DOCSLIB.ORG

5 on the Uncultured Romans

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
5 on the Uncultured Romans Greeks,Practical andTheoretical 69 Planet (or sun) Epicycle Earth Deferent Fig. 8 The epicycle model. The planet moves clockwise round a small circle (epicycle) whose centre moves anticlockwise round a large circle (deferent) centred on the Earth. This explains why some planets (e.g. Mars) sometimes move backwards in relation to the stars. explanation is not so much to say what ‘really’ happens as to give an accurate description from which you can make predictions. Again, the physics, as we would call it, is not considered. In the first model (‘epicyclic’), the sun moves at constant speed round a small circle or ‘epicycle’; and the centre of the epicycle itself moves at constant speed round the ecliptic, with the Earth as centre (see Fig. 8). The second (‘eccentric’) supposes that the sun is travelling at uniform speed around a circle, but that the Earth is not the centre of the circle. It follows that the sun appears to be travelling more slowly when it is further from the Earth than when it is nearer (see Exercise 8). In Appendix B, I give the detailed working out by Ptolemy, from his observations, of where the centre of the orbit is in relation to the Earth. This is a detailed piece of Greek numerical mathematics, based on the geometric tradition. Is it practical? Very much so, in that it makes possible (the beginnings of ) the calculation of where the sun will be. But it is supported by a formidable theoretical apparatus of results about chords in a circle, angles, and so on. Considered as a whole—and this is the justification for devoting so much time to his work—Ptolemy’s Almagest gives more of an impression of the range and variety of Greek mathematics than any other text which we have. Exercise 6. Show that Crd(60 ) 60, and Crd(36 ) 60(( √5 1)/2). ◦ = ◦ = − Exercise 7. How would youfind Crd(θ/2) given Crd(θ)? Exercise 8. Explain the variation in the sun’s apparent speed, on the eccentric hypothesis. Research problem. Find the two reasons why the length of the day varies (a) as we would understand it, (b) as Ptolemy would have put it. (This is called the ‘equation of time’.) 5 On the uncultured Romans With the Greeks geometry was regarded with the utmost respect and consequently none were held in greater honour than mathematicians, but we Romans have delimited the size of this art to the practical purposes of measuring and calculating. (Cicero, Tusculan Disputations, tr. Serafina Cuomo, in Cuomo 2001, p. 192) The above quotation heads Serafina Cuomo’s chapter on the Romans; and her recent book makes thefirst serious attempt to investigate and indeed question a view of their mathematics accepted 70 AHistory ofMathematics since Cicero’s time (first century bce). Briefly, this is that the Romans in contrast to the Greeks made no contribution to mathematics, and that any works of theirs which contain or use it, such as Vitruvius’ architecture, are trivial in comparison with the Greek achievements. The charge has some basis in fact, as Cuomo acknowledges—‘I would be hard put to adduce a Latin equivalent of Euclid, Archimedes or Apollonius’, she admits (p. 194). This seems like an understatement; where are the Latin equivalents of Heron or Nicomachus? True, these second- or third-rate mathematicians worked under Roman rule, and may have been, like St Paul, Roman citizens. However, they wrote in Greek, and in a tradition which was, and continued to be, overwhelmingly Greek. The Romans, with better access to the Greek classics than the ninth-century Arabs or the Renaissance Europeans, never seem to have felt the same need to build on their work and develop it. And while Cuomo also interestingly makes a historicist point about the class angle contained in Cicero’s statement (ideas of ‘the Roman’ and ‘the Greek’ were marks of different kinds of prestige, while many users of numbers, and land-surveyors in particular, were seen as jumped-up technical upstarts), one is still left with an underlying feeling that it is an ideological statement based on good factual evidence. The most interesting part of her argument is a broader one, and does bear serious consideration: that the practice of mathematical methods of some sophistication pervaded the Roman world from top to bottom. Some of her examples, notably the charioteer whose tomb boasts that he drove chariots for 24 years, ran 4,257 starts and won 1,462 victories, 110 in opening races. In single-entry races he won 1,064 victories, winning 92 major purses, 32 of them (including 3 with six-horse teams) at 30,000 sesterces... (CIL 6.10048 (Rome, 146 ce), tr. in Lewis and Reinhold 1990, pp. 146–7) testify to the power of ‘numbers’ to impress rather than to the ability to do anything with them. However, her study of the practice of the despised land-surveyors (see also Dilke 1971), and of Vitruvius show how an appreciation, and application of classical geometry underlay their prac- tice. Perhaps rather than decrying the ‘low level’ of geometry present in Vitruvius’s architecture, we should think about the fact that it was a Roman, rather than a Greek, who bothered to write such a treatise; the architects of Greek temples were not, it would seem, given to exposition. We have different cultures (cohabiting in the same empire) with different ideas of what a book is for. Similarly, the famous tunnel of Eupalinus in Samos, dated at 550–530 bce, is often cited as an amazing example of very early practical Greek geometry; how did the builders of the tunnel, who started from the two sides of a mountain, contrive to meet so accurately in the middle? The answer is again that we do not know, and no Greek sources seem to have taken the trouble to explain how such a recurrent problem could be solved. The Roman surveyors, however, organized as a profession in which a discipline was transmitted by means of ‘textbooks’, both explained how they did it8 and wrote instructions whose foundation is in their training in some derivative of Euclidean geometry. This debate is only now beginning; the same applies to the doubts which Cuomo has cast on the idea that Greek mathematics was ‘in decline’ from (say) the time of Ptolemy,if not before. It is not so much a question of rehabilitating the Romans (awarding points to individuals or to civilizations for their excellence in mathematics should not be part of the business of history, though it often is). Rather, as we saw in Chapter 1 with the pre-OB periods, it is a question of looking at practices 8. See Cuomo (2001, p. 158) for a surveyor’s account of how he helped the weeping villagers whose tunnel had manifestly gone badly wrong. Greeks,Practical andTheoretical 71 which have been dismissed as trivial or non-mathematical and seeing if they do in fact belong in our history—and if so, where. 6 Hypatia Hypatia, the daughter of Theon the mathematician, was initiated in her father’s studies; her learned commentaries have illuminated the geometry of Apollonius and Diophantus, and she publicly taught, both at Athens and Alexandria, the philosophy of Plato and Aristotle. In the bloom of beauty, and in the maturity of wisdom, the modest maid refused her lovers and instructed her disciples; the persons most illustrious for their rank and merit were impatient to visit the female philosopher; and Cyril beheld with a jealous eye the gorgeous train of horses and slaves who crowded the door of her academy. (Gibbon, n.d. chapter XLVII) Hypatia was born in the later part of the Roman Empire, an era when women were not free to pursue careers. This was a time when orthodox belief effectively wiped out centuries of scientific discovery. Ancient Greek works were torched and scholars were murdered. Hypatia was the last proprietor of the Hellenic Age wonder, the Library of Alexandria. She is portrayed as a young adult facing the issues of a changing world. The reader will discover uncanny parallels to many current situations within the United States and, indeed, the world. Hypatia, a real, historically documented heroine, is afind for today’s young adults who are searching for strong, non-fiction role models. (From review of a novel, ‘Dear Future People’, at www.erraticimpact. com/˜feminism/html/women_hypatia.htm) Mathematicians, like engineers and physicists, have very rarely been women—the rarity is far more serious than (for example) for poets and painters. As a result, the study of ‘women mathematicians’ faces a serious difficulty in even getting off the ground, since there has until the twentieth century been no continuing tradition from which to construct a history. The feminist historian (of whom Margaret Alic 1986 was a pioneer) therefore necessarily (a) points out the existence of numerous such women of whom we know little or nothing, and (b) attempts to weave the major lives of which we do know something into some kind of thread. The philosopher and mathematician Hypatia, who was stoned to death by a Christian mob in 415 ce, (this much is undoubtedly historical fact) is the most important early, perhaps the foundingfigure for the tradition, and the questions which surround her life and activity may illustrate the wider problem. For if one were to take any other figure from Greek mathematics as ‘representative’ of something (Nicomachus as a Palestinian, Ptolemy as an African,...), generalizations based on the little that is known of their lives would be hard, although the works at least give some basis for building theories.
Load more

Recommended publications
  • Fiboquadratic Sequences and Extensions of the Cassini Identity Raised from the Study of Rithmomachia
    Fiboquadratic sequences and extensions of the Cassini identity raised from the study of rithmomachia Tom´asGuardia∗ Douglas Jim´enezy October 17, 2018 To David Eugene Smith, in memoriam. Mathematics Subject Classification: 01A20, 01A35, 11B39 and 97A20. Keywords: pythagoreanism, golden ratio, Boethius, Nicomachus, De Arithmetica, fiboquadratic sequences, Cassini's identity and rithmomachia. Abstract In this paper, we introduce fiboquadratic sequences as a consequence of an extension to infinity of the board of rithmomachia. Fiboquadratic sequences approach the golden ratio and provide extensions of Cassini's Identity. 1 Introduction Pythagoreanism was a philosophical tradition, that left a deep influence over the Greek mathematical thought. Its path can be traced until the Middle Ages, and even to present. Among medieval scholars, which expanded the practice of the pythagoreanism, we find Anicius Manlius Severinus Boethius (480-524 A.D.) whom by a free translation of De Institutione Arithmetica by Nicomachus of Gerasa, preserved the pythagorean teaching inside the first universities. In fact, Boethius' book became the guide of study for excellence during quadriv- ium teaching, almost for 1000 years. The learning of arithmetic during the arXiv:1509.03177v3 [math.HO] 22 Nov 2016 quadrivium, made necessary the practice of calculation and handling of basic mathematical operations. Surely, with the mixing of leisure with this exercise, Boethius' followers thought up a strategy game in which, besides the training of mind calculation, it was used to preserve pythagorean traditions coming from the Greeks and medieval philosophers. Maybe this was the origin of the philoso- phers' game or rithmomachia. Rithmomachia (RM, henceforward) became the ∗Department of Mathematics.
    [Show full text]
  • OUT of TOUCH: PHILOPONUS AS SOURCE for DEMOCRITUS Jaap
    OUT OF TOUCH: PHILOPONUS AS SOURCE FOR DEMOCRITUS Jaap Mansfeld 1. Introduction The view that according to Democritus atoms cannot touch each other, or come into contact, has been argued by scholars, most recently and carefully by C.C.W. Taylor, especially in his very useful edition of the fragments of the early Atomists.1 I am not concerned here with the theoretical aspect of this issue, that is to say with the view that the early Atomists should have argued (or posthumously admitted) that atoms cannot touch each other because only the void that separates them prevents fusion. I wish to focus on the ancient evidence for this interpretation. Our only ancient source for this view happens to be Philoponus; to be more precise, one brief passage in his Commentary on Aristotle’s Physics (fr. 54c Taylor) and two brief passages in that on Aristotle’s On Generation and Corruption (54dand54eTaylor~67A7 DK). These commentaries, as is well known, are notes of Ammonius’ lectures, with additions by Philoponus himself. Bodnár has argued that this evidence is not good enough, because all other ancient sources, in the first place Aristotle, are eloquently silent on a ban on contact; what we have here therefore are ‘guesses of Philoponus, which are solely based on the text of Aristotle’.2 Taylor admits the force of this objection, but sticks to his guns: ‘perhaps’, 1 Taylor (1997) 222,(1999) 186–188, 192–193,(1999a) 184, cf. the discussion in Kline and Matheson (1987) and Godfrey (1990). On the problems related to the assumption that attraction plays an important part see further the cautious remarks of Morel (1996) 422–424, who however does not take into account the passages in Philoponus which suggest that atoms cannot touch each other.
    [Show full text]
  • An Introduction to Pythagorean Arithmetic
    AN INTRODUCTION TO PYTHAGOREAN ARITHMETIC by JASON SCOTT NICHOLSON B.Sc. (Pure Mathematics), University of Calgary, 1993 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Mathematics We accept this thesis as conforming tc^ the required standard THE UNIVERSITY OF BRITISH COLUMBIA March 1996 © Jason S. Nicholson, 1996 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my i department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver, Canada Dale //W 39, If96. DE-6 (2/88) Abstract This thesis provides a look at some aspects of Pythagorean Arithmetic. The topic is intro• duced by looking at the historical context in which the Pythagoreans nourished, that is at the arithmetic known to the ancient Egyptians and Babylonians. The view of mathematics that the Pythagoreans held is introduced via a look at the extraordinary life of Pythagoras and a description of the mystical mathematical doctrine that he taught. His disciples, the Pythagore• ans, and their school and history are briefly mentioned. Also, the lives and works of some of the authors of the main sources for Pythagorean arithmetic and thought, namely Euclid and the Neo-Pythagoreans Nicomachus of Gerasa, Theon of Smyrna, and Proclus of Lycia, are looked i at in more detail.
    [Show full text]
  • The Origin of Life:Ahistory of Ancient Greek Theories
    Curriculum Units by Fellows of the Yale-New Haven Teachers Institute 1980 Volume V: Man and the Environment The Origin of Life:Ahistory of Ancient Greek Theories Curriculum Unit 80.05.11 by Joyce Puglia This unit presents a history of scientific thought relating to the origin of life as explained mainly by early Greek scientific philosophers. The unit begins with Greek science during the eighth century B.C. and proceeds quickly into the seventh century B.C., concluding with the fourth century B.C. Since the scope is limited to this time period the unit will end with information that is presently, for the most part, outdated. The teacher must constantly remind the students of this fact. The purpose of this unit is not to impart scientific knowledge for its own sake. Rather, it is to show how scientific thinkers came to their conclusions based upon how science was viewed in the scheme of history. There are various high school courses taught, yet no specific course has been designed to relate the development of the academic disciplines to each other. Many science textbooks include the names of scientists who contributed valuable information upon which specific ideas were developed. Yet, most textbooks provide a minimum amount of information relating to the scientists themselves. It is my feeling that students will better understand the development of scientific thought if an opportunity can be provided in which a connection can be made between science and history. There are four general objectives for this unit. Upon completing the unit students will: 1. be familiar with the ideas of early scientific minds, 2.
    [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]
  • 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]
  • The Project Gutenberg Ebook #31061: a History of Mathematics
    The Project Gutenberg EBook of A History of Mathematics, by Florian Cajori This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org Title: A History of Mathematics Author: Florian Cajori Release Date: January 24, 2010 [EBook #31061] Language: English Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK A HISTORY OF MATHEMATICS *** Produced by Andrew D. Hwang, Peter Vachuska, Carl Hudkins and the Online Distributed Proofreading Team at http://www.pgdp.net transcriber's note Figures may have been moved with respect to the surrounding text. Minor typographical corrections and presentational changes have been made without comment. This PDF file is formatted for screen viewing, but may be easily formatted for printing. Please consult the preamble of the LATEX source file for instructions. A HISTORY OF MATHEMATICS A HISTORY OF MATHEMATICS BY FLORIAN CAJORI, Ph.D. Formerly Professor of Applied Mathematics in the Tulane University of Louisiana; now Professor of Physics in Colorado College \I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history."|J. W. L. Glaisher New York THE MACMILLAN COMPANY LONDON: MACMILLAN & CO., Ltd. 1909 All rights reserved Copyright, 1893, By MACMILLAN AND CO. Set up and electrotyped January, 1894. Reprinted March, 1895; October, 1897; November, 1901; January, 1906; July, 1909. Norwood Pre&: J. S. Cushing & Co.|Berwick & Smith.
    [Show full text]
  • Sources for the Philosophy of Archytas
    Ancient Philosophy 28 (2008) ©Mathesis Publications 1 Sources for the Philosophy of Archytas Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King. By Carl Huffman. Cambridge: Cambridge University Press, 2005. Pp. xv + 665. $175.00 (cloth). ISBN 0521837464. Monte Ransome Johnson Although Archytas of Tarentum was one of the most important philosophers of the classical period, he has, like a second-rate scholar, become consigned to the oblivion of footnotes. Awkwardly, these are often footnotes to Pythagoreanism and fifth century philosophy. Yet he wrote and influenced fourth (not fifth) cen- tury philosophy; and it is an open question to what extent, or in what sense, and even whether, Archytas was really a Pythagorean. The source of the difficulties is to be found in the cruel, irrational, and occa- sionally fraudulent history of textual transmission. According to Huffman, only four genuine fragments of Archytas survive. Paucity of genuine material is a common problem in early Greek philosophy. But there is a further, special prob- lem with Archytas: the number of dubious fragments (or spurious fragments, as they are considered by Huffman) attributed to him in antiquity. While the gen- uine fragments in Huffman’s edition amount to just 73 lines, the standard edition of later Pythagorean material accumulates over 1300 lines under the name ‘Archytas’ (The Pythagorean Texts of the Hellenistic Period Collected and Edited by H. Thesleff [Åbo, 1965] 2-48). As I will argue at the end of this essay, there is hope, although it is not inspired by Huffman, that more of the material collected by Thesleff can be counted as evidence of Archytas’ thought, or at least cannot be ruled out as paraphrasing his words; they should at any rate be included in a complete edition of his philosophy.
    [Show full text]
  • The Beginnings of Greek Mathematics Greeks Were Not Confined to A
    Chapter 3: The Beginnings of Greek Mathematics Greeks were not confined to a neighborhood or the Aegean and the Peloponnesis. They ranged far and wide including present day Italy and Sicily and many lived in North Africa including Egypt. This is of course before the expansion of the Roman Empire (Punic Wars, 3rd Century B.C. and the Second Punic War was 218-201 B.C.) The Greeks introduced abstraction and gave logical arguments. For example Greeks were interested in triangles and not simply triangular fields. Thales of Miletus (ca. 625-547) (Miletus is in Asia Minor). Thales is sometimes known as the father of geometry probably because he was the first to use the deductive method. He proved among other things (see page 83 of the text) that a triangle inscribed inside a semi-circle (with one side the diameter) must be a right triangle. He also observed that the sides similar triangles are proportional. We do not have any mathematical works directly attributable to Thales or Pythagoras. Euclid’s Elements (Euclid 323-285) and Nicomachus of Gerasa’s Introductio Arithmeticae written ca. 100 B.C. are two math texts which we depend on but neither gives credit to the originators and discoverers of the results. Introductio Arithmeticae unlike Elements was a popular textbook for teaching geometry. Thales is credited with using similar triangles to discover the height of a the Great Pyramid of Gizeh (2600 B.C.) He similarly estimated distance to a ship offshore from a tower above the shore. See page 84 of the text. Pythagoras of Samos (580-500 B.C.; or 569-475 B.C.) (Samos is an Island in the northern Aegean near Asia Minor) His father was given honorary citizenship for bringing corn (!) in a time of famine.
    [Show full text]
  • Research and Experiment in Early Greek Thought by Tyler Mayo A
    Research and Experiment in Early Greek Thought by Tyler Mayo A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Classical Studies) in the University of Michigan 2019 Doctoral Committee: Professor Francesca Schironi, Chair Professor Sara Ahbel-Rappe Professor Richard Janko Associate Professor Ian Moyer Tyler Edward Mayo [email protected] ORCID iD: 0000-0002-2442-7127 To my mother and father ii ACKNOWLEDGMENTS First, ad consuetudinem maiorum, I would like to begin by acknowledging and expressing my gratitude to the members of my committee: Professors Richard Janko, Ian Moyer, and Sara Abhel-Rappe. Their suggestions and criticisms helped me to rethink some, and alter other, points within this dissertation to its improvement, and saved me from numerous errors within the text, many of which surely still lurk within these pages and are my responsibility alone. However, I owe a special debt to my chair, Francesca Schironi, whose support not only made this dissertation possible, but who acted as a mentor throughout my entire time at Michigan. Her honesty and counsel were always welcome, and her careful philology can be seen within these pages, although I fear only as an imperfect reflection. Outside Angell Hall, others made my studies in Ann Arbor possible. The Posch family— John, Dyanna, Isabel, and most recently, Jude—acted as a family away from home, not least for their generous hospitality in boarding me. I shall always remember and cherish their ξενία. My wife Liz is certainly owed a place of honor in the beginning of this dissertation. Her support was essential in its creation as in all other things.
    [Show full text]
  • The Hellenistic Period1
    The Hellenistic Period1 In this brief section, we show what type of problems mathemati- cians solved, and the extent of Greek mathematics before the collapse of the mathematical world in about 400 CE. 1 Aristarchus of Samos (CA. 310-230 BCE) Aristarchus of Samos was considered by the ancients, particularly Vit- ruvius2, who considered him to be one of the few great men knowl- edgeable in all sciences, especially astronomy and mathematics. Note that his dates are only surmised. For example, he lived before the Sand Reckoner of Archimedes, a work published before 216 BCE. He is also known to have observed the summer solstice in about 280 BCE. Perhaps, foremost among them is that he formulated the Coperni- can hypothesis He was the first to formulate the Copernican hypotheses and is sometimes called the Ancient Copernican. His heliocentric the- ory was never accepted in his day and remained dormant until it was proposed again by Copernicus. His contributions to science and math- ematics are many. He discovered an improved sundial, with a concave hemispherical circle. In supporting his heliocentric theory, he countered the non parallax objection by asserting that the stars to be so far dis- tant that parallax was not measurable. For this he needed the following measure of distance to the stars. distance(earth, stars) distance(radius of the sun) » He also determined a more accurate estimate of the solar year. He wrote as well on light and colors. He wrote On the Sizes and Distances of the Sun and Moon,in which by the way the heliocentric ideas are not mentioned or in any event are not present in the copied version extant.
    [Show full text]
  • Scepticism, Number and Appearances the Ἀριθμητικὴ Τέχνη and Sextus’ Targets in M I-VI
    Philosophie antique Problèmes, Renaissances, Usages 15 | 2015 Questions sur le scepticisme pyrrhonien Scepticism, number and appearances The ἀριθμητικὴ τέχνη and Sextus’ targets in M I-VI Lorenzo Corti Electronic version URL: http://journals.openedition.org/philosant/376 DOI: 10.4000/philosant.376 ISSN: 2648-2789 Publisher Presses universitaires du Septentrion Printed version Date of publication: 24 November 2015 Number of pages: 121-145 ISBN: 978-2-7574-1141-4 ISSN: 1634-4561 Electronic reference Lorenzo Corti, « Scepticism, number and appearances », Philosophie antique [Online], 15 | 2015, Online since 01 November 2018, connection on 19 April 2019. URL : http://journals.openedition.org/ philosant/376 ; DOI : 10.4000/philosant.376 La revue Philosophie antique est mise à disposition selon les termes de la Licence Creative Commons Attribution - Pas d'Utilisation Commerciale - Pas de Modification 4.0 International. SCEPTICISM, NUMBER AND APPEARANCES : The ἀριθμητικὴ τέχνη and Sextus’ targets in M I-VI Lorenzo CORTI Archives Henri Poincaré (Nancy) RÉSUMÉ. Cet article s’interroge sur ce qu’est l’ἀριθμητική τέχνη visée par Sextus dans le Contre les arithméticiens. Après avoir rappelé brièvement le contenu de M IV, on examine la nature de cette discipline. Une fois clarifiée la question de savoir en quoi consistait l’ἀριθμητική τέχνη dans l’Antiquité – et donc ce que visait Sextus dans M IV –, on examine son rapport avec les autres disciplines critiquées par Sextus dans le Contre les Professeurs. Cette enquête mène à mettre en lumière une importante présupposition implicite dans l’attitude de Sextus à l’égard des sciences. SUMMARY. This paper is devoted to Sextus’ target in Against the Arithme- ticians: the ἀριθμητικὴ τέχνη.
    [Show full text]