,
    author={{Thurstone, L. L.}},
    year = {1934},
    title={The Vectors of Mind},
    journal={Psychological Review},
    volume={41},
    pages={1--32},
    doi={10.1037/h0075959},
    url={https://psycnet.apa.org/doiLanding?doi=10.1037%2Fh0075959}
}
@book{Thurstone1935,
    author={{Thurstone, L. L.}},
    year = {1935},
    title={The Vectors of Mind. Multiple-Factor Analysis for the Isolation of Primary Traits},
    address={Chicago, Illinois},
    publisher={University of Chicago Press},     url={https://archive.org/details/vectorsofmindmul010122mbp/page/n7/mode/1up}
}
@article{Cattell1966,
    author = {{Cattell, R. B.}},
    title = {The Scree Test For The Number Of Factors},
    journal = {Multivariate Behavioral Research},
    volume = {1},
    number = {2},
    pages = {245-276},
    year  = {1966},
    publisher = {Routledge},
    doi = {10.1207/s15327906mbr0102\_10},
    note ={PMID: 26828106},
    URL = {https://doi.org/10.1207/s15327906mbr0102_10}
}
@book{Arnauld1970,
	address = {Paris},
	author = {{Arnauld, A., Claire, P., Girbal, F., & Nicole, P.}},
	editor = {{Nicole, P.}},
	publisher = {Flammarion},
	title = {La Logique: Ou, L'art de Penser: Contenant, Outre les Regles Communes, Plusieurs Observations Nouvelles, Propres a Former le Jugement},
	year = {1970},
   url={https://philpapers.org/rec/ARNLLO-8}
}
@article{vanEvra1997,
	author = {{van Evra, J.}},
	journal = {Philosophy in Review},
	number = {3},
	pages = {153--155},
	title = {Antoine Arnauld and Pierre Nicole, Logic or the Art of Thinking},
	volume = {17},
	year = {1997},
   url={https://philpapers.org/rec/VANAAA-13}
}
@article{Finocchiaro1997,
	author = {{Finocchiaro, M. A.}},
	journal = {Argumentation},
	number = {4},
	pages = {393--410},
	title = {The Port-Royal Logic's Theory of Argument},
	volume = {11},
	year = {1997},
   url={https://doi.org/10.1023/A:1007756105432}
}
@article{Dessi1997,
	author = {{Dessì, P., & Albury, W. R}},
	doi = {10.1080/01445349708837281},
	journal = {History and Philosophy of Logic},
	number = {2},
	pages = {121--122},
	publisher = {{Taylor & Francis}},
	title = {Book Reviews},
	volume = {18},
	year = {1997}
}
@software{Schrausser7655056,
  author       ={{Schrausser, D. G.}},
  title        = {{Schrausser/ConsoleApp\_Integral: Console 
                   applications for integral and interpolation}},
  month        = feb,
  year         = 2023,
  publisher    = {Zenodo},
  version      = {v1.0.0},
  doi          = {10.5281/zenodo.7655056},
  url          = {https://doi.org/10.5281/zenodo.7655056}
}
@software{Schrausser7651660,
  author       ={{Schrausser, D. G.}},
  title        = {{Schrausser/FunktionWin: Windows Interface for 
                   distribution functions}},
  month        = feb,
  year         = 2023,
  publisher    = {Zenodo},
  version      = {{v1.0.0}},
  doi          = {10.5281/zenodo.7651660},
  url          = {https://doi.org/10.5281/zenodo.7651660}
}
@software{Schrausser7664088,
  author       ={{Schrausser, D. G.}},
  title        = {{Schrausser/PCE500\_MATH: Mathematical and 
                   statistical applications for SHARP PC-E500}},
  month        = feb,
  year         = 2023,
  publisher    = {Zenodo},
  version      = {v1.0.0},
  doi          = {10.5281/zenodo.7664088},
  url          = {https://doi.org/10.5281/zenodo.7664088}
}
@software{Schrausser7664141,
  author       ={{Schrausser, D. G.}},
  title        = {{Schrausser/ConsoleApp\_DistributionFunctions: 
                   Console applications for distribution functions}},
  month        = feb,
  year         = 2023,
  publisher    = {Zenodo},
  version      = {v1.0.0},
  doi          = {10.5281/zenodo.7664141},
  url          = {https://doi.org/10.5281/zenodo.7664141}
}
@incollection{SCHNEIDER200588,
    title = {{Chapter 6 - Jakob Bernoulli, Ars conjectandi (1713)}},
    editor = {{Grattan-Guinness, I., Cooke, R., Corry, L., Crépel, P., & Guicciardini, N.}},
    booktitle = {{Landmark Writings in Western Mathematics 1640-1940}},
    publisher = {Elsevier Science},
    address = {Amsterdam},
    pages = {88--104},
    year = {2005},
    isbn = {978-0-444-50871-3},
    doi = {10.1016/B978-044450871-3/50087-5},
    url = {https://www.sciencedirect.com/science/article/pii/B9780444508713500875},
    author = {{Schneider, I.}}
}
@incollection{SCHNEIDER200502,
    title = {{Chapter 7 -Abraham De Moivre, The Doctrine of Chances (1718, 1738, 1756)}},
    editor = {{Grattan-Guinness, I., Cooke, R., Corry, L., Crépel, P., & Guicciardini, N.}},
    booktitle = {{Landmark Writings in Western Mathematics 1640-1940}},
    publisher = {Elsevier Science},
    address = {Amsterdam},
    pages = {105--120},
    year = {2005},
    isbn = {0-444-50871-6},
    doi = {10.1016/B978-044450871-3/50087-5},
    url = {https://doi.org/10.1016/B978-044450871-3/50088-7},
    author = {{Schneider, I.}}
}
@book{jahnke1933,
    title={Funktionentafeln mit Formeln und Kurven},
    author={{Jahnke, E., & Emde, F.}},
    lccn={34015277},
    series={Mathematisch-physikalische Schriften f{\"u}r Ingenieure und Studierende},
    edition={2},
    url={https://books.google.com/books?id=SB5tAAAAMAAJ},
    year={1933},
    address={Leipzig},
    publisher={B. G. Teubner}
}
@book{jahnke1938,
    title={Funktionentafeln mit Formeln und Kurven},
    author={{Jahnke, E., & Emde, F.}},
    lccn={ac38004000},
    edition={3},
    url={https://books.google.com/books?id=5vlrAAAAIAAJ},
    year={1938},
    address={Leipzig},
    publisher={Teubner}
}
@journal{Knoll1939,
    author={{Knoll, F.}},
    year={1939},
    title={{Funktionentafeln mit Formeln und Kurven}},
    journal={{Monatshefte für Mathematik und Physik}},
    pages={{A14--A14}},
    volume= {47},
    url={https://doi.org/10.1007/BF01695545},
    doi={10.1007/BF01695545}
}
@book{jahnke1945,
  title={Funktionentafeln mit Formeln und Kurven},
  author={{Jahnke, E., & Emde, F.}},
  isbn={9780486601335},
  lccn={45006764},
  series={Dover Book},
  edition={4},
  url={https://archive.org/details/tablesoffunction0000jahn/page/n1/mode/1up},
  year={1945},
  address={New York},
  publisher={Dover Publications}
}
@book{jahnke1966,
  title={{Tafeln höherer Funktionen}},
  author={{Jahnke, E., Emde, F., & Lösch, F.}},
  edition={7}, url={https://dokumen.pub/jahnke-emde-lsch-tafeln-hherer-funktionen-tables-of-higher-functions-7nbsped.html},
  year={1966},
  address={Stuttgart},
  publisher={B. G. Teubner Verlagsgesellschaft}
}
@article{Efron1981,
    author = {{Efron, B.}},
    title = {Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods},
    journal = {Biometrika},
    volume = {68},
    number = {3},
    pages = {589--599},
    year = {1981},
    month = {12},
    abstract = {We discuss several nonparametric methods for attaching a standard error to a point estimate: the jackknife, the bootstrap, half-sampling, subsampling, balanced repeated replications, the infinitesimal jackknife, influence function techniques and the delta method. The last three methods are shown to be identical. All the methods derive from the same basic idea, which is also the idea underlying the common parametric methods. Extended numerical comparisons are made for the special case of the correlation coefficient.},
    issn = {0006-3444},
    doi = {10.1093/biomet/68.3.589},
    url = {https://doi.org/10.1093/biomet/68.3.589}
}
@book{Efron1982,
    author = {{Efron, B.}},
    title = {The Jackknife, the Bootstrap and Other Resampling Plans},
    publisher = {{SIAM, Society for Industrial and Applied Mathematics}},
    year = {1982},
    doi = {10.1137/1.9781611970319},
    address = {Philadelphia},
    series   = {CBMS-NSF Regional Conference Series in Applied Mathematics, Monograph 38},
    URL = {https://epubs.siam.org/doi/abs/10.1137/1.9781611970319}
}
@book{Katz2009,
    author={{Katz, V.}},
    year={2009},
    title={{Elementary Probability. A History of Mathematics: An Introduction}},
    address={London},
    publisher={Pearson},
    edition={3},
    ISBN={9780321387004},  url={https://www.gettextbooks.com/isbn/9780321387004/}
}
@book{Boyer1968,
    author={{Boyer, C. B.}},
    title={A History of Mathematics},
    year={1968},
    edition={1},
    publisher = {John Wiley & Sons, Inc.},
    address={New York},
    url={https://archive.org/details/ahistoryofmathematicscarlbboyer1968_315_t}
}
@book{neugebauer1969,
  title={The Exact Sciences in Antiquity},
  author={{Neugebauer, O.}},
  isbn={9780486223322},
  lccn={69020421},
  edition={2},
  series={Acta historica scientiarum naturalium et medicinalium},
  url={https://books.google.com/books?id=JVhTtVA2zr8C},
  year={1969},
  publisher={Dover Publications},
  address={New York}
}
@book{neugebauer1969,
  title={The Exact Sciences in Antiquity},
  author={{Neugebauer, O.}},
  isbn={9780486223322},
  lccn={69020421},
  edition={2},
  series={Acta historica scientiarum naturalium et medicinalium},
  url={https://books.google.com/books?id=JVhTtVA2zr8C},
  year={1969},
  publisher={Dover Publications},
  address={New York}
}
@book{heath1921history1,
  title={A History of Greek Mathematics},
  author={{Heath, T. L.}},
  volume={{I From Thales to Euclid}},
  isbn={},
  lccn={},
  url={https://archive.org/details/cu31924008704219},
  year={1921},
  address={Oxford},
  publisher={At the Clarendon Press}
}
@book{heath1921history2,
  title={A History of Greek Mathematics},
  author={{Heath, T. L.}},
  volume={{II From Aristarchus to Diophantus}},
  isbn={},
  lccn={}, url={https://archive.org/details/historyofgreekma029268mbp},
  year={1921},
  address={Oxford},
  publisher={At the Clarendon Press}
}
@book{suter1887,
  title={{Die Mathematik auf den Universitäten des Mittelalters}},
  author={{Suter, H.}},
  doi={10.3931/e-rara-65095},
  url={https://doi.org/10.3931/e-rara-65095},
  year={1887},
  address={Zürich},
  publisher={Druck von Zürcher und Furrer}
}
@book{heath1908_1,
  title={The Thirteen Books of Euclid's Elements translated from the Text of Heiberg with Introduction and Commentary},
  author={{Heath, T. L.}},
  volume={{I Introduction and Books I, II}},
  isbn={},
  lccn={}, url={https://archive.org/details/thirteenbookseu02heibgoog/page/n4/mode/1up},
  year={1908},
  address={Cambridge},
  publisher={University Press}
}
@book{heath1908_2,
  title={The Thirteen Books of Euclid's Elements translated from the Text of Heiberg with Introduction and Commentary},
  author={{Heath, T. L.}},
  volume={{II Books III-IX}},
  isbn={},
  lccn={}, url={https://archive.org/details/thirteenbookseu00heibgoog/page/n8/mode/1up},
  year={1908},
  address={Cambridge},
  publisher={University Press}
}
@book{heath1908_3,
  title={The Thirteen Books of Euclid's Elements translated from the Text of Heiberg with Introduction and Commentary},
  author={{Heath, T. L.}},
  volume={{III Books X-XIII and Appendix}},
  isbn={},
  lccn={}, url={https://archive.org/details/thirteenbookseu03heibgoog/page/n7/mode/1up},
  year={1908},
  address={Cambridge},
  publisher={University Press}
}
@article{schrausser_2024,
 title={Ptolemy's table of chords: Implications considered and discussed},
 DOI={10.5281/zenodo.11356370},
 publisher={OSF},
 author={{Schrausser, D. G.}},
 year={2024},
 month={05}
}
@book{Euler17481,
    author={{Euler, L.}},
    year={1748},
    title={{Introductio in analysin infinitorum}},
    volume={1},
    publisher={Apud Marcum-Michaelem Bousqujet & Socio},
    address={Lausannae},
    url={https://scholarlycommons.pacific.edu/euler-works/101/}
}
@book{Euler17482,
    author={{Euler, L.}},
    year={1748},
    title={{Introductio in analysin infinitorum}},
    volume={2},
    publisher={Apud Marcum-Michaelem Bousqujet & Socio},
    address={Lausannae},
    url={https://scholarlycommons.pacific.edu/euler-works/102/},
    note={In the Introductio in analysin infinitorum (this volume, together with E101), Euler lays the foundations of modern mathematical analysis.}
}
@inbook{Alten2014,
author={{Alten, H. -W., Naini, A. D., Eick, B., Folkerts, M., Schlosser, H., Schlote, K. -H.,  Wesemüller-Kock, H., & Wussing, H.}},
title={Algebra im Europa des Mittelalters und der Renaissance},
bookTitle={4000 Jahre Algebra: Geschichte -- Kulturen -- Menschen},
year={2014},
publisher={Springer},
address={Berlin, Heidelberg},
pages={207--263},
isbn={978-3-642-38239-0},
doi={10.1007/978-3-642-38239-0_4}
}
@article{malet2006,
title = {Renaissance notions of number and magnitude},
journal = {Historia Mathematica},
volume = {33},
number = {1},
pages = {63--81},
year = {2006},
note = {The Origins of Algebra: From al-Khwarizmi to Descartes},
issn = {0315-0860},
doi = {10.1016/j.hm.2004.11.011},
author = {{Malet, A.}}
}
@article{walter1982,
 ISSN = {00029890, 19300972},
 URL = {http://www.jstor.org/stable/2320218},
 author = {{Walter, W.}},
 journal = {The American Mathematical Monthly},
 number = {4},
 pages = {225--230},
 publisher = {Mathematical Association of America},
 title = {Old and New Approaches to Euler's Trigonometric Expansions},
 volume = {89},
 year = {1982}
}
@article{bochner1978,
   author={{Bochner, S.}},
   title={The Emergence of Analysis in the Renaissance and after},
   journal={Rice Institute Pamphlet - Rice University Studies},
   volume={64},
   number={2-3},
   year={1978},
   url={https://hdl.handle.net/1911/63315}
}
@book{calinger2016,
 ISBN = {9780691119274},
 URL = {http://www.jstor.org/stable/j.ctv7h0smb},
 author = {{Calinger, R. S.}},
 address={Princeton, New Jersey},
 publisher = {Princeton University Press},
 title = {Leonhard Euler: Mathematical Genius in the Enlightenment},
 year = {2016}
}
@article{finkel1897,
 ISSN = {00029890, 19300972},
 URL = {http://www.jstor.org/stable/2968971},
 author = {{Finkel, B. F.}},
 journal = {The American Mathematical Monthly},
 number = {12},
 pages = {297--302},
 publisher = {Mathematical Association of America},
 title = {Biography: Leonhard Euler},
 volume = {4},
 year = {1897}
}
@book{arndt2001,
  title={Pi - Unleashed},
  author={{Arndt, J., & Haenel, C.}},
  isbn={9783540665724},
  lccn={00066062},
  url={https://books.google.com/books?id=QwwcmweJCDQC},
  year={2001},
  address={Berlin, Heidelberg},
  publisher={Springer}
}
@book{Leibniz2012,
    author={{Leibniz, G. W.}},
    year={2012},
    title={{Sämtliche Schriften und Briefe}},
   series={{7: Mathematische Schriften}},
   volume={{6: 1673–1676: Arithmetische Kreisquadratur}},
   editor = {{Berlin-Brandenburgischen Akademie der Wissenschaften, & Akademie der Wissenschaften zu Göttingen}},
    publisher={Akademie Verlag},
    address={Berlin},
    url={https://doi.org/10.26015/adwdocs-1924}
}
@article{Leibniz1682,
    author={{Leibniz, G. W.}},
    year={1682},
    title={{De vera proportione circuli ad quadratum circumscriptum in numeris rationalibus}},
    journal={{Acta eruditorum anno MDCLXXXII}},
    pages={41--46},
    address={Lipsiae},      
    url={https://books.google.com/books/about/Acta_eruditorum.html?id=E7MasYIsMKQC&redir_esc=y}
}
@misc{Newton1669,
    author={{Newton, I.}},
    year={1669},
    month={07},
    day={31},
    title={{De analysi per aequationes numero terminorum infinitas. Sent by Dr. Barrow to Mr. Collins in a Letter dated July 31. 1669}},
    publisher={Royal Society Library},
    address={{London}},
    url={https://www.newtonproject.ox.ac.uk/view/texts/normalized/NATP00204}
}
@book{Newton1711,
    author={{Newton, I.}},
    year={1711},
    title={{Analysis per quantitatum series, fluxiones, ac differentias: cum enumeratione linearum tertii ordinis}},
    address={Londini},
    publisher={{ex officina Pearsoniana}},     
    url={https://doi.org/10.3931/e-rara-8934},
    doi={10.3931/e-rara-8934}
} 
@software{schrausser_2024_14183565,
  author       = {{Schrausser, D. G.}},
  title        = {Schrausser/Abh_Wkt: 1.5},
  month        = nov,
  year         = 2024,
  publisher    = {Zenodo},
  version      = {v1.5.0},
  doi          = {10.5281/zenodo.14183565},
  url          = {https://doi.org/10.5281/zenodo.14183565}
}
@book{Schrausser10.5281/zenodo.10969144,
  abstract = {Summarizing presentation of the fundamentally most important distribution functions with distribution graphics and formulation. Examples for the calculation in SCHRAUSSER-MAT syntax, as well as an extensive collection of formulas with transformations according to parameters of interest in the appendix.},
  added-at = {2024-04-13T10:12:55.000+0200},
  author = {{Schrausser, D. G.}},
  biburl = {https://www.bibsonomy.org/bibtex/296c3affc687e22f136a69544acac0822/schrausser},
  doi = {10.5281/zenodo.10969144},
  interhash = {7905f1250c208c6de994640115b1dab8},
  intrahash = {96c3affc687e22f136a69544acac0822},
  keywords = {myown probability statistics},
  language = {de},
  publisher = {PsyArXiv},
  timestamp = {2024-04-13T10:14:52.000+0200},
  title = {Handbook: Distribution Functions (Verteilungs Funktionen)},
  year = 2024
}