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was addressed to a lady of noble birth, at whose request
Nicomachus wrote the book, which suggests that he was a respected scholar of some status. He mentions his intent to write a more advanced work, and how the journeys he frequently undertakes leave him short of time.The approximate dates in which
479:), on the Pythagorean mystical properties of numbers in two books is mentioned by Photius. There is an extant work sometimes attributed to Iamblichus under this title written two centuries later which contains a great deal of material thought to have been copied or paraphrased from Nicomachus' work.
776:, Nicomachus points out that if one writes a list of the odd numbers, the first is the cube of 1, the sum of the next two is the cube of 2, the sum of the next three is the cube of 3, and so on. He does not go further than this, but from this it follows that the sum of the first
369:. Nicomachus distinguishes between the wholly conceptual immaterial number, which he regards as the 'divine number', and the numbers which measure material things, the 'scientific' number. Nicomachus provided one of the earliest Greco-Roman
592:
centuries earlier. Propositions are typically stated and illustrated with one example, but not proven through inference. In some instances this results in patently false assertions. For example, he states that from
644:'s epiphany outside of a smithy that pitch is determined by numeric ratios. Nicomachus also gives the first in-depth account of the relationship between music and the ordering of the universe via the "
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writing commentaries on it. A Latin paraphrase by
Boethius of Nicomachus's works on arithmetic and music became standard textbooks in medieval education.
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The treasury of mathematics: a collection of source material in mathematics edited and presented with introductory biographical and historical sketches
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565:) is the only extant work on mathematics by Nicomachus. The work contains both philosophical prose and basic mathematical ideas. Nicomachus refers to
281:) can only be estimated based on which other authors he refers to in his work, as well as which later mathematicians who refer to him. He mentions
2782:
1361:"Boethian Number Theory - Michael Masi: Boethian Number Theory: A Translation of the De Institutione Arithmetica (with Introduction and Notes)"
506:
has not survived. Among his known lost work is another larger work on music, promised by
Nicomachus himself, and apparently referred to by
325:
properties rather than their mathematical properties, citing an extensive amount of
Pythagorean literature in his work, including works by
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states that a square whose side length is a triangular number can be partitioned into squares and half-squares whose areas add to cubes
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and
Pythagorean concerns, normally regarded as antitheses. In the midst of theoretical discussions, Nicomachus also describes the
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Musici scriptores graeci. Aristoteles, Euclides, Nicomachus, Bacchius, Gaudentius, Alypius et melodiarum veterum quidquid exstat
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of
Nicomachus was a standard textbook in Neoplatonic schools, and commentaries on it were written by
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1277:. Source books in the history of the sciences. Vol. 13. Harvard University Press. p. 17.
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and the sensible world, however, he also makes more
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Pengelley, David (2002), "The bridge between continuous and discrete via original sources",
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realm. The work consists of two books, twenty-three and twenty-nine chapters, respectively.
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Plato (left) and
Nicomachus (right), as inventors of music, from a 12th-century manuscript
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History of
Mathematics, Volume I: General Survey of the History of Elementary Mathematics
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241:. Nicomachus' work on arithmetic became a standard text for Neoplatonic education in
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Many early mathematicians have studied and provided proofs of
Nicomachus's theorem.
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D'Ooge, Martin Luther; Robbins, Frank Egleston; Karpinski, Louis Charles (1926).
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1st century AD Neopythagorean philosopher, mathematician, and music theorist
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says that Nicomachus's philosophy "fits comfortably within the spectrum of
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1490:(in Ancient Greek). Lipsiae, in aedibus B. G. Teubneri. pp. 209–282
1411:, National Center for Mathematics Education, Univ. of Gothenburg, Sweden
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as the supreme first principle is both the demiurge and the Intellect (
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Arnold, Jonathan; Bjornlie, Shane; Sessa, Kristina (April 18, 2016).
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of his time, also providing a valuable resource. In addition to the
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1125:, New York: Dover Publications (a reprint of the 1951 publication),
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The work of Boethius on arithmetic and music was a core part of the
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survive in fragments, epitomes, and summaries by later authors. The
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and basic mathematical ideas are eternal and unchanging, and in an
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Nicomachi Geraseni Pythagorei Introductionis arithmeticae libri II
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Little is known about the life of Nicomachus except that he was a
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1510:(Cambridge: Cambridge University Press, 1989), pp. 245–69.
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1320:. Brill's Companions to European History. Brill. p. 332.
640:. It provides the earliest surviving record of the legend of
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also became the basis of the Boethius' Latin treatise titled
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1443:(in Ancient Greek). Lipsiae : in aedibvs B.G. Teubneri
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is ontologically prior to the other mathematical sciences (
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are extant in a complete form, and two others, a work on
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415:, Nicomachus makes no attempt to distinguish between the
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Nicomachus, of Gerasa; Hoche, Richard Gottfried (1866).
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to make a distinction between the intelligible world of
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Nicomachus's presentation is much less rigorous than
393:." In his work on arithmetic, Nicomachus quotes from
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numbers. Unlike many other Neopythagoreans, such as
1313:
611:is in large part a Latin translation of this work.
560:
1616:
1355:
1210:
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754:liberal arts and had a great diffusion during the
601:, only because this is true for a=6, b=5 and c=3.
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385:Although Nicomachus is considered a Pythagorean,
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1587:Dillon, John M. (1996). "Nicomachus of Gerasa".
1521:Iamblichus (January 1989). Gillian Clark (ed.).
823:odd numbers, that is, the odd numbers from 1 to
321:based on his tendency to view numbers as having
1436:
1428:
1010:{\displaystyle {\bigl (}n(n+1)/2{\bigr )}^{2}.}
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573:can only be possible if one knows enough about
1593:. Cornell University Press. pp. 352–361.
1571:from the original on May 16, 2021 – via
435:), which Nicomachus also equates to being the
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1672:
1483:
1405:Study the Masters: The Abel-Fauvel Conference
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510:in his comment on the sphere and cylinder of
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864:. The average of these numbers is obviously
301:,while he makes no mention at all of either
1212:"Nicomachus [Nikomachos] of Gerasa"
502:, referred to by Nicomachus himself in the
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1665:
1590:The Middle Platonists, 80 B.C. to A.D. 220
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443:from which all actualities are created.
1623:. Philosophical Library. pp. 15–16.
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1646:MacTutor History of Mathematics Archive
1231:10.1093/gmo/9781561592630.article.19911
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30:For other people named Nicomachus, see
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2708:Latin translations of the 12th century
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1459:Nicomachus' Introduction to Arithmetic
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229:, which are an important resource on
2403:Incircle and excircles of a triangle
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535:: Oriental Manuscripts, Add MS 7473.
486:was one of the main sources used by
341:, especially on the significance of
1110:The European Mathematical Awakening
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1514:
1484:Jan, Karl von; Nicomachus (1895).
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780:cubes equals the sum of the first
25:
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1628:
1550:Anonymous, Theology of Arithmetic
1274:A Source Book in Medieval Science
720:and a partial translation of the
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317:Historians consider Nicomachus a
2920:
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1371:(1). The Classical Association,
1317:A Companion to Ostrogothic Italy
772:At the end of Chapter 20 of his
577:. Nicomachus also describes how
1615:Midonick, Henrietta O. (1965).
1418:
1395:
1349:
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293:was apparently translated into
2962:2nd-century Greek philosophers
2957:1st-century Greek philosophers
2740:A History of Greek Mathematics
2253:The Quadrature of the Parabola
1527:. Liverpool University Press.
1195:. Vol. 1. pp. 97–98.
1193:A History of Greek Mathematics
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1097:The development of mathematics
1095:Eric Temple Bell (1940),
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451:Two of Nicomachus' works, the
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569:quite often, and writes that
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2521:Intersecting secants theorem
1508:Harmonic and Acoustic Theory
1255:UK public library membership
738:Medieval European philosophy
423:which serves as the supreme
245:, with philosophers such as
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2516:Intersecting chords theorem
2383:Doctrine of proportionality
1560:De institutione arithmetica
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711:De Institutione Arithmetica
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609:De institutione arithmetica
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504:Introduction to Arithmetic,
337:. He writes extensively on
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2165:On the Sizes and Distances
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774:Introduction to Arithmetic
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722:Introduction to Arithmetic
692:Introduction to Arithmetic
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547:Introduction to Arithmetic
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524:Introduction to Arithmetic
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453:Introduction to Arithmetic
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1688:Ancient Greek mathematics
1424:Editions and translations
1381:10.1017/S0009840X00107462
950:of them, so their sum is
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628:) is the first important
597:it can be concluded that
305:'s work on arithmetic or
231:Ancient Greek mathematics
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2585:Aristarchus's inequality
2158:On Conoids and Spheroids
1651:University of St Andrews
1373:Harvard University Press
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943:{\displaystyle n(n+1)/2}
900:{\displaystyle n(n+1)/2}
857:{\displaystyle n(n+1)-1}
816:{\displaystyle n(n+1)/2}
624:(Ἐγχειρίδιον ἁρμονικῆς,
500:Introduction to Geometry
477:Θεολογούμενα ἀριθμητικῆς
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119:Ancient Roman philosophy
2693:Ancient Greek astronomy
2506:Inscribed angle theorem
2496:Greek geometric algebra
2151:Measurement of a Circle
1524:On the Pythagorean Life
1502:Andrew Barker, editor,
1223:Oxford University Press
1121:David E. Smith (1958),
1108:Frank J. Swetz (2013),
626:Encheiridion Harmonikes
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207:Roman province of Syria
2927:Mathematics portal
2713:Non-Euclidean geometry
2668:Mouseion of Alexandria
2541:Tangent-secant theorem
2491:Geometric mean theorem
2476:Exterior angle theorem
2471:Angle bisector theorem
2175:On Sizes and Distances
1504:Greek Musical Writings
1027:Superparticular number
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731:De institutione musica
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469:Theology of Arithmetic
461:Theology of Arithmetic
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2551:Theorem of the gnomon
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2299:Problem of Apollonius
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2101:Archimedes Palimpsest
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595:(a-b) ∶ (b-c) ∷ c ∶ a
521:Arabic manuscript of
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159:Multiplication tables
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2628:Ptolemy's inequality
2569:Apollonius's theorem
2408:Method of exhaustion
2378:Diophantine equation
2368:Circumscribed circle
2185:On the Moving Sphere
1637:Robertson, Edmund F.
1365:The Classical Review
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713:) of Boethius was a
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2423:Lune of Hippocrates
2292:Squaring the circle
2048:Theon of Alexandria
1723:Aristaeus the Elder
1635:O'Connor, John J.;
1477:Manual of Harmonics
1152:, pp. 353–358.
1067:, pp. 352–353.
726:Manual of Harmonics
616:Manual of Harmonics
556:Ἀριθμητικὴ εἰσαγωγή
457:Manual of Harmonics
287:Manual of Harmonics
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235:Ancient Greek music
227:Manual of Harmonics
105:Manual of Harmonics
2977:People from Jerash
2610:Menelaus's theorem
2600:Irrational numbers
2413:Parallel postulate
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1357:Ivor Bulmer-Thomas
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498:of Pythagoras. An
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2638:Ptolemy's theorem
2511:Intercept theorem
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2287:Doubling the cube
2260:The Sand Reckoner
1600:978-0-8014-8316-5
1359:(April 1, 1985).
1253:(subscription or
1240:978-1-56159-263-0
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201:philosopher from
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16:(Redirected from
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889:
869:
866:
865:
828:
825:
824:
805:
785:
782:
781:
777:
770:
764:
746:
740:
700:John Philoponus
688:
682:
666:
619:
598:
594:
579:natural numbers
544:
533:British Library
449:
425:first principle
383:
347:perfect numbers
315:
303:Theon of Smyrna
278:
259:
251:John Philoponus
191:
187:
155:
139:
103:
95:
88:
77:
68:
65:
54:
42:
35:
28:
23:
22:
15:
12:
11:
5:
3015:
3005:
3004:
2999:
2994:
2989:
2984:
2979:
2974:
2969:
2964:
2959:
2954:
2949:
2932:
2931:
2904:
2901:
2900:
2897:
2896:
2894:
2893:
2888:
2883:
2878:
2873:
2868:
2863:
2857:
2855:
2854:Other cultures
2851:
2850:
2848:
2847:
2846:
2845:
2835:
2834:
2833:
2823:
2822:
2821:
2811:
2810:
2809:
2799:
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2797:
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2775:
2774:
2773:
2763:
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2761:
2751:
2750:
2749:
2735:
2733:
2729:
2728:
2726:
2725:
2720:
2715:
2710:
2705:
2703:Greek numerals
2700:
2698:Attic numerals
2695:
2689:
2683:
2679:
2678:
2676:
2675:
2670:
2665:
2659:
2657:
2653:
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2640:
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2607:
2602:
2597:
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2579:
2575:
2574:
2572:
2571:
2565:
2563:
2557:
2556:
2554:
2553:
2548:
2543:
2538:
2533:
2528:
2526:Law of cosines
2523:
2518:
2513:
2508:
2503:
2498:
2493:
2488:
2483:
2478:
2473:
2467:
2465:
2453:
2449:
2448:
2446:
2445:
2440:
2435:
2430:
2425:
2420:
2418:Platonic solid
2415:
2410:
2405:
2400:
2398:Greek numerals
2395:
2390:
2385:
2380:
2375:
2370:
2365:
2364:
2363:
2358:
2348:
2343:
2342:
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2311:
2305:
2304:
2302:
2301:
2296:
2295:
2294:
2289:
2284:
2273:
2271:
2267:
2266:
2264:
2263:
2256:
2249:
2239:
2229:
2226:Planisphaerium
2222:
2215:
2208:
2201:
2191:
2181:
2171:
2161:
2154:
2147:
2137:
2127:
2120:
2110:
2103:
2098:
2090:
2088:
2084:
2083:
2081:
2080:
2075:
2070:
2065:
2060:
2055:
2050:
2045:
2040:
2035:
2030:
2025:
2020:
2015:
2010:
2005:
2000:
1995:
1990:
1985:
1980:
1975:
1970:
1965:
1960:
1955:
1950:
1945:
1940:
1935:
1930:
1925:
1920:
1915:
1910:
1905:
1900:
1895:
1890:
1885:
1880:
1875:
1870:
1865:
1860:
1855:
1850:
1845:
1840:
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1825:
1820:
1815:
1810:
1805:
1800:
1795:
1790:
1785:
1780:
1775:
1770:
1765:
1760:
1755:
1750:
1745:
1740:
1735:
1730:
1725:
1720:
1715:
1710:
1704:
1702:
1696:Mathematicians
1692:
1691:
1684:
1683:
1676:
1669:
1661:
1655:
1654:
1630:
1629:External links
1627:
1626:
1625:
1612:
1599:
1582:
1579:
1578:
1577:
1565:Erhard Ratdolt
1551:
1548:
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1500:
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844:
841:
838:
835:
832:
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801:
798:
795:
792:
789:
766:Main article:
763:
760:
739:
736:
681:
680:Late antiquity
678:
665:
662:
618:
613:
543:
538:
448:
445:
387:John M. Dillon
382:
379:
375:British Museum
319:Neopythagorean
314:
311:
265:who came from
258:
255:
243:Late antiquity
199:Neopythagorean
166:
165:
162:
161:
156:
153:
150:
149:
140:
138:Main interests
137:
134:
133:
128:
122:
121:
116:
112:
111:
108:
107:
98:
92:
91:
83:
79:
78:
69:
60:
56:
55:
52:
44:
43:
40:
26:
9:
6:
4:
3:
2:
3014:
3003:
3000:
2998:
2995:
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2796:
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2631:
2629:
2626:
2624:
2623:
2618:
2616:
2613:
2611:
2608:
2606:
2603:
2601:
2598:
2596:
2593:
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2588:
2586:
2583:
2582:
2580:
2576:
2570:
2567:
2566:
2564:
2562:
2558:
2552:
2549:
2547:
2544:
2542:
2539:
2537:
2534:
2532:
2531:Pons asinorum
2529:
2527:
2524:
2522:
2519:
2517:
2514:
2512:
2509:
2507:
2504:
2502:
2501:Hinge theorem
2499:
2497:
2494:
2492:
2489:
2487:
2484:
2482:
2479:
2477:
2474:
2472:
2469:
2468:
2466:
2464:
2463:
2457:
2454:
2450:
2444:
2441:
2439:
2436:
2434:
2431:
2429:
2426:
2424:
2421:
2419:
2416:
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2411:
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2401:
2399:
2396:
2394:
2391:
2389:
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2336:
2335:
2332:
2328:
2325:
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2320:
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2315:
2314:
2312:
2306:
2300:
2297:
2293:
2290:
2288:
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2278:
2275:
2274:
2272:
2268:
2262:
2261:
2257:
2255:
2254:
2250:
2248:
2244:
2240:
2238:
2234:
2230:
2228:
2227:
2223:
2221:
2220:
2216:
2214:
2213:
2209:
2207:
2206:
2202:
2200:
2196:
2192:
2190:
2186:
2182:
2180:
2176:
2172:
2170:
2168:(Aristarchus)
2166:
2162:
2160:
2159:
2155:
2153:
2152:
2148:
2146:
2142:
2138:
2136:
2132:
2128:
2126:
2125:
2121:
2119:
2115:
2111:
2109:
2108:
2104:
2102:
2099:
2097:
2096:
2092:
2091:
2089:
2085:
2079:
2076:
2074:
2073:Zeno of Sidon
2071:
2069:
2066:
2064:
2061:
2059:
2056:
2054:
2051:
2049:
2046:
2044:
2041:
2039:
2036:
2034:
2031:
2029:
2026:
2024:
2021:
2019:
2016:
2014:
2011:
2009:
2006:
2004:
2001:
1999:
1996:
1994:
1991:
1989:
1986:
1984:
1981:
1979:
1976:
1974:
1971:
1969:
1966:
1964:
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1954:
1951:
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1936:
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1911:
1909:
1906:
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1889:
1886:
1884:
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1849:
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1724:
1721:
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1711:
1709:
1706:
1705:
1703:
1701:
1697:
1693:
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1677:
1675:
1670:
1668:
1663:
1662:
1659:
1652:
1648:
1647:
1642:
1638:
1633:
1632:
1621:
1620:
1613:
1602:
1596:
1592:
1591:
1585:
1584:
1574:
1570:
1566:
1562:
1561:
1556:
1552:
1549:
1547:
1543:
1540:
1536:
1534:9780853233268
1530:
1526:
1525:
1519:
1518:
1509:
1505:
1501:
1489:
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1482:
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1478:
1461:
1460:
1454:
1442:
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1435:
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1407:
1406:
1398:
1390:
1386:
1382:
1378:
1374:
1370:
1366:
1362:
1358:
1352:
1337:
1333:
1329:
1327:9789004315938
1323:
1319:
1318:
1310:
1302:
1298:
1294:
1290:
1286:
1284:9780674823600
1280:
1276:
1275:
1270:
1264:
1256:
1242:
1236:
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1228:
1224:
1220:
1219:
1213:
1208:
1202:
1194:
1190:
1189:Heath, Thomas
1184:
1177:
1171:
1164:
1158:
1151:
1146:
1144:
1142:
1140:
1133:, pp 58, 129.
1132:
1131:0-486-20429-4
1128:
1124:
1118:
1111:
1105:
1098:
1092:
1085:
1084:Midonick 1965
1080:
1078:
1076:
1074:
1066:
1061:
1059:
1057:
1055:
1053:
1051:
1049:
1047:
1042:
1033:
1030:
1028:
1025:
1024:
1018:
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983:
976:
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964:
937:
933:
926:
923:
920:
914:
894:
890:
883:
880:
877:
871:
851:
848:
842:
839:
836:
830:
810:
806:
799:
796:
793:
787:
775:
769:
759:
757:
753:
752:
745:
735:
733:
732:
727:
723:
719:
716:
712:
708:
703:
701:
697:
693:
687:
674:
670:
661:
659:
655:
651:
647:
643:
639:
635:
631:
627:
623:
617:
612:
610:
606:
602:
591:
586:
584:
580:
576:
572:
568:
563:
552:
548:
542:
534:
530:
526:
525:
519:
515:
513:
509:
505:
501:
497:
493:
489:
485:
484:
481:Nicomachus's
474:
473:Ancient Greek
470:
466:
462:
458:
454:
444:
442:
438:
434:
430:
426:
422:
418:
414:
410:
406:
402:
401:
396:
392:
388:
378:
376:
372:
368:
364:
360:
356:
352:
348:
344:
343:prime numbers
340:
336:
332:
328:
324:
320:
310:
308:
304:
300:
296:
292:
288:
284:
279: 100 AD
272:
268:
264:
254:
252:
248:
244:
240:
236:
232:
228:
224:
220:
217:). Like many
216:
212:
208:
204:
200:
197:
196:Ancient Greek
192: 120 AD
176:
172:
163:
160:
157:
154:Notable ideas
151:
148:
144:
141:
135:
132:
129:
127:
123:
120:
117:
113:
109:
106:
102:
99:
93:
84:
80:
76:
72:
61:
57:
50:
45:
38:
33:
19:
2918:
2905:
2747:Thomas Heath
2738:
2621:
2605:Law of sines
2461:
2393:Golden ratio
2258:
2251:
2242:
2236:(Theodosius)
2232:
2224:
2217:
2210:
2203:
2194:
2184:
2178:(Hipparchus)
2174:
2164:
2156:
2149:
2140:
2130:
2122:
2117:(Apollonius)
2113:
2105:
2093:
2068:Zeno of Elea
1927:
1828:Eratosthenes
1818:Dionysodorus
1644:
1641:"Nicomachus"
1618:
1604:. Retrieved
1589:
1563:(in Latin).
1559:
1523:
1507:
1503:
1492:. Retrieved
1486:
1476:
1464:. Retrieved
1458:
1445:. Retrieved
1439:
1429:
1419:Bibliography
1404:
1397:
1368:
1364:
1351:
1339:. Retrieved
1316:
1309:
1273:
1269:Edward Grant
1263:
1246:25 September
1244:. Retrieved
1216:
1201:
1192:
1183:
1175:
1174:Nicomachus,
1170:
1162:
1157:
1122:
1117:
1109:
1104:
1096:
1091:
773:
771:
749:
747:
729:
725:
721:
710:
706:
704:
691:
689:
686:Neoplatonism
657:
650:Aristoxenian
630:music theory
625:
621:
620:
615:
608:
603:
587:
546:
545:
540:
523:
522:
503:
499:
495:
482:
468:
464:
460:
456:
452:
450:
441:potentiality
409:Odd and even
398:
384:
316:
290:
286:
270:
260:
239:Roman period
226:
222:
219:Pythagoreans
170:
169:
104:
100:
96:Notable work
2814:mathematics
2622:Arithmetica
2219:Ostomachion
2188:(Autolycus)
2107:Arithmetica
1883:Hippocrates
1813:Dinostratus
1798:Dicaearchus
1728:Aristarchus
1546:Bibliotheca
1462:. Macmillan
1178:, ii. 6. 1.
1176:Arithmetica
1150:Dillon 1996
1065:Dillon 1996
756:Middle Ages
709:(in Latin:
654:instruments
634:Aristoxenus
575:mathematics
381:Metaphysics
263:Pythagorean
75:Roman Syria
2952:120 deaths
2941:Categories
2866:Babylonian
2766:arithmetic
2732:History of
2561:Apollonius
2246:(Menelaus)
2205:On Spirals
2124:Catoptrics
2063:Xenocrates
2058:Thymaridas
2043:Theodosius
2028:Theaetetus
2008:Simplicius
1998:Pythagoras
1983:Posidonius
1968:Philonides
1928:Nicomachus
1923:Metrodorus
1913:Menaechmus
1868:Hipparchus
1858:Heliodorus
1808:Diophantus
1793:Democritus
1773:Chrysippus
1743:Archimedes
1738:Apollonius
1708:Anaxagoras
1700:(timeline)
1581:References
1336:1016025625
1221:. Oxford:
1099:, page 83.
751:Quadrivium
744:Quadrivium
742:See also:
718:paraphrase
707:Arithmetic
696:Iamblichus
684:See also:
642:Pythagoras
571:philosophy
531:(d. 901).
512:Archimedes
492:Iamblichus
351:arithmetic
335:Androcydes
313:Philosophy
289:, and his
283:Thrasyllus
274:he lived (
247:Iamblichus
194:) was an
190: – c.
143:Arithmetic
89: 120
2947:60 births
2327:Inscribed
2087:Treatises
2078:Zenodorus
2038:Theodorus
2013:Sosigenes
1958:Philolaus
1943:Oenopides
1938:Nicoteles
1933:Nicomedes
1893:Hypsicles
1788:Ctesibius
1778:Cleomedes
1763:Callippus
1748:Autolycus
1733:Aristotle
1713:Anthemius
1389:125741349
1375:: 86–87.
1293:1556-9063
1257:required)
849:−
363:astronomy
327:Philolaus
205:, in the
188: 60
180:Νικόμαχος
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2891:Japanese
2876:Egyptian
2819:timeline
2807:timeline
2795:timeline
2790:geometry
2783:timeline
2778:calculus
2771:timeline
2759:timeline
2462:Elements
2308:Concepts
2270:Problems
2243:Spherics
2233:Spherics
2198:(Euclid)
2144:(Euclid)
2141:Elements
2134:(Euclid)
2095:Almagest
2003:Serenus
1978:Porphyry
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1848:Eutocius
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1718:Archytas
1606:16 April
1569:Archived
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1494:16 April
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1447:16 April
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1021:See also
605:Boethius
583:abstract
508:Eutocius
488:Porphyry
455:and the
417:Demiurge
359:geometry
331:Archytas
323:mystical
299:Apuleius
2871:Chinese
2826:numbers
2754:algebra
2682:Related
2656:Centers
2452:Results
2322:Central
1993:Ptolemy
1988:Proclus
1953:Perseus
1908:Marinus
1888:Hypatia
1878:Hippias
1853:Geminus
1843:Eudoxus
1833:Eudemus
1803:Diocles
1542:Photius
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1341:May 16,
1301:1066603
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400:Timaeus
339:numbers
307:Ptolemy
285:in his
237:in the
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447:Works
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405:Forms
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367:cause
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