DOCSLIB.ORG

Index of Names *

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Index of Names * Indexof Names* Acontius , jacobus , 242 Aristaeus , 157 Adrastus , 29jJ , 173 , 325 , 122 , 247 , Aristotle , 8f looff , 158f , 161f , 253 , 254 179f , 116, 316, 326 (] o7f ) Adrianus Romanus , 157 , 225 Categories 1 58 Albert of Saxony , 227 , 323 ( 304 ) , Metaphysics, IS, 53, 63.fJ., 69, 71, 333 89, 9 If. , 100, I58f. , 161, Alexander ( Aristotle Commentator I79f. , 37, 52, 55, 63, 74, 95, ) , 48 100 Alhazen , 286 Physics, 47f. , 62, 105, 109 Ammonius , 220 On Meillory , 326 (307) Anatollus , 41 , 147 , 4 , 149 ( 245 ) , 188 , On The Soul, 326 (307! ) 249 Posterior Analytics, IS, 100, 124, Anderson , Alexander , 208 , 239 ( 271 ) 169 Antoinette d ' Aubeterre , 150 Topics, 54 Apollonius of Perga , 32 , 124 , 131 , Aristoxcnus , 3 I 145 , 157 , 346 , 36 , 131 , 157 , 214 , 233 ( 266 ) , 268 ( 279 ) , Bachet de Mcziriac , 176ff., 213, 329, 323 ( 306 ) 149 (248), 160, 20] , 26] Aquinas , Thomas , 132 , 316 ( 297 ) Bacon , Francis , 152 Archimedes , 129 , 131 , 145 , 54 , 233 Baillct , Adrien , ] 17 ( 266 ) , 238 ( 270 ) Bakh ~Hall, 296 Archytas of Tarentum , 124 , 20 , 41 , Baliani , Giovanni Batista, ] 2] (305) 268 ( 279 ) Barocius, Franciscus, 181ff., 197 Barrow , Isaac , 152 * Italics refer to Note numbers . Numbers Bcaune , Florimond dc , ] ] 1 in parentheses following Note Bccker , Oskar , 62 , 97 numbers refer to pages on which Bceckman, Isaac, 276, 279 (284), names occur . ] 06, ] 08, ] 2] (302f.) 355 356 INDEX Docckh , August , 68f 345 , 129 , 133 - 19 , 24 , 244 , Docthius , Anicius , 125 245 , 249 , 25 , 261 , 266 , 3 4 Dombclli , Rafacl , 148 , 151 , 183 , Domninus of Larissa , 16 , 32JJ , 52 , 189 , 19 , 212 , 238 (270 ) , 239 , 58 , 61 , 149 ( 247 ) , 294 246 , 249 , 282 , 3 4 , 3 6 (293 ) Donasoni , Paolo , 238 (270 ) Epictctus , 316 ( 296 ) Dortolotti , E ., 238 (270 ) Eratosthcncs , 30 Dr adward u1c , Thomas , 227 , 323 Euclid , 15 , 27 , 33 , 40 , 43f , 58 , III , (305 ) 123 , 127 , 13 , 135f , 143 , Drahe , Tycho , 323(30r) 157 , 160 , 173 , 189f , 201 , Dressieu , 217 219 . ff . , 37 , 48 , 121 , 217 , 226 , Bungus, Petrus, 313 342 , 348 Buteo, Johannes, 217 (260), 238 Eudcmus of Rhodcs , 63 (270), 251, 297 Eudoxus , 51 , 159 , 39 , 52 , 121 Euler , Leonhard , 326 ( 308 ) Camerarius, Joachim, 313 Eurytos , 78 Candalla (Franc;ois de Foix-Can- Eustachius a Sancto Paulo , 206 . ff . , dalle), 217 324 Cantor, Moritz, 171 Eutocius , 36 ( 230 ) , 268 ( 279 ) Cardano, Geronimo, 147, 151, 183, 212,225 Faulhaber , Johann , 274 , 306 ( 293 ) , Cataldi, Pietro Antonio, 183, 273 313 Catherine of Parthcnay, 315 (2), Fcrmat , Picrrede , 133 , 133 , 323 ( 306 ) 197 Fcrrari , Luigi , 225 Chrysippus, 52, 326 (307) Ficino , Marsilio , 270 Chuquet, Nicolas, 238 (270), 260, Forcadcl , Eticnnc , 217 , 305 3 4, 3 5 Frank , E . , 40 Clavius, Christopher, I83, 217 Frcdcricus , Frater , 176 (260), 3 5 (292), 306 (293) Cleanthes, 326 (307) Galcn , 316 ( 297f . ) , 326 ( 308 ) Coignet, M ., 206 Galilco , 119 , 153 , 227 , 316 ( 298 ) , Commandinus, I53, 175, 214 323 ( 303 ) Cook-Wilson, J., 62 Gcminus , II , 16 , 41 , 4 , 220 Copernicus, Nicolaus, I53, 208 Gcmma Frisius , R . , 3 5 , 306 ( 293 ) Gcrard of Crcmona , 191 Dcscartcs, Rcne, 119, 15211:, 171, Ghctaldi , Marino , 183 , 206 , 208 , 181jJ, 197jJ, 212,2 9 (257f.), 275 ( 282 ) 212, 215, 225, 227, 235, 245, Girard , Albcrt , 283 , 3 3 27 , 274-279, 299,3 6-328, Golius , Jacobus , 306 331,335,337,341,345 Gosselin , Guillaume , 181 , 212 , 217 , Dilthcy, Wilhelm, 316 (297), 326 225 , 249 , 3 5 Diogcneslacrtius, 55 Grotius , Hugo , 283 , 288 , 306 Dionysius, Saint, 129 Grynacus , Simon , the Eldcr , 181 Diophantus, 4f , 9, 117, 12(ff , 151, 162f, 17 , 175, 178J, 188, Hammcr - Jcnscn , Ingcborg , 149 195, 321J (10), 329ff. (22), ( 246J . ) INDEX 357 Hankel , H . , 163 Nicolaus of Cusa , 227 , 279 (285 ) Harriot , Thomas , 211 , 221 , 275 , Nicomachus of Gerasa , 13 , 16 , 329 , 341 26jf , 51, 54, 58, 128, 172, 61 Heath , Thomas L . , 126 , 14 , 149 Nicomedes , 238 (270 ) ( 245 ) Nonius , Petrus , 147 , 151 , 286 Heiberg , J . L . , 149 ( 246f ) Hermes Trismegistos , 189 Olschi , Leonardo , 126 Heron , 112 , 126 , 133 , 9 , 125 , 149 Olympiodorus , II , I3jf , 60, 10, 14 ( 245ff . ) , 163 , 169 , 220 Orcme , Nicholas , 323 Hipparchus , 188 Oughtred , William , 211, 322, 329, Hippocrates , 127 338, 341 (311) Hippolytos , 149 ( 245f ) Homer , 318 ( 4 ) Pacioli , Luca , 212 , 227 Hultsch , F . , 36 , 149 ( 245 ) Pappus, 124, 131, I55jf , 131, 157, Huygens , Constant in , 306 214 , 215 , 218 , 235 , 245 Hypatia , 136 Pasquier, Es tienne, 233 (267) Peletier,Jacques, 151, 201, 212, 217, Iamblichus, 5IJ., III , 137, 26, 38, 302 173 Peurbach, Georg, 292, 297 Philolaos , 66 , 68 Kepler, Johannes, 69, 119, 152, 227 Fico della Mirandola , 270 Khowarizmi, aI-, 5 Planudes , Maximus , 148, 176, 187 Plato, 6jf , II , I7jf , 31J, 37jf , 49jf , Lauterbach, Johannes, 313 69jf , 105, 126, 175, 320, 46, Leon, 127 101, 326 (307) Leonardoof Pisa, 147,191 Charmides, 17, 24, 59, 69J Lipsius, Justus, 316 scholium,7, I Ijf , 47, 126 Lucian, 53 Critias , 64 Lucillus, Galus, 149 (247) Epinomis, 268 (279) Euthydemus, 79, 93 MarcusAurelius, 316 (297) Gorgias, 24, 59, 7 Marinus of Tyre, 220 sdlolium, 7, I4jf , 60, 12, 73 Maurice of Orange, 282, 283, 306 Hippias Major , 79ff, 94 Mclusinc, 316 (2) Ion , 19 Mersenne, Mar Ul, 278, 279 (284) Ladles , 83 Metius, Adrianus, 247, 258, 319 Laws, 12, 20J, 34, 57 (300) Lysis, 59 Modcratus, 52 " Meno , 218 Montucla, JeanEticnne, 134 Parmenides , 15 , 80 Phaedo, 57, 73, 75J , 85 Natorp, Paul Gerhard, 76 Philebus , 22, 69, 78, 86 Nesselmann, G. H. F., 126, 133, 146 Republic, I8.fJ, 23J , 3 , 37jf , Neugebauer, 0 ., 127, 8, 149 (248), 46, 74jf , 98, 15, 84, 92, 116 296 Sevent /~ Letter , 103 Newton, Sir Isaac, 152, 245 (273) Sophist, 82ff., 93ff. , 81 Nicarchos, 149(247) Statesmal ~, 39 , 57 358 INDEX Plato (continued) Stifel, Michael, 147, 176 Theaetetus, 15. 19.23. 38. 46. 55. Stobaeus, Johannes, 316 (297) 75Jf.. 22, 57, 58, 218(261) Sturm, Johannes, 233 (267) Timaeus, 28. 69f. Syrianus, 52, 54 Plutarch, 224 Primkius, Christianus, 313 Tannery, P., 126jJ., 28,36, 60,147, Proclus, 11ff, 41j. 47, 135, 159.0:, 149 (245jJ.), 218(261) 162, I 8oj. , 197, 12, 48, 233 Tartaglia, Niccolo, 147, 151, 153, (266), 268, 270 171,183.225 Psellus, Michacl, 149 Theaetetus, 43, 48, 94, 121 Ptolemy, 188,149(246), 209,296 Theodosiusof Tripolis, 37 Theon of Smyrna, 16, 28jJ., 4 , 51J., 58, 154J., 157, 166, 172, I~amus, Petrus, ISI.! , 201, 217, 225, 233, (266[.), 235 (268), 241, 346,122,174, 217,232, 233 251,269 (266), 247, 253 Theudios, 127, 121 Recordc, Robert, 332 (25) Thou, JacquesAuguste de, 207 Regiomontanus, 157f, 2O], 2] 8 Thrasyllus, 29 (270), 292 Thymaridas, 36,126,63,110,178 Reinhold, Erasmus, 208(256) Toeplitz, Otto, 68, 99 Remmelin, Johann, 313 Tropfke, J., 141 Ritter, Frcdcric, 193 Roberval, GiliesPcrsonne dc, 225 Tuning, Jean, 283 Roche, Es tiennede la, 238 (270) Ursus, Raimarus, 247 (274) Rodet, icon , 146f. Rohan, Henri and Rene of, 315 (2) Vanini, Lucilio, 270 Roth, Peter, 274 Vesalius, Andreas, 316 (298) Ruska, J., 177 Viera (Fran~oisVicte), S, 139, IS0.fJ, 197, 206, 216, 218, 31Sff, Scaligcr,] oscph, 205, 285,306 193-275, 292,334, 335 Schaner, Lazarus, 201, 212 Vinci, Leonardoda, 323 (30S) Schootcn, F. van, 212, 277, 331 Schor, Hcinrich, 233 (267) Wallis, John, 21Iff. , 321 (10), 245 Schulz, Otto, 149(2471) (273), 329-348 Seneca, LuciusAnnacus, J16 Warner, Walter, 275 SextusEmpiricus, 111, 316 (297) Snell, Rudolph, 233(267),306 (293) Xcnocratcs, 99 Snell, Willebrord, 283 Xylandcr, I48, ISI, I76, 160, 202, Speusippus, 66, 92, 99 217, 231 Stampioen, 225 Stenzel,julius, 61f, 60, 106 Zcno, 326 (307) Stevin, Simon, 119, 148, 183, 186ff., Zcuthcn, HicronymousGeorg, 62f, 212, 214, 274, 281-306, 122 336, 341 Zeuxippus, 13I .
Load more

Recommended publications
  • A Short History of Greek Mathematics
    Cambridge Library Co ll e C t i o n Books of enduring scholarly value Classics From the Renaissance to the nineteenth century, Latin and Greek were compulsory subjects in almost all European universities, and most early modern scholars published their research and conducted international correspondence in Latin. Latin had continued in use in Western Europe long after the fall of the Roman empire as the lingua franca of the educated classes and of law, diplomacy, religion and university teaching. The flight of Greek scholars to the West after the fall of Constantinople in 1453 gave impetus to the study of ancient Greek literature and the Greek New Testament. Eventually, just as nineteenth-century reforms of university curricula were beginning to erode this ascendancy, developments in textual criticism and linguistic analysis, and new ways of studying ancient societies, especially archaeology, led to renewed enthusiasm for the Classics. This collection offers works of criticism, interpretation and synthesis by the outstanding scholars of the nineteenth century. A Short History of Greek Mathematics James Gow’s Short History of Greek Mathematics (1884) provided the first full account of the subject available in English, and it today remains a clear and thorough guide to early arithmetic and geometry. Beginning with the origins of the numerical system and proceeding through the theorems of Pythagoras, Euclid, Archimedes and many others, the Short History offers in-depth analysis and useful translations of individual texts as well as a broad historical overview of the development of mathematics. Parts I and II concern Greek arithmetic, including the origin of alphabetic numerals and the nomenclature for operations; Part III constitutes a complete history of Greek geometry, from its earliest precursors in Egypt and Babylon through to the innovations of the Ionic, Sophistic, and Academic schools and their followers.
    [Show full text]
  • Welcome to the Complete Pythagoras
    Welcome to The Complete Pythagoras A full-text, public domain edition for the generalist & specialist Edited by Patrick Rousell for the World Wide Web. I first came across Kenneth Sylvan Guthrie’s edition of the Complete Pythagoras while researching a book on Leonardo. I had been surfing these deep waters for a while and so the value of Guthrie’s publication was immediately apparent. As Guthrie explains in his own introduction, which is at the beginning of the second book (p 168), he was initially prompted to publish these writings in the 1920’s for fear that this information would become lost. As it is, much of this information has since been published in fairly good modern editions. However, these are still hard to access and there is no current complete collection as presented by Guthrie. The advantage here is that we have a fairly comprehensive collection of works on Pythagoras and the Pythagoreans, translated from the origin- al Greek into English, and presented as a unified, albeit electronic edition. The Complete Pythagoras is a compilation of two books. The first is entitled The Life Of Py- thagoras and contains the four biographies of Pythagoras that have survived from antiquity: that of Iamblichus (280-333 A.D.), Porphry (233-306 A.D.), Photius (ca 820- ca 891 A.D.) and Diogenes Laertius (180 A.D.). The second is entitled Pythagorean Library and is a complete collection of the surviving fragments from the Pythagoreans. The first book was published in 1920, the second a year later, and released together as a bound edition.
    [Show full text]
  • Pythagoras and the Pythagoreans1
    Pythagoras and the Pythagoreans1 Historically, the name Pythagoras meansmuchmorethanthe familiar namesake of the famous theorem about right triangles. The philosophy of Pythagoras and his school has become a part of the very fiber of mathematics, physics, and even the western tradition of liberal education, no matter what the discipline. The stamp above depicts a coin issued by Greece on August 20, 1955, to commemorate the 2500th anniversary of the founding of the first school of philosophy by Pythagoras. Pythagorean philosophy was the prime source of inspiration for Plato and Aristotle whose influence on western thought is without question and is immeasurable. 1 c G. Donald Allen, 1999 ° Pythagoras and the Pythagoreans 2 1 Pythagoras and the Pythagoreans Of his life, little is known. Pythagoras (fl 580-500, BC) was born in Samos on the western coast of what is now Turkey. He was reportedly the son of a substantial citizen, Mnesarchos. He met Thales, likely as a young man, who recommended he travel to Egypt. It seems certain that he gained much of his knowledge from the Egyptians, as had Thales before him. He had a reputation of having a wide range of knowledge over many subjects, though to one author as having little wisdom (Her- aclitus) and to another as profoundly wise (Empedocles). Like Thales, there are no extant written works by Pythagoras or the Pythagoreans. Our knowledge about the Pythagoreans comes from others, including Aristotle, Theon of Smyrna, Plato, Herodotus, Philolaus of Tarentum, and others. Samos Miletus Cnidus Pythagoras lived on Samos for many years under the rule of the tyrant Polycrates, who had a tendency to switch alliances in times of conflict — which were frequent.
    [Show full text]
  • Too Many Metrodoruses? the Compiler of the Ἀριθμητικά from AP XIV
    Grillo, F. (2019) Too many Metrodoruses? The compiler of the ἀριθμητικά from AP XIV. Eikasmós, 30, pp. 249-264. There may be differences between this version and the published version. You are advised to consult the publisher’s version if you wish to cite from it. http://eprints.gla.ac.uk/204331/ Deposited on: 29 November 2019 Enlighten – Research publications by members of the University of Glasgow http://eprints.gla.ac.uk This is the author’s accepted manuscript. Please refer to the published journal article as follows: Grillo, F. (2019) ‘Too many Metrodoruses? The compiler of the ἀριθμητικά from AP XIV’, Eikasmós 30: 249-264. For the published version, see http://www2.classics.unibo.it/eikasmos/index.php?page=schedasingola&schedavis=1572 1 Too many Metrodoruses? The compiler of the ἀριθμητικά from AP XIV* In book fourteen of the Palatine Anthology we find a number of arithmetic problems (1-4, 6f., 11-13, 48-51, 116-147), the vast majority provided with mathematical scholia1. Most of the poems are attributed to a certain Metrodorus (116-146; cf. lemma to 116 Μητροδώρου ἐπιγράμματα ἀριθμητικά)2, a shadowy figure whose original collection comprised also problems 2f., 6f. and possibly 11-133. The identity of Metrodorus has received some attention, especially in late eighteenth- and nineteenth-century scholarship, but some crucial evidence has been repeatedly overlooked or misconstrued. Moreover, despite recent discussions, the question still remains unsettled, and it is unclear whether Metrodorus limited himself to compiling his collection or whether he also authored some poems4. Either way, a broad terminus post quem (or, less probably, ad quem) for his activity is provided by the epigram about the life-span of Diophantus (AP XIV 126), whose date is uncertain, but who is traditionally supposed to have lived in the mid- to late third century AD5.
    [Show full text]
  • A History of Elementary Mathematics, with Hints on Methods of Teaching
    ;-NRLF I 1 UNIVERSITY OF CALIFORNIA PEFARTMENT OF CIVIL ENGINEERING BERKELEY, CALIFORNIA Engineering Library A HISTORY OF ELEMENTARY MATHEMATICS THE MACMILLAN COMPANY NEW YORK BOSTON CHICAGO DALLAS ATLANTA SAN FRANCISCO MACMILLAN & CO., LIMITED LONDON BOMBAY CALCUTTA MELBOURNE THE MACMILLAN CO. OF CANADA, LTD. TORONTO A HISTORY OF ELEMENTARY MATHEMATICS WITH HINTS ON METHODS OF TEACHING BY FLORIAN CAJORI, PH.D. PROFESSOR OF MATHEMATICS IN COLORADO COLLEGE REVISED AND ENLARGED EDITION THE MACMILLAN COMPANY LONDON : MACMILLAN & CO., LTD. 1917 All rights reserved Engineering Library COPYRIGHT, 1896 AND 1917, BY THE MACMILLAN COMPANY. Set up and electrotyped September, 1896. Reprinted August, 1897; March, 1905; October, 1907; August, 1910; February, 1914. Revised and enlarged edition, February, 1917. o ^ PREFACE TO THE FIRST EDITION "THE education of the child must accord both in mode and arrangement with the education of mankind as consid- ered in other the of historically ; or, words, genesis knowledge in the individual must follow the same course as the genesis of knowledge in the race. To M. Comte we believe society owes the enunciation of this doctrine a doctrine which we may accept without committing ourselves to his theory of 1 the genesis of knowledge, either in its causes or its order." If this principle, held also by Pestalozzi and Froebel, be correct, then it would seem as if the knowledge of the history of a science must be an effectual aid in teaching that science. Be this doctrine true or false, certainly the experience of many instructors establishes the importance 2 of mathematical history in teaching. With the hope of being of some assistance to my fellow-teachers, I have pre- pared this book and have interlined my narrative with occasional remarks and suggestions on methods of teaching.
    [Show full text]
  • Women in Early Pythagoreanism
    Women in Early Pythagoreanism Caterina Pellò Faculty of Classics University of Cambridge Clare Hall February 2018 This dissertation is submitted for the degree of Doctor of Philosophy Alla nonna Ninni, che mi ha insegnato a leggere e scrivere Abstract Women in Early Pythagoreanism Caterina Pellò The sixth-century-BCE Pythagorean communities included both male and female members. This thesis focuses on the Pythagorean women and aims to explore what reasons lie behind the prominence of women in Pythagoreanism and what roles women played in early Pythagorean societies and thought. In the first chapter, I analyse the social conditions of women in Southern Italy, where the first Pythagorean communities were founded. In the second chapter, I compare Pythagorean societies with ancient Greek political clubs and religious sects. Compared to mainland Greece, South Italian women enjoyed higher legal and socio-political status. Similarly, religious groups included female initiates, assigning them authoritative roles. Consequently, the fact that the Pythagoreans founded their communities in Croton and further afield, and that in some respects these communities resembled ancient sects helps to explain why they opened their doors to the female gender to begin with. The third chapter discusses Pythagoras’ teachings to and about women. Pythagorean doctrines did not exclusively affect the followers’ way of thinking and public activities, but also their private way of living. Thus, they also regulated key aspects of the female everyday life, such as marriage and motherhood. I argue that the Pythagorean women entered the communities as wives, mothers and daughters. Nonetheless, some of them were able to gain authority over their fellow Pythagoreans and engage in intellectual activities, thus overcoming the female traditional domestic roles.
    [Show full text]
  • Bibliography
    Bibliography A. Aaboe, Episodes from the Early History of Mathematics (Random House, New York, 1964) A.D. Aczel, Fermat’s Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem (Four Walls Eight Windows, New York, 1996) D. Adamson, Blaise Pascal: Mathematician, Physicist, and Thinker About God (St. Martin’s Press, New York, 1995) R.P. Agarwal, H. Agarwal, S.K. Sen, Birth, Growth and Computation of Pi to ten trillion digits. Adv. Differ. Equat. 2013, 100 (2013) A.A. Al-Daffa’, The Muslim Contribution to Mathematics (Humanities Press, Atlantic Highlands, 1977) A.A. Al-Daffa’, J.J. Stroyls, Studies in the Exact Sciences in Medieval Islam (Wiley, New York, 1984) E.J. Aiton, Leibniz: A Biography (A. Hilger, Bristol, Boston, 1984) R.E. Allen, Greek Philosophy: Thales to Aristotle (The Free Press, New York, 1966) G.J. Allman, Greek Geometry from Thales to Euclid (Arno Press, New York, 1976) E.N. da C. Andrade, Sir Issac Newton, His Life and Work (Doubleday & Co., New York, 1954) W.S. Anglin, Mathematics: A Concise History and Philosophy (Springer, New York, 1994) W.S. Anglin, The Queen of Mathematics (Kluwer, Dordrecht, 1995) H.D. Anthony, Sir Isaac Newton (Abelard-Schuman, New York, 1960) H.G. Apostle, Aristotle’s Philosophy of Mathematics (The University of Chicago Press, Chicago, 1952) R.C. Archibald, Outline of the history of mathematics.Am. Math. Monthly 56 (1949) B. Artmann, Euclid: The Creation of Mathematics (Springer, New York, 1999) C.N. Srinivasa Ayyangar, The History of Ancient Indian Mathematics (World Press Private Ltd., Calcutta, 1967) A.K. Bag, Mathematics in Ancient and Medieval India (Chaukhambha Orientalia, Varanasi, 1979) W.W.R.
    [Show full text]
  • Wisdom» –Neopythagoreans and Others?
    AIMS Mathematics, 1(2): 77-95 DOI: 10.3934/Math.2016.2.77 Received: 29 March 2016 Accepted: 8 April 2016 Published: 17 May 2016 http://www.aimspress.com/journal/Math Research article Which kind of mathematics was known and referred to by those who wanted to integrate mathematics in «Wisdom» –Neopythagoreans and others? Jens Høyrup* Section for philosophy and Science Studies, Roskilde University, Denmark * Correspondence: Email: [email protected]. Abstract: Plato, so the story goes, held mathematics in high esteem, and those philosopher-kings that ought to rule his republic should have a thorough foundation in mathematics. This may well be true – but an observation made by Aristotle suggests that the mathematics which Plato intends is not the one based on theorems and proofs which we normally identify with “Greek mathematics”. Most other ancient writers who speak of mathematics as a road toward Wisdom also appear to be blissfully ignorant of the mathematics of Euclid, Archimedes, Apollonios, etc. – though not necessarily of their names. The aim of the paper is to identify the kinds of mathematics which were available as external sources for this current (on the whole leaving out of consideration Liberal-Arts mathematics as not properly external). A number of borrowings can be traced to various practitioners' traditions – but always as bits borrowed out of context. Keywords: Ancient Greek mathematics; Neopythagoreans; Plato; Practitioners' mathematics; Recreational mathematics; Side-and-diagonal-numbers algorithm Contents Remarks about Plato
    [Show full text]
  • A Concise History of the Philosophy of Mathematics
    A Thumbnail History of the Philosophy of Mathematics "It is beyond a doubt that all our knowledge begins with experience." - Imannuel Kant ( 1724 – 1804 ) ( However naïve realism is no substitute for truth [1] ) [1] " ... concepts have reference to sensible experience, but they are never, in a logical sense, deducible from them. For this reason I have never been able to comprehend the problem of the á priori as posed by Kant", from "The Problem of Space, Ether, and the Field in Physics" ( "Das Raum-, Äether- und Feld-Problem der Physik." ), by Albert Einstein, 1934 - source: "Beyond Geometry: Classic Papers from Riemann to Einstein", Dover Publications, by Peter Pesic, St. John's College, Sante Fe, New Mexico Mathematics does not have a universally accepted definition during any period of its development throughout the history of human thought. However for the last 2,500 years, beginning first with the pre - Hellenic Egyptians and Babylonians, mathematics encompasses possible deductive relationships concerned solely with logical truths derived by accepted philosophic methods of logic which the classical Greek thinkers of antiquity pioneered. Although it is normally associated with formulaic algorithms ( i.e., mechanical methods ), mathematics somehow arises in the human mind by the correspondence of observation and inductive experiential thinking together with its practical predictive powers in interpreting future as well as "seemingly" ephemeral phenomena. Why all of this is true in human progress, no one can answer faithfully. In other words, human experiences and intuitive thinking first suggest to the human mind the abstract symbols for which the economy of human thinking mathematics is well known; but it is those parts of mathematics most disconnected from observation and experience and therefore relying almost wholly upon its internal, self - consistent, deductive logics giving mathematics an independent reified, almost ontological, reality, that mathematics most powerfully interprets the ultimate hidden mysteries of nature.
    [Show full text]
  • Signature Redacted Signature of Author • • • • • • I'-• •~•· ••
    SOME ASPECTS OF THE EARLY HISTORY OF MATHEMATICS by JUDITH GORENSTEIN Submitted in Partial Fulfilkent of the Requirements for the Degree of Bachelor of Science at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June, 1956 . Signature redacted Signature of Author • • • • • • i'-• •~•· ••-.-...................... .. · ~ Di -~nt_pi· Mat1le11U:~ics, May 7,1956 Signature redacted Certified by ........ ..--....... r ,.,. ................................... .. _ ,,--r -. _.. Thesis Advisor . Signature redacted Accepted by..................................................... ~ ............................ Chairman, Departmental Committee on Theses I have enumerated some of the reasons for studying the history of mathematics and have shown examples of the misconceptions about the subject which many people have. Then I investigated the definition of mathematics, and on the basis of that definition, I tried to list some facets of mathematics which can be measured to enable a historian to evaluate the degree of progress in its development. To illustrate these features, I considered, briefly, the history of igebra from its origins to the end of the sixteenth century, showing how it progressed and retrogressed. Emphasis was given in proportion to the need thereof, additional detail being given where there was greater prevalence of erroneous ideas. I concluded with a short hiory of Hindu algebra paralleling the Western work. i P~L~ift~ ABSTRACT TABLE OF CONTENTS 11 1. REASONS FOR THE STUDY OF THE HISTORY OF MATHEMATICS Introduction 1 General Misconceptions 3 II. THE NATURE OF THE PROBLES IN THE INVESTIGATION OF THE HISTORY OF MATHEMATICS What Mathematics Consists of 6 Measuring Progress in Mathematics 7 III. SOME ASPECTS OF THE HISTORY OF ALGEBRA FROM THE BABYLONIANS TO THE ITALIANS AND kRENCH OF THE SIXTEENTH CENTURY The Beginnings 9 Egyptian Arithmetic and Algebra 11 Babylonian Algebra 13 The Greeks 15 The Romans 18 Arabic Algebra 18 Early Italian and French Algebra 21 Hindu Algebra 23 BIBLIOGRAPHY 29 ii.
    [Show full text]
  • View This Volume's Front and Back Matter
    An Introduction to the History of Algebra Solving Equations from Mesopotamian Times to the Renaissance http://dx.doi.org/10.1090/mawrld/027 MATHEMATICAL WORLD VOLUME 27 An Introduction to the History of Algebra Solving Equations from Mesopotamian Times to the Renaissance Jacques Sesiano Translated by Anna Pierrehumbert Providence, Rhode Island This work was originally published in French under the title: “Une introduction `a l’histoire de l’alg`ebre: R´esolution des ´equations des M´esopotamiens `a la Renaissance”. c 1999 Presses polytechniques et universitaires romandes, Lausanne. All rights reserved. Translated by Anna Pierrehumbert 2000 Mathematics Subject Classification. Primary 01A05, 17–XX, 20–XX, 30–XX, 35–XX, 40–XX. For additional information and updates on this book, visit www.ams.org/bookpages/mawrld-27 Library of Congress Cataloging-in-Publication Data Sesiano, Jacques. [Introduction `a l’histoire de l’alg`ebre. English] An introduction to the history of algebra : solving equations from Mesopotamian times to the Renaissance / Jacques Sesiano ; translated by Anna Pierrehumbert. p. cm. – (Mathematical world ; v. 27) Includes index. ISBN 978-0-8218-4473-1 (alk. paper) 1. Algebra—History. I. Title. QA151.S4513 2009 512.009–dc22 2009008068 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society.
    [Show full text]
  • IN MEMORIAM Evangelos S. Stamatis (1898-L 990)
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector HISTORIA MATHEMATICA 19 (1992), 99-105 IN MEMORIAM Evangelos S. Stamatis (1898-l 990) Evangelos S. Stamatis is widely known in the international community of histori- ans of mathematics as a modern Greek scholar of ancient Greek science. This is due to the fact that today his name is associated with the monumental editions of the Elements of Euclid and the Opera Omnia of Archimedes by the Leipzig firm of B. G. Teubner. Of course, these particular achievements were not isolated but rather part of an extensive and long-term preoccupation with the scientific heritage of ancient Greece. The bibliographical references to his studies, for example, in the Bibliographia Mathematics della Grecia classica e di antiche (1981) of Angiolo Procissi, in The Evolution of Euclidean Elements (1975) by W. R. Knorr, and in the collection Selections Illustrating the History of Greek Mathematics, 2 vols (1939-1941; reprinted 1980) in the Loeb Classical Library series give some idea of the scope and quality of his work. Today, as this admirer and scholar of ancient Greek science no longer is among us, his memory has prompted this biobibliograph- ical profile, intended to honor not only the scholar but also the man. Evangelos Stamatis was born on September 13, 1898, in Thiva. His father Stamatios was a priest, and Evangelos was the sixth of ten children. He received his general education in his native country, and after graduation from high school 99 03150860/92 $3.00 Copyright 0 1992 by Academic Press, Inc.
    [Show full text]