38:
271:
1282:. His constructive approach appears even in his geometry's postulates, as the first and third postulates stating the existence of a line and circle are constructive. Instead of stating that lines and circles exist per his prior definitions, he states that it is possible to 'construct' a line and circle. It also appears that, for him to use a figure in one of his proofs, he needs to construct it in an earlier proposition. For example, he proves the Pythagorean theorem by first inscribing a square on the sides of a right triangle, but only after constructing a square on a given line one proposition earlier.
2412:. It is thought that this book may have been composed by Hypsicles on the basis of a treatise (now lost) by Apollonius comparing the dodecahedron and icosahedron. The spurious Book XV, which is inferior, is thought to have been (at least in part) the work of Isidore of Miletus (fl. ca. A.D. 532), architect of the cathedral of Holy Wisdom (Hagia Sophia) at Constantinople. This book also deals with the regular solids, counting the number of edges and solid angles in the solids, and finding the measures of the dihedral angles of faces meeting at an edge.
1514:
5413:
1305:'setting-out', which gives the figure and denotes particular geometrical objects by letters. Next comes the 'definition' or 'specification', which restates the enunciation in terms of the particular figure. Then the 'construction' or 'machinery' follows. Here, the original figure is extended to forward the proof. Then, the 'proof' itself follows. Finally, the 'conclusion' connects the proof to the enunciation by stating the specific conclusions drawn in the proof, in the general terms of the enunciation.
486:
1253:
553:
299:
4133:
1318:. Some scholars have tried to find fault in Euclid's use of figures in his proofs, accusing him of writing proofs that depended on the specific figures drawn rather than the general underlying logic, especially concerning Proposition II of Book I. However, Euclid's original proof of this proposition, is general, valid, and does not depend on the figure used as an example to illustrate one given configuration.
5400:
1473:
256:
699:
1339:; during these considerations he uses some properties of superposition, but these properties are not described explicitly in the treatise. If superposition is to be considered a valid method of geometric proof, all of geometry would be full of such proofs. For example, propositions I.2 and I.3 can be proved trivially by using superposition.
2354:
include a fourteenth and even a fifteenth book, both shown by later scholars to be apocryphal. The so-called Book XIV continues Euclid's comparison of the regular solids inscribed in a sphere, the chief results being that the ratio of the surfaces of the dodecahedron and icosahedron inscribed in the
457:
translated it into Latin from an Arabic translation. A relatively recent discovery was made of a Greek-to-Latin translation from the 12th century at
Palermo, Sicily. The name of the translator is not known other than he was an anonymous medical student from Salerno who was visiting Palermo in order
1296:
Euclid's presentation was limited by the mathematical ideas and notations in common currency in his era, and this causes the treatment to seem awkward to the modern reader in some places. For example, there was no notion of an angle greater than two right angles, the number 1 was sometimes treated
1334:
For example, in the first construction of Book 1, Euclid used a premise that was neither postulated nor proved: that two circles with centers at the distance of their radius will intersect in two points. Later, in the fourth construction, he used superposition (moving the triangles on top of each
655:
is due primarily to its logical presentation of most of the mathematical knowledge available to Euclid. Much of the material is not original to him, although many of the proofs are his. However, Euclid's systematic development of his subject, from a small set of axioms to deep results, and the
2283:
appeared at Venice in 1482, one of the very earliest of mathematical books to be set in type; it has been estimated that since then at least a thousand editions have been published. Perhaps no book other than the Bible can boast so many editions, and certainly no mathematical work has had an
1304:
The presentation of each result is given in a stylized form, which, although not invented by Euclid, is recognized as typically classical. It has six different parts: First is the 'enunciation', which states the result in general terms (i.e., the statement of the proposition). Then comes the
1330:
was not exhaustive, but represented the principles that were the most important. His proofs often invoke axiomatic notions which were not originally presented in his list of axioms. Later editors have interpolated Euclid's implicit axiomatic assumptions in the list of formal axioms.
481:
relied heavily on these Arabic translations to create his edition (sometime before 1260) which ultimately came to dominate Latin editions until the availability of Greek manuscripts in the 16th century. There are more than 100 pre-1482 Campanus manuscripts still available today.
1297:
separately from other positive integers, and as multiplication was treated geometrically he did not use the product of more than 3 different numbers. The geometrical treatment of number theory may have been because the alternative would have been the extremely awkward
1241:
2243:, p. 278 states, "Euclid's Elements subsequently became the basis of all mathematical education, not only in the Roman and Byzantine periods, but right down to the mid-20th century, and it could be argued that it is the most successful textbook ever written."
706:
This postulate plagued mathematicians for centuries due to its apparent complexity compared with the other four postulates. Many attempts were made to prove the fifth postulate based on the other four, but they never succeeded. Eventually in 1829, mathematician
521:
in Oxford. The manuscripts available are of variable quality, and invariably incomplete. By careful analysis of the translations and originals, hypotheses have been made about the contents of the original text (copies of which are no longer available).
544:, or annotations to the text. These additions, which often distinguished themselves from the main text (depending on the manuscript), gradually accumulated over time as opinions varied upon what was worthy of explanation or further study.
1456:
497:
The first printed edition appeared in 1482 (based on
Campanus's translation), and since then it has been translated into many languages and published in about a thousand different editions. Theon's Greek edition was recovered and
631:
kept a copy of Euclid in his saddlebag, and studied it late at night by lamplight; he related that he said to himself, "You never can make a lawyer if you do not understand what demonstrate means; and I left my situation in
715:), a geometry which assumed a different form of the parallel postulate. It is in fact possible to create a valid geometry without the fifth postulate entirely, or with different versions of the fifth postulate (
246:
was required of all students. Not until the 20th century, by which time its content was universally taught through other school textbooks, did it cease to be considered something all educated people had read.
2325:
One older work claims
Adelard disguised himself as a Muslim student to obtain a copy in Muslim Córdoba. However, more recent biographical work has turned up no clear documentation that Adelard ever went to
1346:
put the criticisms in perspective, remarking that "the fact that for two thousand years was the usual text-book on the subject raises a strong presumption that it is not unsuitable for that purpose."
382:
may have been based on an earlier textbook by
Hippocrates of Chios, who also may have originated the use of letters to refer to figures. Other similar works are also reported to have been written by
37:
489:
Euclidis – Elementorum libri XV Paris, Hieronymum de Marnef & Guillaume
Cavelat, 1573 (second edition after the 1557 ed.); in 8:350, (2)pp. THOMAS–STANFORD, Early Editions of Euclid's
2255:, p. 100 notes, "As teachers at the school he called a band of leading scholars, among whom was the author of the most fabulously successful mathematics textbook ever written – the
469:
who wrote an edition around 1140, Robert of
Chester (his manuscripts are referred to collectively as Adelard II, written on or before 1251), Johannes de Tinemue, possibly also known as
270:
1464:. This book covers topics such as counting the number of edges and solid angles in the regular solids, and finding the measure of dihedral angles of faces that meet at an edge.
1381:
624:, have attempted to create their own foundational "Elements" for their respective disciplines, by adopting the axiomatized deductive structures that Euclid's work introduced.
4169:
2279:
of Euclid not only was the earliest major Greek mathematical work to come down to us, but also the most influential textbook of all times. The first printed versions of the
2410:
909:
2733:
5273:
2350:, pp. 118–119 writes, "In ancient times it was not uncommon to attribute to a celebrated author works that were not by him; thus, some versions of Euclid's
2540:
529:
itself, and to other mathematical theories that were current at the time it was written, are also important in this process. Such analyses are conducted by
1278:
Many of Euclid's propositions were constructive, demonstrating the existence of some figure by detailing the steps he used to construct the object using a
465:
After the translation by
Adelard of Bath (known as Adelard I), there was a flurry of translations from Arabic. Notable translators in this period include
2803:
957:, and shows, for example, that the volume of a cone is a third of the volume of the corresponding cylinder. It concludes by showing that the volume of a
644:", "O blinding hour, O holy, terrible day, / When first the shaft into his vision shone / Of light anatomized!". Albert Einstein recalled a copy of the
3123:"The First Printed Edition of the Greek Text of Euclid is also the First Edition to Include the Diagrams within the Text : History of Information"
5452:
5351:
627:
The austere beauty of
Euclidean geometry has been seen by many in western culture as a glimpse of an otherworldly system of perfection and certainty.
1289:
in several different cases, Euclid often proved only one of them (often the most difficult), leaving the others to the reader. Later editors such as
4654:
4190:
1370:. The book continues Euclid's comparison of regular solids inscribed in spheres, with the chief result being that the ratio of the surfaces of the
4162:
3956:
3801:(freely downloadable PDF, typeset in a two-column format with the original Greek beside a modern English translation; also available in print as
2585:
Murdoch, John E. (1967). "Euclides Graeco-Latinus: A Hitherto
Unknown Medieval Latin Translation of the Elements Made Directly from the Greek".
915:
lines into thirteen disjoint categories. Euclid here introduces the term "irrational", which has a different meaning than the modern concept of
664:
still influences modern geometry books. Furthermore, its logical, axiomatic approach and rigorous proofs remain the cornerstone of mathematics.
5198:
188:
4928:
3714:
3650:
3606:
3578:
3554:
3504:
3392:
3357:
2786:
2355:
same sphere is the same as the ratio of their volumes, the ratio being that of the edge of the cube to the edge of the icosahedron, that is,
1279:
2330:, although he spent time in Norman-ruled Sicily and Crusader-ruled Antioch, both of which had Arabic-speaking populations. Charles Burnett,
648:
and a magnetic compass as two gifts that had a great influence on him as a boy, referring to the Euclid as the "holy little geometry book".
4893:
1354:
It was not uncommon in ancient times to attribute to celebrated authors works that were not written by them. It is by these means that the
499:
238:
in the number of editions published since the first printing in 1482, the number reaching well over one thousand. For centuries, when the
2867:
2759:
506:
provided a widely respected "Mathematical
Preface", along with copious notes and supplementary material, to the first English edition by
5261:
4873:
4664:
1867:
5328:
4155:
3806:
2168:
2134:
449:
commissioned the copying of one of the extant Greek manuscripts of Euclid in the late ninth century. Although known in Byzantium, the
641:
4051:
3742:
3419:
3327:
3291:
2120:
2112:
2104:
2090:
2076:
3887:
3892:
2901:
5467:
4092:
3989:
3170:
1714:
1611:
530:
411:
3700:
2011:
5447:
5297:
5230:
4863:
4743:
2154:
912:
378:
408–355 BC) for book V, while books IV, VI, XI, and XII probably came from other Pythagorean or Athenian mathematicians. The
204:
99:
477:(sometime after 1120 but before 1187). The exact details concerning these translations is still an active area of research.
348:', and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors".
636:, went home to my father's house, and stayed there till I could give any proposition in the six books of Euclid at sight".
5437:
2174:
5462:
5366:
5123:
5011:
4186:
3846:
1522:
693:, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.
470:
1594:, reviewed by Stephanus Gracilis (only propositions, no full proofs, includes original Greek and the Latin translation)
961:
is proportional to the cube of its radius (in modern language) by approximating its volume by a union of many pyramids.
5472:
5442:
5006:
3880:– a course in how to read Euclid in the original Greek, with English translations and commentaries (HTML with figures)
877:
211:
is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of
5075:
1244:
An animation showing how Euclid constructed a hexagon (Book IV, Proposition 15). Every two-dimensional figure in the
930:
Book 11 generalizes the results of book 6 to solid figures: perpendicularity, parallelism, volumes and similarity of
2537:
4702:
4518:
4493:
3911:
345:
332:(412–485 AD), a Greek mathematician who lived around seven centuries after Euclid, wrote in his commentary on the
5237:
5208:
4568:
4423:
4087:
3486:
Heath's authoritative translation plus extensive historical research and detailed commentary throughout the text.
3596:
1513:
1314:
does provide instruction about how to approach the types of problems encountered in the first four books of the
5457:
5371:
4648:
1698:
503:
5105:
3099:"Editio Princeps of Euclid's Elements, the Most Famous Textbook Ever Published : History of Information"
5333:
5309:
5183:
5118:
5059:
4996:
4986:
4722:
4641:
4503:
4413:
4293:
3951:
3931:
by Nasīr al-Dīn al-Ṭūsī. Published by Medici Oriental Press(also, Typographia Medicea). Facsimile hosted by
2873:. Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA. p. 3. Archived from
1943:
859:
793:
752:
637:
5356:
5304:
5203:
5031:
4981:
4966:
4961:
4732:
4533:
4468:
4458:
4408:
4118:
4034:
3255:
617:
415:
287:
1734:
5404:
5256:
5041:
4918:
4841:
4789:
4591:
4498:
4348:
1721:
1584:
1336:
870:
863:
836:
633:
5412:
5100:
744:, parallelism, the sum of the angles in a triangle, and the construction of various geometric figures.
402:
produced an edition of Euclid which was so widely used that it became the only surviving source until
5381:
5321:
5285:
5128:
4951:
4898:
4868:
4858:
4767:
4523:
4438:
4393:
4373:
4218:
4203:
3982:
3773:
3525:
2924:
2863:
1771:
950:
387:
383:
359:
2688:
1915:
485:
418:
is a tiny fragment of an even older manuscript, but only contains the statement of one proposition.
5361:
5280:
5268:
5249:
5213:
5133:
5051:
5036:
5026:
4976:
4971:
4913:
4782:
4674:
4603:
4538:
4528:
4428:
4398:
4338:
4313:
4238:
4228:
4213:
4066:
4061:
3411:
3311:
3279:
3000:
2760:"Mathematical Treasures - Greek Edition of Euclid's Elements | Mathematical Association of America"
2572:
2358:
2033:
1956:
1889:
1802:
1795:
1785:
1710:
1656:
1598:
1542:
1535:
1518:
1367:
1290:
1257:
946:
924:
920:
855:
748:
737:
712:
708:
585:
534:
466:
446:
403:
399:
2996:
2992:
2975:
2495:
2479:
1589:
1252:
242:
was included in the curriculum of all university students, knowledge of at least part of Euclid's
5417:
5376:
5316:
5244:
5110:
4903:
4878:
4846:
4443:
4388:
4353:
4248:
4071:
4056:
3896:
3688:
3660:
2851:
2657:
2649:
2602:
1461:
1286:
1272:
942:
890:
733:
720:
686:
673:
478:
264:
196:
192:
87:
5085:
4684:
4027:
2622:"John of Tynemouth alias John of London: Emerging Portrait of a Singular Medieval Mathematician"
2099:, translation and commentaries by Heath, Thomas L. (1956) in three volumes. Dover Publications.
1854:
771:
1739:
5090:
5001:
4851:
4777:
4750:
4513:
4333:
4323:
4258:
4178:
3877:
3871:
3802:
3738:
3710:
3680:
3646:
3602:
3574:
3568:
3550:
3500:
3477:
3415:
3388:
3353:
3323:
3287:
3098:
2874:
2782:
2727:
2641:
2164:
2150:
2130:
2116:
2108:
2100:
2086:
2072:
2001:
1902:
1692:
1629:
1605:
916:
797:
716:
507:
474:
371:
341:
166:
3515:
2822:
835:
Book 6 applies proportions to plane geometry, especially the construction and recognition of
5292:
5163:
5080:
4836:
4824:
4772:
4508:
4013:
3672:
3564:
3347:
3297:
3267:
3178:
2633:
2594:
2216:
1748:
1650:
1491:
1343:
1268:
851:
672:
One of the most notable influences of Euclid on modern mathematics is the discussion of the
621:
608:, and applied their knowledge of it to their work. Mathematicians and philosophers, such as
518:
275:
55:
3938:
3901:
3122:
2804:"One of the world's most influential math texts is getting a beautiful, minimalist edition"
552:
4933:
4923:
4817:
4543:
4136:
4102:
3975:
3784:
3768:
3476:. Vol. 3. Books X to XIII and Appendix (2nd ed.). New York: Dover Publications.
3457:
3437:
3301:
2544:
1973:
1758:
1754:
1557, Jean Magnien and Pierre de Montdoré, reviewed by Stephanus Gracilis (Greek to Latin)
1704:
1573:
1564:
1451:{\displaystyle {\sqrt {\frac {10}{3(5-{\sqrt {5}})}}}={\sqrt {\frac {5+{\sqrt {5}}}{6}}}.}
1261:
938:
786:
628:
597:
593:
589:
514:
454:
438:
407:
303:
3798:
3598:
Encyclopaedia of the history of science, technology, and medicine in non-western cultures
1362:
were sometimes included in the collection. The spurious Book XIV was probably written by
968:
inscribed in a sphere and compares the ratios of their edges to the radius of the sphere.
414:
manuscript, is from a Byzantine workshop around 900 and is the basis of modern editions.
326:
is largely a compilation of propositions based on books by earlier Greek mathematicians.
230:
ever written. It was one of the very earliest mathematical works to be printed after the
1378:
inscribed in the same sphere is the same as the ratio of their volumes, the ratio being
425:, for instance, no record exists of the text having been translated into Latin prior to
298:
5193:
5188:
5016:
4908:
4888:
4716:
4273:
4243:
3812:
2893:
2533:
1834:
1776:
1578:
1559:
1308:
No indication is given of the method of reasoning that led to the result, although the
1298:
1240:
965:
931:
881:
613:
561:
144:
91:
473:(his manuscripts are referred to collectively as Adelard III), late 12th century, and
17:
5431:
5153:
5021:
4991:
4812:
4620:
4563:
4097:
3842:
3592:
3407:
3378:
3316:
2661:
1841:
1683:
1671:
1552:
1310:
609:
200:
95:
77:
3692:
3272:
3258:; Greenwalt, William S. (2012), "About the cover: Billingsley's Euclid in English",
5095:
4883:
4558:
4318:
4308:
3858:
1823:
1641:
1483:
1371:
847:
843:
782:
756:
682:
601:
231:
180:
3849:
who used color rather than labels such as ABC (scanned page images, public domain)
887:
Book 10 proves the irrationality of the square roots of non-square integers (e.g.
736:) and 5 common notions, and covers important topics of plane geometry such as the
3838:
3831:
3827:
3823:
3819:
3704:
3636:
3544:
3494:
3382:
2708:
2071:, Based on Heath's translation, edited by Dana Densmore, et al. Green Lion Press
759:
and a way of constructing a square equal in area to any rectilineal plane figure.
4709:
4597:
4303:
4288:
3883:
3588:
3490:
3469:
3449:
3429:
2308:
became the foundation of mathematical education. More than 1000 editions of the
2184:
1813:
1635:
1375:
702:
The different versions of the parallel postulate result in different geometries.
690:
577:
367:
159:
47:
3924:
3546:
Scribes and scholars: a guide to the transmission of Greek and Latin literature
2534:
The Earliest Surviving Manuscript Closest to Euclid's Original Text (Circa 850)
2508:
580:. In historical context, it has proven enormously influential in many areas of
493:, n°32. Mentioned in T.L. Heath's translation. Private collection Hector Zenil.
4695:
4614:
4553:
4548:
4488:
4473:
4418:
4403:
4358:
4298:
4283:
4263:
4233:
4198:
3921:
copied by Stephen the Clerk for Arethas of Patras, in Constantinople in 888 AD
2637:
2327:
1827:
1662:
1487:
1472:
1355:
351:
239:
176:
3818:
Heath's English translation and commentary, with the figures (Google Books):
3684:
3481:
3456:. Vol. 2. Books III to IX (2nd ed.). New York: Dover Publications.
2779:
The thirteen books of Euclid's Elements. Vol. 1: Introduction and books I, II
2645:
751:
concerning the equality of rectangles and squares, sometimes referred to as "
4448:
4433:
4383:
4278:
4268:
4253:
4223:
4147:
3441:
3436:. Vol. 1. Books I and II (2nd ed.). New York: Dover Publications.
1363:
1335:
other) to prove that if two sides and their angles are equal, then they are
796:, gives the highly sophisticated theory of proportion probably developed by
3915:
3617:
3461:
3337:
Bunt, Lucas Nicolaas Hendrik; Jones, Phillip S.; Bedient, Jack D. (1988).
2055:
1891,1896, The Harpur Euclid by Edward Langley and Seys Phillips (English)
676:. In Book I, Euclid lists five postulates, the fifth of which stipulates
255:
4585:
4363:
4208:
2521:
2179:, Kronecker Wallis, 2019, a modern redrawing extended to the rest of the
954:
778:
763:
459:
426:
227:
162:
3759:
2781:(Second revised with additions ed.). New York: Dover Publications.
2316:, the most widely spread book in the civilization of the Western world."
2026:
1953, 1958, 1975, Evangelos Stamatis (Ευάγγελος Σταμάτης) (Modern Greek)
513:
Copies of the Greek text still exist, some of which can be found in the
42:
Title page of Sir Henry Billingsley's first English version of Euclid's
5158:
4483:
4478:
4378:
4368:
4343:
3815:(HTML, without the figures, public domain) (accessed February 4, 2010)
3676:
2653:
2621:
2304:
became known to Western Europe via the Arabs and the Moors. There, the
1285:
As was common in ancient mathematical texts, when a proposition needed
767:
689:
forming two interior angles on the same side that sum to less than two
581:
541:
329:
216:
184:
2606:
1963:, which enables him to provide a first definitive version in 1814–1818
698:
4453:
4328:
3998:
3529:
2509:
Digging for Structure into the Elements: Euclid, Hilbert, and Mueller
1966:
1807, Józef Czech (Polish based on Greek, Latin and English editions)
1480:
958:
434:
422:
318:
into Latin, done in the 12th-century work and translated from Arabic.
169:
153:
67:
51:
3864:
3852:
3368:
876:
Book 9 applies the results of the preceding two books and gives the
762:
Book 3 deals with circles and their properties: finding the center,
2598:
1905:(Sanskrit, based on the Arabic translation of Nasir al-Din al-Tusi)
453:
was lost to Western Europe until about 1120, when the English monk
219:, and its logical rigor was not surpassed until the 19th century .
4829:
4807:
4463:
3932:
1512:
1477:
1471:
1251:
1239:
573:
551:
484:
297:
269:
254:
235:
212:
433:
from the Byzantines around 760; this version was translated into
3861:, animated and explained by Sandy Bultena, contains books I-VII.
2129:, based on John Casey's translation, edited by Daniel Callahan,
1460:
The spurious Book XV was probably written, at least in part, by
741:
358:
570–495 BC) was probably the source for most of books I and II,
314:
1309–1316; Adelard's is the oldest surviving translation of the
283:
4151:
3971:
410:
of a manuscript not derived from Theon's. This manuscript, the
719:). If one takes the fifth postulate as a given, the result is
660:, encouraged its use as a textbook for about 2,000 years. The
462:
to Latin. The Euclid manuscript is extant and quite complete.
2069:
Euclid's Elements – All thirteen books complete in one volume
148:
3234:
3232:
2206:, contains books IV–VIII, based on John Casey's translation.
502:
based on Paris gr. 2343 and Venetus Marcianus 301. In 1570,
226:
has been referred to as the most successful and influential
3543:
Reynolds, Leighton Durham; Wilson, Nigel Guy (9 May 1991).
2940:
2938:
2085:(2006), Translated by Sir Thomas Heath, Barnes & Noble
2200:, contains books I–III, based on John Casey's translation.
3967:
1924:
1749, Methodios Anthrakitis (Μεθόδιος Ανθρακίτης) (Greek)
1248:
can be constructed using only a compass and straightedge.
556:
A page with marginalia from the first printed edition of
2444:
2442:
2440:
1949:
1789, Pr. Suvoroff nad Yos. Nikitin (Russian from Greek)
1224:• "To draw a straight line from any point to any point."
572:
is still considered a masterpiece in the application of
1226:• "To describe a circle with any center and distance."
2882:: about Max Talmud visited on Thursdays for six years.
429:
in the fifth or sixth century. The Arabs received the
3927:
Arabic translation of the thirteen books of Euclid's
3663:(1993). "A new look at euclid's second proposition".
3085:
2361:
1499:
1384:
893:
732:
Book 1 contains 5 postulates (including the infamous
195:
of the propositions. The books cover plane and solid
3145:
2083:
The Elements: Books I–XIII – Complete and Unabridged
1293:
often interpolated their own proofs of these cases.
869:
Book 8 deals with the construction and existence of
5344:
5222:
5172:
5146:
5068:
5050:
4949:
4942:
4798:
4760:
4577:
4185:
4111:
4080:
4044:
4005:
3346:Busard, H.L.L. (2005). "Introduction to the Text".
2967:
2965:
2127:
Plane Geometry (Euclid's elements Redux) Books I–VI
2029:
1999, Maja Hudoletnjak Grgić (Book I-VI) (Croatian)
127:
114:
106:
83:
73:
63:
3315:
2471:
2469:
2404:
2312:are known. In all probability, it is, next to the
1450:
903:
800:, and proves properties such as "alternation" (if
3737:. Translated by Hudoletnjak Grgić, Maja. KruZak.
3570:History of Western Philosophy: Collectors Edition
2176:Euclid’s Elements: Completing Oliver Byrne's work
2141:Selected editions based on Oliver Byrne's edition
165:consisting of 13 books attributed to the ancient
2297:
2052:1886, Euclid Book I Hall & Stevens (English)
1217:
234:and has been estimated to be second only to the
2460:
1882:1694, Ant. Ernst Burkh v. Pirckenstein (German)
1222:
3339:The Historical Roots of Elementary Mathematics
2626:The British Journal for the History of Science
2556:
2332:Adelard of Bath: Conversations with his Nephew
711:published a description of acute geometry (or
4163:
3983:
3303:A Short Account of the History of Mathematics
3286:New York, Berlin, Heidelberg: Springer 1999,
3260:Bulletin of the American Mathematical Society
3238:
2147:The first six books of the Elements of Euclid
1997:1850, H. A. Witt and M. E. Areskong (Swedish)
1991:1844, 1845, 1859, P. R. Bråkenhjelm (Swedish)
1504:
8:
3795:In HTML with Java-based interactive figures.
2149:, edited by Werner Oechslin, Taschen, 2010,
1908:1731, Guido Grandi (abbreviation to Italian)
842:Book 7 deals with elementary number theory:
755:", and concludes with a construction of the
30:
2732:: CS1 maint: numeric names: authors list (
2284:influence comparable with that of Euclid's
656:consistency of his approach throughout the
302:An illumination from a manuscript based on
175:300 BC. It is a collection of definitions,
5176:
4946:
4170:
4156:
4148:
3990:
3976:
3968:
3322:(Second ed.). John Wiley & Sons.
2956:
2944:
1982:1828, Joh. Josh and Ign. Hoffmann (German)
36:
29:
3549:(2nd ed.). Oxford: Clarendon Press.
3271:
3025:
2387:
2367:
2362:
2360:
1959:(French). Peyrard discovered in 1808 the
1927:1745, Ernest Gottlieb Ziegenbalg (Danish)
1863:1663, Domenico Magni (Italian from Latin)
1529:and published in colored version in 1847.
1431:
1421:
1404:
1385:
1383:
1218:Euclid's method and style of presentation
894:
892:
3349:Campanus of Novara and Euclid's Elements
1911:1738, Ivan Satarov (Russian from French)
971:
697:
3957:Complete Library of the Four Treasuries
3799:Richard Fitzpatrick's bilingual edition
3474:The Thirteen Books of Euclid's Elements
3454:The Thirteen Books of Euclid's Elements
3434:The Thirteen Books of Euclid's Elements
2839:
2448:
2424:
2233:
2097:The Thirteen Books of Euclid's Elements
1979:1820, Benjamin of Lesbos (Modern Greek)
5199:Latin translations of the 12th century
3783:Euclid (1997) . David E. Joyce (ed.).
3381:; Hagar, Amit (2009). "Introduction".
3367:Callahan, Daniel; Casey, John (2015).
3223:
3211:
3199:
3061:
3049:
3037:
2746:
2725:
2674:
2587:Harvard Studies in Classical Philology
2240:
1805:(edition of the Arabic translation of
642:Euclid alone has looked on Beauty bare
4929:Straightedge and compass construction
3853:Web adapted version of Byrne’s Euclid
3284:Euclid – The Creation of Mathematics.
3157:
3073:
3013:
2431:
2347:
2272:
2252:
2058:1949, Henry Regnery Company (English)
1486:(left) and the Chinese mathematician
911:) and classifies the square roots of
7:
4894:Incircle and excircles of a triangle
3870:by John Casey and Euclid scanned by
3536:The Recension of Euclid's "Elements"
2987:
2971:
2802:Andrew., Liptak (2 September 2017).
2568:
2491:
2475:
2334:(Cambridge, 1999); Charles Burnett,
2063:Selected editions currently in print
1807:The Recension of Euclid's "Elements"
964:Book 13 constructs the five regular
3352:. Stuttgart: Franz Steiner Verlag.
3769:Clark University Euclid's elements
2894:"Albert Einstein – Young Einstein"
1936:1768, Angelo Brunelli (Portuguese)
25:
3520:. New York: Perkins Book Company.
3086:Alexanderson & Greenwalt 2012
2904:from the original on 10 June 2017
2823:"How Euclid once ruled the world"
2204:Euclid's Elements Redux, Volume 2
2198:Euclid's Elements Redux, Volume 1
2161:Oliver Byrne's Elements of Euclid
1994:1850, F. A. A. Lundgren (Swedish)
1939:1773, 1781, J. F. Lorenz (German)
1819:1606, Jan Pieterszoon Dou (Dutch)
880:and the construction of all even
525:Ancient texts which refer to the
366:470–410 BC, not the better known
5453:Ancient Greek mathematical works
5411:
5398:
4132:
4131:
3945:, an open textbook based on the
3701:Van der Waerden, Bartel Leendert
3314:(1991). "Euclid of Alexandria".
3171:"JNUL Digitized Book Repository"
2039:2019, Ali Sinan Sertöz (Turkish)
2007:1873, Masakuni Yamada (Japanese)
1930:1752, Leonardo Ximenes (Italian)
1885:1695, Claes Jansz Vooght (Dutch)
1879:1690, Vincenzo Viviani (Italian)
1868:Claude François Milliet Dechales
1860:1651, Heinrich Hoffmann (German)
1847:1617, Frans van Schooten (Dutch)
1767:1562, Wilhelm Holtzmann (German)
1548:Many medieval editions, pre 1482
336:: "Euclid, who put together the
3916:The thirteen books of Euclid's
3273:10.1090/S0273-0979-2011-01365-9
2522:Plato as "Architect of Science"
1873:1680, Vitale Giordano (Italian)
1646:1661, John Leeke and Geo. Serle
1326:Euclid's list of axioms in the
1235:, Book I, Postulates 1 & 3.
937:Book 12 studies the volumes of
537:in their editions of the text.
344:' theorems, perfecting many of
232:invention of the printing press
27:Mathematical treatise by Euclid
5231:A History of Greek Mathematics
4744:The Quadrature of the Parabola
3726:Encyclopedia of Ancient Greece
3665:The Mathematical Intelligencer
3387:. Cambridge University Press.
3177:. 22 June 2009. Archived from
2511:. Historia Mathematica 12, 176
2397:
2394:
2378:
2372:
2298:Bunt, Jones & Bedient 1988
2171:, a facsimile of Byrne (1847).
2157:, a facsimile of Byrne (1847).
2023:1907, František Servít (Czech)
1411:
1395:
1366:on the basis of a treatise by
1299:Alexandrian system of numerals
390:, and Hermotimus of Colophon.
1:
3778:in the Bibliotheca Polyglotta
3645:] (in Turkish). Tübitak.
3619:Eukleidovy Zaklady (Elementa)
3496:A Manual of Greek Mathematics
2405:{\displaystyle {\sqrt {10/}}}
2338:(University of London, 1987).
1969:1807, J. K. F. Hauff (German)
1898:1714, Chr. Schessler (German)
973:Summary Contents of Euclid's
442:
421:Although Euclid was known to
375:
363:
355:
311:
172:
120:
5012:Intersecting secants theorem
3925:Kitāb Taḥrīr uṣūl li-Ūqlīdis
3855:designed by Nicholas Rougeux
3531:Kitāb taḥrīr uṣūl li-Uqlīdus
3384:Euclid and His Modern Rivals
3103:www.historyofinformation.com
1952:1803, H.C. Linderup (Danish)
1933:1763, Pibo Steenstra (Dutch)
1490:(right) published the first
1342:Mathematician and historian
1260:from manuscript held in the
1256:Scan of pages demonstrating
747:Book 2 contains a number of
445:800). The Byzantine scholar
154:
5007:Intersecting chords theorem
4874:Doctrine of proportionality
3865:The First Six Books of the
3839:Oliver Byrne's 1847 edition
3813:Heath's English translation
3709:. Noordhoff International.
3517:The Life of Abraham Lincoln
3404:Geometry: Euclid and Beyond
2163:, Art Meets Science, 2022,
1895:1702, Hendrik Coets (Dutch)
1876:1689, Jacob Knesa (Spanish)
1850:1637, L. Carduchi (Spanish)
1791:1575, Commandinus (Italian)
1764:1562, Jacob Kündig (German)
1676:1781, 1788 James Williamson
1538:, 888 AD manuscript extant.
1500:
904:{\displaystyle {\sqrt {2}}}
878:infinitude of prime numbers
789:with 4, 5, 6, and 15 sides.
604:were all influenced by the
540:Also of importance are the
5489:
4703:On the Sphere and Cylinder
4656:On the Sizes and Distances
3912:Clay Mathematics Institute
3724:Wilson, Nigel Guy (2006).
3638:Öklidin Elemanlari: Ciltli
3635:Sertöz, Ali Sinan (2019).
3616:Servít, František (1907).
3402:Hartshorne, Robin (2000).
3306:(6th ed.). MacMillan.
3298:Ball, Walter William Rouse
2925:"Book X, Proposition XXIX"
2923:Joyce, D. E. (June 1997),
2898:www.alberteinsteinsite.com
2707:Campanus``, Pal.lat.1348.
2557:Reynolds & Wilson 1991
2300:, p. 142 state, "the
2275:, p. 119 notes, "The
1985:1833, E. S. Unger (German)
1583:1557, by Jean Magnien and
792:Book 5, on proportions of
785:of a triangle, as well as
322:Scholars believe that the
278:Arabic Translation of the
149:
5405:Ancient Greece portal
5394:
5209:Philosophy of mathematics
5179:
5124:Ptolemy's table of chords
4179:Ancient Greek mathematics
4127:
3954:reprinted as part of the
3952:1607 Chinese translations
3906:– The original Greek text
3845:)– an unusual version by
3370:Euclid's "Elements" Redux
3239:Callahan & Casey 2015
3146:Nasir al-Din al-Tusi 1594
2852:Euclid as Founding Father
2690:Euclid in Medieval Europe
2638:10.1017/S0007087400044009
2620:Knorr, Wilbur R. (1990).
2183:, originally launched on
2042:2022, Ján Čižmár (Slovak)
2017:1897, Thyra Eibe (Danish)
2012:Vachtchenko-Zakhartchenko
1505:
1275:were widely influential.
740:, equality of angles and
406:'s 1808 discovery at the
35:
5076:Aristarchus's inequality
4649:On Conoids and Spheroids
3933:Islamic Heritage Project
3774:Multilingual edition of
3318:A History of Mathematics
3127:historyofinformation.com
2687:Menso, Folkerts (1989).
2020:1901, Max Simon (German)
1921:1749, Dechales (Italian)
1699:Thomas Perronet Thompson
1358:books XIV and XV of the
1280:compass and straightedge
770:, the power of a point,
685:intersects two straight
394:Transmission of the text
5468:Foundations of geometry
5184:Ancient Greek astronomy
4997:Inscribed angle theorem
4987:Greek geometric algebra
4642:Measurement of a Circle
3514:Ketcham, Henry (1901).
3256:Alexanderson, Gerald L.
2868:"Einstein as a Student"
2140:
1988:1836, H. Falk (Swedish)
1944:Baruch Schick of Shklov
1713:(revised in 1926) from
1541:9th century, Pre-Theon
949:in detail by using the
860:greatest common divisor
638:Edna St. Vincent Millay
398:In the 4th century AD,
259:A fragment of Euclid's
52:commonly conflated with
5418:Mathematics portal
5204:Non-Euclidean geometry
5159:Mouseion of Alexandria
5032:Tangent-secant theorem
4982:Geometric mean theorem
4967:Exterior angle theorem
4962:Angle bisector theorem
4666:On Sizes and Distances
4119:Papyrus Oxyrhynchus 29
3499:. Dover Publications.
2777:Thomas, Heath (1956).
2406:
1816:de Bar-le-Duc (French)
1530:
1527:The Elements of Euclid
1510:
1452:
1264:
1249:
1228:
905:
850:and their relation to
777:Book 4 constructs the
703:
696:
618:Alfred North Whitehead
565:
494:
416:Papyrus Oxyrhynchus 29
319:
306:'s translation of the
290:
288:Chester Beatty Library
267:
18:Euclid's elements
5448:Mathematics textbooks
5106:Pappus's area theorem
5042:Theorem of the gnomon
4919:Quadratrix of Hippias
4842:Circles of Apollonius
4790:Problem of Apollonius
4768:Constructible numbers
4592:Archimedes Palimpsest
3914:Historical Archive –
2696:. Benjamin catalogue.
2407:
2032:2009, Irineu Bicudo (
1961:Vaticanus Graecus 190
1722:R. Catesby Taliaferro
1688:1826, George Phillips
1577:of the Greek text by
1516:
1475:
1453:
1255:
1243:
906:
864:least common multiple
701:
678:
668:In modern mathematics
640:wrote in her sonnet "
555:
488:
340:, collecting many of
301:
294:Basis in earlier work
274:Double-page from the
273:
258:
5438:3rd-century BC books
5322:prehistoric counting
5119:Ptolemy's inequality
5060:Apollonius's theorem
4899:Method of exhaustion
4869:Diophantine equation
4859:Circumscribed circle
4676:On the Moving Sphere
4093:Johan Ludvig Heiberg
3526:Nasir al-Din al-Tusi
2461:Van der Waerden 1975
2359:
1715:Johan Ludvig Heiberg
1679:1781, William Austin
1612:Johan Ludvig Heiberg
1382:
1273:constructive methods
951:method of exhaustion
891:
384:Theudius of Magnesia
370:) for book III, and
360:Hippocrates of Chios
5463:History of geometry
5408: •
5214:Neusis construction
5134:Spiral of Theodorus
5027:Pythagorean theorem
4972:Euclidean algorithm
4914:Lune of Hippocrates
4783:Squaring the circle
4539:Theon of Alexandria
4214:Aristaeus the Elder
4062:Euclidean algorithm
3661:Toussaint, Godfried
3379:Dodgson, Charles L.
3160:, pp. 460–461.
3076:, pp. 118–119.
2821:Grabiner., Judith.
2507:Unguru, S. (1985).
1803:Typographia Medicea
1796:Rodrigo de Zamorano
1781:de Béziers (French)
1735:Bartolomeo Zamberti
1711:Thomas Little Heath
1657:Charles Scarborough
1536:Theon of Alexandria
1519:Pythagorean theorem
1258:Pythagorean Theorum
977:
925:Pythagorean triples
871:geometric sequences
738:Pythagorean theorem
713:hyperbolic geometry
709:Nikolai Lobachevsky
651:The success of the
586:Nicolaus Copernicus
535:Thomas Little Heath
467:Herman of Carinthia
400:Theon of Alexandria
193:mathematical proofs
167:Greek mathematician
46:, 1570. During the
32:
5473:Geometry education
5443:Euclidean geometry
5101:Menelaus's theorem
5091:Irrational numbers
4904:Parallel postulate
4879:Euclidean geometry
4847:Apollonian circles
4389:Isidore of Miletus
4072:Euclidean relation
4057:Euclidean geometry
3897:Aethelhard of Bath
3765:by ratherthanpaper
3677:10.1007/BF03024252
3538:] (in Arabic).
2931:, Clark University
2864:Herschbach, Dudley
2543:2009-12-20 at the
2524:. Phonesis 43, 211
2520:Zhmud, L. (1998).
2402:
2328:Muslim-ruled Spain
1585:Pierre de Montdoré
1531:
1511:
1462:Isidore of Miletus
1448:
1269:axiomatic approach
1265:
1250:
972:
919:. He also gives a
917:irrational numbers
901:
856:Euclid's algorithm
734:parallel postulate
721:Euclidean geometry
704:
674:parallel postulate
566:
495:
479:Campanus of Novara
368:Hippocrates of Kos
320:
291:
276:Ishaq ibn Hunayn's
268:
265:Oxyrhynchus papyri
197:Euclidean geometry
5425:
5424:
5390:
5389:
5142:
5141:
5129:Ptolemy's theorem
5002:Intercept theorem
4852:Apollonian gasket
4778:Doubling the cube
4751:The Sand Reckoner
4145:
4144:
3893:Latin translation
3872:Project Gutenberg
3716:978-90-01-93102-5
3706:Science awakening
3652:978-605-312-329-3
3643:Euclid's Elements
3624:Euclid's Elements
3608:978-0-7923-4066-9
3580:978-1-135-69284-1
3565:Russell, Bertrand
3556:978-0-19-872145-1
3506:978-0-486-43231-1
3394:978-1-108-00100-7
3359:978-3-515-08645-5
3028:, pp. 12–23.
2959:, pp. 18–20.
2929:Euclid's Elements
2892:Prindle, Joseph.
2788:978-0-486-60088-8
2400:
2392:
1903:Jagannatha Samrat
1693:Dionysius Lardner
1630:Henry Billingsley
1606:Christoph Clavius
1496:Euclid's Elements
1443:
1442:
1436:
1416:
1415:
1409:
1215:
1214:
953:, a precursor to
899:
852:composite numbers
753:geometric algebra
717:elliptic geometry
508:Henry Billingsley
500:published in 1533
475:Gerard of Cremona
471:John of Tynemouth
458:to translate the
372:Eudoxus of Cnidus
135:
134:
16:(Redirected from
5480:
5416:
5415:
5403:
5402:
5401:
5177:
5164:Platonic Academy
5111:Problem II.8 of
5081:Crossbar theorem
5037:Thales's theorem
4977:Euclid's theorem
4947:
4864:Commensurability
4825:Axiomatic system
4773:Angle trisection
4738:
4728:
4690:
4680:
4670:
4660:
4636:
4626:
4609:
4172:
4165:
4158:
4149:
4135:
4134:
4067:Euclid's theorem
3992:
3985:
3978:
3969:
3859:Video adaptation
3841:(also hosted at
3794:
3792:
3791:
3748:
3729:
3720:
3696:
3656:
3631:
3629:
3612:
3584:
3560:
3539:
3521:
3510:
3491:Heath, Thomas L.
3485:
3470:Heath, Thomas L.
3465:
3450:Heath, Thomas L.
3445:
3430:Heath, Thomas L.
3425:
3406:(2nd ed.).
3398:
3374:
3363:
3342:
3333:
3321:
3307:
3276:
3275:
3242:
3236:
3227:
3221:
3215:
3209:
3203:
3197:
3191:
3190:
3188:
3186:
3167:
3161:
3155:
3149:
3143:
3137:
3136:
3134:
3133:
3119:
3113:
3112:
3110:
3109:
3095:
3089:
3083:
3077:
3071:
3065:
3059:
3053:
3047:
3041:
3035:
3029:
3023:
3017:
3011:
3005:
3003:
2985:
2979:
2969:
2960:
2954:
2948:
2942:
2933:
2932:
2920:
2914:
2913:
2911:
2909:
2889:
2883:
2881:
2879:
2872:
2860:
2854:
2849:
2843:
2837:
2831:
2830:
2818:
2812:
2811:
2799:
2793:
2792:
2774:
2768:
2767:
2756:
2750:
2744:
2738:
2737:
2731:
2723:
2721:
2719:
2704:
2698:
2697:
2695:
2684:
2678:
2672:
2666:
2665:
2617:
2611:
2610:
2582:
2576:
2566:
2560:
2554:
2548:
2531:
2525:
2518:
2512:
2505:
2499:
2489:
2483:
2473:
2464:
2458:
2452:
2446:
2435:
2429:
2413:
2411:
2409:
2408:
2403:
2401:
2393:
2388:
2371:
2363:
2345:
2339:
2323:
2317:
2295:
2289:
2270:
2264:
2250:
2244:
2238:
1957:François Peyrard
1780:
1749:Nicolo Tartaglia
1743:
1667:1714, W. Whiston
1651:William Hallifax
1593:
1508:
1507:
1503:
1457:
1455:
1454:
1449:
1444:
1438:
1437:
1432:
1423:
1422:
1417:
1414:
1410:
1405:
1387:
1386:
1344:W. W. Rouse Ball
1236:
978:
910:
908:
907:
902:
900:
895:
858:for finding the
787:regular polygons
622:Bertrand Russell
519:Bodleian Library
444:
404:François Peyrard
377:
365:
357:
313:
174:
157:
152:
151:
122:
116:Publication date
56:Euclid of Megara
54:the philosopher
40:
33:
21:
5488:
5487:
5483:
5482:
5481:
5479:
5478:
5477:
5458:Works by Euclid
5428:
5427:
5426:
5421:
5410:
5399:
5397:
5386:
5352:Arabian/Islamic
5340:
5329:numeral systems
5218:
5168:
5138:
5086:Heron's formula
5064:
5046:
4938:
4934:Triangle center
4924:Regular polygon
4801:and definitions
4800:
4794:
4756:
4736:
4726:
4688:
4678:
4668:
4658:
4634:
4624:
4607:
4573:
4544:Theon of Smyrna
4189:
4181:
4176:
4146:
4141:
4123:
4107:
4103:Isaac Todhunter
4076:
4040:
4001:
3996:
3884:Sir Thomas More
3789:
3787:
3782:
3763:with highlights
3756:
3751:
3745:
3733:Euklid (1999).
3732:
3723:
3717:
3699:
3659:
3653:
3634:
3627:
3615:
3609:
3587:
3581:
3563:
3557:
3542:
3524:
3513:
3507:
3489:
3468:
3448:
3428:
3422:
3401:
3395:
3377:
3366:
3360:
3345:
3336:
3330:
3310:
3296:
3254:
3250:
3245:
3237:
3230:
3222:
3218:
3210:
3206:
3198:
3194:
3184:
3182:
3181:on 22 June 2009
3169:
3168:
3164:
3156:
3152:
3144:
3140:
3131:
3129:
3121:
3120:
3116:
3107:
3105:
3097:
3096:
3092:
3084:
3080:
3072:
3068:
3060:
3056:
3048:
3044:
3036:
3032:
3024:
3020:
3012:
3008:
2991:
2986:
2982:
2970:
2963:
2957:Hartshorne 2000
2955:
2951:
2945:Hartshorne 2000
2943:
2936:
2922:
2921:
2917:
2907:
2905:
2891:
2890:
2886:
2877:
2870:
2862:
2861:
2857:
2850:
2846:
2838:
2834:
2820:
2819:
2815:
2801:
2800:
2796:
2789:
2776:
2775:
2771:
2758:
2757:
2753:
2745:
2741:
2724:
2717:
2715:
2706:
2705:
2701:
2693:
2686:
2685:
2681:
2673:
2669:
2619:
2618:
2614:
2584:
2583:
2579:
2567:
2563:
2555:
2551:
2545:Wayback Machine
2532:
2528:
2519:
2515:
2506:
2502:
2490:
2486:
2474:
2467:
2459:
2455:
2447:
2438:
2430:
2426:
2422:
2417:
2416:
2357:
2356:
2346:
2342:
2336:Adelard of Bath
2324:
2320:
2296:
2292:
2271:
2267:
2251:
2247:
2239:
2235:
2230:
2225:
2213:
2194:
2143:
2065:
2049:
2047:Book I Editions
1974:Vincenzo Flauti
1855:Pierre Hérigone
1774:
1772:Pierre Forcadel
1759:Johann Scheubel
1737:
1730:
1728:Other languages
1705:Isaac Todhunter
1625:
1620:
1587:
1574:editio princeps
1565:editio princeps
1470:
1424:
1391:
1380:
1379:
1352:
1324:
1262:Vatican Library
1238:
1230:
1225:
1220:
1122:Common Notions
966:Platonic solids
932:parallelepipeds
913:incommensurable
889:
888:
882:perfect numbers
772:Thales' theorem
729:
670:
629:Abraham Lincoln
598:Albert Einstein
594:Galileo Galilei
590:Johannes Kepler
550:
515:Vatican Library
455:Adelard of Bath
439:Harun al-Rashid
396:
304:Adelard of Bath
296:
263:on part of the
253:
205:incommensurable
117:
100:incommensurable
59:
28:
23:
22:
15:
12:
11:
5:
5486:
5484:
5476:
5475:
5470:
5465:
5460:
5455:
5450:
5445:
5440:
5430:
5429:
5423:
5422:
5395:
5392:
5391:
5388:
5387:
5385:
5384:
5379:
5374:
5369:
5364:
5359:
5354:
5348:
5346:
5345:Other cultures
5342:
5341:
5339:
5338:
5337:
5336:
5326:
5325:
5324:
5314:
5313:
5312:
5302:
5301:
5300:
5290:
5289:
5288:
5278:
5277:
5276:
5266:
5265:
5264:
5254:
5253:
5252:
5242:
5241:
5240:
5226:
5224:
5220:
5219:
5217:
5216:
5211:
5206:
5201:
5196:
5194:Greek numerals
5191:
5189:Attic numerals
5186:
5180:
5174:
5170:
5169:
5167:
5166:
5161:
5156:
5150:
5148:
5144:
5143:
5140:
5139:
5137:
5136:
5131:
5126:
5121:
5116:
5108:
5103:
5098:
5093:
5088:
5083:
5078:
5072:
5070:
5066:
5065:
5063:
5062:
5056:
5054:
5048:
5047:
5045:
5044:
5039:
5034:
5029:
5024:
5019:
5017:Law of cosines
5014:
5009:
5004:
4999:
4994:
4989:
4984:
4979:
4974:
4969:
4964:
4958:
4956:
4944:
4940:
4939:
4937:
4936:
4931:
4926:
4921:
4916:
4911:
4909:Platonic solid
4906:
4901:
4896:
4891:
4889:Greek numerals
4886:
4881:
4876:
4871:
4866:
4861:
4856:
4855:
4854:
4849:
4839:
4834:
4833:
4832:
4822:
4821:
4820:
4815:
4804:
4802:
4796:
4795:
4793:
4792:
4787:
4786:
4785:
4780:
4775:
4764:
4762:
4758:
4757:
4755:
4754:
4747:
4740:
4730:
4720:
4717:Planisphaerium
4713:
4706:
4699:
4692:
4682:
4672:
4662:
4652:
4645:
4638:
4628:
4618:
4611:
4601:
4594:
4589:
4581:
4579:
4575:
4574:
4572:
4571:
4566:
4561:
4556:
4551:
4546:
4541:
4536:
4531:
4526:
4521:
4516:
4511:
4506:
4501:
4496:
4491:
4486:
4481:
4476:
4471:
4466:
4461:
4456:
4451:
4446:
4441:
4436:
4431:
4426:
4421:
4416:
4411:
4406:
4401:
4396:
4391:
4386:
4381:
4376:
4371:
4366:
4361:
4356:
4351:
4346:
4341:
4336:
4331:
4326:
4321:
4316:
4311:
4306:
4301:
4296:
4291:
4286:
4281:
4276:
4271:
4266:
4261:
4256:
4251:
4246:
4241:
4236:
4231:
4226:
4221:
4216:
4211:
4206:
4201:
4195:
4193:
4187:Mathematicians
4183:
4182:
4177:
4175:
4174:
4167:
4160:
4152:
4143:
4142:
4140:
4139:
4128:
4125:
4124:
4122:
4121:
4115:
4113:
4109:
4108:
4106:
4105:
4100:
4095:
4090:
4084:
4082:
4078:
4077:
4075:
4074:
4069:
4064:
4059:
4054:
4048:
4046:
4042:
4041:
4039:
4038:
4031:
4024:
4017:
4009:
4007:
4003:
4002:
3997:
3995:
3994:
3987:
3980:
3972:
3966:
3965:
3949:
3936:
3922:
3909:
3899:
3890:
3881:
3878:Reading Euclid
3875:
3862:
3856:
3850:
3836:
3835:
3834:
3810:
3807:979-8589564587
3796:
3780:
3771:
3766:
3755:
3754:External links
3752:
3750:
3749:
3743:
3730:
3721:
3715:
3697:
3657:
3651:
3632:
3613:
3607:
3593:Selin, Helaine
3585:
3579:
3561:
3555:
3540:
3522:
3511:
3505:
3487:
3466:
3446:
3426:
3420:
3399:
3393:
3375:
3364:
3358:
3343:
3334:
3328:
3312:Boyer, Carl B.
3308:
3294:
3280:Artmann, Benno
3277:
3266:(1): 163–167,
3262:, New Series,
3251:
3249:
3246:
3244:
3243:
3228:
3216:
3204:
3192:
3162:
3150:
3138:
3114:
3090:
3078:
3066:
3064:, p. 249.
3054:
3052:, p. 242.
3042:
3030:
3026:Toussaint 1993
3018:
3016:, p. 216.
3006:
2980:
2961:
2949:
2934:
2915:
2884:
2880:on 2009-02-26.
2855:
2844:
2832:
2813:
2794:
2787:
2769:
2751:
2739:
2713:digi.vatlib.it
2699:
2679:
2667:
2632:(3): 293–330.
2612:
2599:10.2307/310767
2577:
2561:
2549:
2526:
2513:
2500:
2484:
2465:
2463:, p. 197.
2453:
2451:, p. 177.
2436:
2434:, p. 100.
2423:
2421:
2418:
2415:
2414:
2399:
2396:
2391:
2386:
2383:
2380:
2377:
2374:
2370:
2366:
2340:
2318:
2290:
2265:
2245:
2232:
2231:
2229:
2226:
2224:
2221:
2220:
2219:
2212:
2209:
2208:
2207:
2201:
2193:
2190:
2189:
2188:
2172:
2169:978-1528770439
2158:
2142:
2139:
2138:
2137:
2135:978-1977730039
2124:
2094:
2080:
2064:
2061:
2060:
2059:
2056:
2053:
2048:
2045:
2044:
2043:
2040:
2037:
2030:
2027:
2024:
2021:
2018:
2015:
2008:
2005:
2002:Sámuel Brassai
1998:
1995:
1992:
1989:
1986:
1983:
1980:
1977:
1970:
1967:
1964:
1953:
1950:
1947:
1940:
1937:
1934:
1931:
1928:
1925:
1922:
1919:
1916:Mårten Strömer
1912:
1909:
1906:
1899:
1896:
1893:
1886:
1883:
1880:
1877:
1874:
1871:
1864:
1861:
1858:
1851:
1848:
1845:
1838:
1835:Pietro Cataldi
1831:
1820:
1817:
1810:
1799:
1792:
1789:
1782:
1768:
1765:
1762:
1755:
1752:
1745:
1729:
1726:
1725:
1724:
1718:
1707:
1701:
1695:
1689:
1686:
1680:
1677:
1674:
1668:
1665:
1659:
1653:
1647:
1644:
1638:
1632:
1624:
1621:
1619:
1616:
1615:
1614:
1608:
1602:
1595:
1581:
1569:
1560:Erhard Ratdolt
1556:
1549:
1546:
1539:
1469:
1466:
1447:
1441:
1435:
1430:
1427:
1420:
1413:
1408:
1403:
1400:
1397:
1394:
1390:
1351:
1348:
1323:
1320:
1221:
1219:
1216:
1213:
1212:
1209:
1206:
1203:
1200:
1197:
1194:
1191:
1188:
1185:
1182:
1179:
1176:
1173:
1170:
1166:
1165:
1162:
1159:
1156:
1153:
1150:
1147:
1144:
1141:
1138:
1135:
1132:
1129:
1126:
1123:
1119:
1118:
1115:
1112:
1109:
1106:
1103:
1100:
1097:
1094:
1091:
1088:
1085:
1082:
1079:
1076:
1072:
1071:
1068:
1065:
1062:
1059:
1056:
1053:
1050:
1047:
1044:
1041:
1038:
1035:
1032:
1029:
1025:
1024:
1021:
1018:
1015:
1012:
1009:
1006:
1003:
1000:
997:
994:
991:
988:
985:
982:
970:
969:
962:
935:
928:
898:
885:
874:
867:
862:, finding the
840:
833:
790:
775:
760:
745:
728:
725:
669:
666:
614:Baruch Spinoza
562:Erhard Ratdolt
549:
546:
395:
392:
295:
292:
252:
249:
133:
132:
129:
125:
124:
118:
115:
112:
111:
108:
104:
103:
92:solid geometry
85:
81:
80:
75:
71:
70:
65:
61:
60:
41:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
5485:
5474:
5471:
5469:
5466:
5464:
5461:
5459:
5456:
5454:
5451:
5449:
5446:
5444:
5441:
5439:
5436:
5435:
5433:
5420:
5419:
5414:
5407:
5406:
5393:
5383:
5380:
5378:
5375:
5373:
5370:
5368:
5365:
5363:
5360:
5358:
5355:
5353:
5350:
5349:
5347:
5343:
5335:
5332:
5331:
5330:
5327:
5323:
5320:
5319:
5318:
5315:
5311:
5308:
5307:
5306:
5303:
5299:
5296:
5295:
5294:
5291:
5287:
5284:
5283:
5282:
5279:
5275:
5272:
5271:
5270:
5267:
5263:
5260:
5259:
5258:
5255:
5251:
5248:
5247:
5246:
5243:
5239:
5235:
5234:
5233:
5232:
5228:
5227:
5225:
5221:
5215:
5212:
5210:
5207:
5205:
5202:
5200:
5197:
5195:
5192:
5190:
5187:
5185:
5182:
5181:
5178:
5175:
5171:
5165:
5162:
5160:
5157:
5155:
5152:
5151:
5149:
5145:
5135:
5132:
5130:
5127:
5125:
5122:
5120:
5117:
5115:
5114:
5109:
5107:
5104:
5102:
5099:
5097:
5094:
5092:
5089:
5087:
5084:
5082:
5079:
5077:
5074:
5073:
5071:
5067:
5061:
5058:
5057:
5055:
5053:
5049:
5043:
5040:
5038:
5035:
5033:
5030:
5028:
5025:
5023:
5022:Pons asinorum
5020:
5018:
5015:
5013:
5010:
5008:
5005:
5003:
5000:
4998:
4995:
4993:
4992:Hinge theorem
4990:
4988:
4985:
4983:
4980:
4978:
4975:
4973:
4970:
4968:
4965:
4963:
4960:
4959:
4957:
4955:
4954:
4948:
4945:
4941:
4935:
4932:
4930:
4927:
4925:
4922:
4920:
4917:
4915:
4912:
4910:
4907:
4905:
4902:
4900:
4897:
4895:
4892:
4890:
4887:
4885:
4882:
4880:
4877:
4875:
4872:
4870:
4867:
4865:
4862:
4860:
4857:
4853:
4850:
4848:
4845:
4844:
4843:
4840:
4838:
4835:
4831:
4828:
4827:
4826:
4823:
4819:
4816:
4814:
4811:
4810:
4809:
4806:
4805:
4803:
4797:
4791:
4788:
4784:
4781:
4779:
4776:
4774:
4771:
4770:
4769:
4766:
4765:
4763:
4759:
4753:
4752:
4748:
4746:
4745:
4741:
4739:
4735:
4731:
4729:
4725:
4721:
4719:
4718:
4714:
4712:
4711:
4707:
4705:
4704:
4700:
4698:
4697:
4693:
4691:
4687:
4683:
4681:
4677:
4673:
4671:
4667:
4663:
4661:
4659:(Aristarchus)
4657:
4653:
4651:
4650:
4646:
4644:
4643:
4639:
4637:
4633:
4629:
4627:
4623:
4619:
4617:
4616:
4612:
4610:
4606:
4602:
4600:
4599:
4595:
4593:
4590:
4588:
4587:
4583:
4582:
4580:
4576:
4570:
4567:
4565:
4564:Zeno of Sidon
4562:
4560:
4557:
4555:
4552:
4550:
4547:
4545:
4542:
4540:
4537:
4535:
4532:
4530:
4527:
4525:
4522:
4520:
4517:
4515:
4512:
4510:
4507:
4505:
4502:
4500:
4497:
4495:
4492:
4490:
4487:
4485:
4482:
4480:
4477:
4475:
4472:
4470:
4467:
4465:
4462:
4460:
4457:
4455:
4452:
4450:
4447:
4445:
4442:
4440:
4437:
4435:
4432:
4430:
4427:
4425:
4422:
4420:
4417:
4415:
4412:
4410:
4407:
4405:
4402:
4400:
4397:
4395:
4392:
4390:
4387:
4385:
4382:
4380:
4377:
4375:
4372:
4370:
4367:
4365:
4362:
4360:
4357:
4355:
4352:
4350:
4347:
4345:
4342:
4340:
4337:
4335:
4332:
4330:
4327:
4325:
4322:
4320:
4317:
4315:
4312:
4310:
4307:
4305:
4302:
4300:
4297:
4295:
4292:
4290:
4287:
4285:
4282:
4280:
4277:
4275:
4272:
4270:
4267:
4265:
4262:
4260:
4257:
4255:
4252:
4250:
4247:
4245:
4242:
4240:
4237:
4235:
4232:
4230:
4227:
4225:
4222:
4220:
4217:
4215:
4212:
4210:
4207:
4205:
4202:
4200:
4197:
4196:
4194:
4192:
4188:
4184:
4180:
4173:
4168:
4166:
4161:
4159:
4154:
4153:
4150:
4138:
4130:
4129:
4126:
4120:
4117:
4116:
4114:
4110:
4104:
4101:
4099:
4098:Robert Simson
4096:
4094:
4091:
4089:
4086:
4085:
4083:
4079:
4073:
4070:
4068:
4065:
4063:
4060:
4058:
4055:
4053:
4050:
4049:
4047:
4043:
4037:
4036:
4032:
4030:
4029:
4025:
4023:
4022:
4018:
4016:
4015:
4011:
4010:
4008:
4004:
4000:
3993:
3988:
3986:
3981:
3979:
3974:
3973:
3970:
3963:
3959:
3958:
3953:
3950:
3948:
3944:
3942:
3937:
3934:
3930:
3926:
3923:
3920:
3919:
3913:
3910:
3907:
3905:
3900:
3898:
3894:
3891:
3889:
3885:
3882:
3879:
3876:
3873:
3869:
3868:
3863:
3860:
3857:
3854:
3851:
3848:
3844:
3840:
3837:
3833:
3829:
3825:
3821:
3817:
3816:
3814:
3811:
3808:
3804:
3800:
3797:
3786:
3781:
3779:
3777:
3772:
3770:
3767:
3764:
3762:
3758:
3757:
3753:
3746:
3744:953-96477-6-2
3740:
3736:
3735:Elementi I-VI
3731:
3727:
3722:
3718:
3712:
3708:
3707:
3702:
3698:
3694:
3690:
3686:
3682:
3678:
3674:
3670:
3666:
3662:
3658:
3654:
3648:
3644:
3640:
3639:
3633:
3625:
3621:
3620:
3614:
3610:
3604:
3600:
3599:
3594:
3590:
3586:
3582:
3576:
3573:. Routledge.
3572:
3571:
3566:
3562:
3558:
3552:
3548:
3547:
3541:
3537:
3533:
3532:
3527:
3523:
3519:
3518:
3512:
3508:
3502:
3498:
3497:
3492:
3488:
3483:
3479:
3475:
3471:
3467:
3463:
3459:
3455:
3451:
3447:
3443:
3439:
3435:
3431:
3427:
3423:
3421:9780387986500
3417:
3413:
3409:
3405:
3400:
3396:
3390:
3386:
3385:
3380:
3376:
3372:
3371:
3365:
3361:
3355:
3351:
3350:
3344:
3340:
3335:
3331:
3329:0-471-54397-7
3325:
3320:
3319:
3313:
3309:
3305:
3304:
3299:
3295:
3293:
3292:0-387-98423-2
3289:
3285:
3281:
3278:
3274:
3269:
3265:
3261:
3257:
3253:
3252:
3247:
3240:
3235:
3233:
3229:
3225:
3220:
3217:
3213:
3208:
3205:
3201:
3196:
3193:
3180:
3176:
3172:
3166:
3163:
3159:
3154:
3151:
3147:
3142:
3139:
3128:
3124:
3118:
3115:
3104:
3100:
3094:
3091:
3087:
3082:
3079:
3075:
3070:
3067:
3063:
3058:
3055:
3051:
3046:
3043:
3040:, p. 62.
3039:
3034:
3031:
3027:
3022:
3019:
3015:
3010:
3007:
3002:
2998:
2994:
2989:
2984:
2981:
2977:
2973:
2968:
2966:
2962:
2958:
2953:
2950:
2947:, p. 18.
2946:
2941:
2939:
2935:
2930:
2926:
2919:
2916:
2903:
2899:
2895:
2888:
2885:
2876:
2869:
2865:
2859:
2856:
2853:
2848:
2845:
2841:
2836:
2833:
2828:
2827:Plus Magazine
2824:
2817:
2814:
2809:
2805:
2798:
2795:
2790:
2784:
2780:
2773:
2770:
2765:
2761:
2755:
2752:
2748:
2743:
2740:
2735:
2729:
2714:
2710:
2703:
2700:
2692:
2691:
2683:
2680:
2676:
2671:
2668:
2663:
2659:
2655:
2651:
2647:
2643:
2639:
2635:
2631:
2627:
2623:
2616:
2613:
2608:
2604:
2600:
2596:
2592:
2588:
2581:
2578:
2574:
2570:
2565:
2562:
2559:, p. 57.
2558:
2553:
2550:
2546:
2542:
2539:
2535:
2530:
2527:
2523:
2517:
2514:
2510:
2504:
2501:
2497:
2493:
2488:
2485:
2481:
2477:
2472:
2470:
2466:
2462:
2457:
2454:
2450:
2445:
2443:
2441:
2437:
2433:
2428:
2425:
2419:
2389:
2384:
2381:
2375:
2368:
2364:
2353:
2349:
2344:
2341:
2337:
2333:
2329:
2322:
2319:
2315:
2311:
2307:
2303:
2299:
2294:
2291:
2287:
2282:
2278:
2274:
2269:
2266:
2263:) of Euclid".
2262:
2258:
2254:
2249:
2246:
2242:
2237:
2234:
2227:
2222:
2218:
2217:Bride's Chair
2215:
2214:
2210:
2205:
2202:
2199:
2196:
2195:
2192:Free versions
2191:
2186:
2182:
2178:
2177:
2173:
2170:
2166:
2162:
2159:
2156:
2152:
2148:
2145:
2144:
2136:
2132:
2128:
2125:
2122:
2121:0-486-60090-4
2118:
2114:
2113:0-486-60089-0
2110:
2106:
2105:0-486-60088-2
2102:
2098:
2095:
2092:
2091:0-7607-6312-7
2088:
2084:
2081:
2078:
2077:1-888009-18-7
2074:
2070:
2067:
2066:
2062:
2057:
2054:
2051:
2050:
2046:
2041:
2038:
2035:
2031:
2028:
2025:
2022:
2019:
2016:
2013:
2009:
2006:
2003:
1999:
1996:
1993:
1990:
1987:
1984:
1981:
1978:
1975:
1971:
1968:
1965:
1962:
1958:
1954:
1951:
1948:
1945:
1941:
1938:
1935:
1932:
1929:
1926:
1923:
1920:
1917:
1913:
1910:
1907:
1904:
1900:
1897:
1894:
1891:
1890:Samuel Reyher
1887:
1884:
1881:
1878:
1875:
1872:
1869:
1865:
1862:
1859:
1856:
1852:
1849:
1846:
1843:
1842:Denis Henrion
1839:
1836:
1832:
1829:
1825:
1821:
1818:
1815:
1811:
1808:
1804:
1800:
1797:
1793:
1790:
1787:
1783:
1778:
1773:
1769:
1766:
1763:
1760:
1756:
1753:
1750:
1746:
1741:
1736:
1732:
1731:
1727:
1723:
1719:
1716:
1712:
1708:
1706:
1702:
1700:
1696:
1694:
1690:
1687:
1685:
1684:John Playfair
1681:
1678:
1675:
1673:
1672:Robert Simson
1669:
1666:
1664:
1660:
1658:
1654:
1652:
1648:
1645:
1643:
1639:
1637:
1633:
1631:
1627:
1626:
1622:
1617:
1613:
1609:
1607:
1603:
1601:Latin edition
1600:
1596:
1591:
1586:
1582:
1580:
1579:Simon Grynäus
1576:
1575:
1570:
1567:
1566:
1561:
1557:
1554:
1553:Regiomontanus
1550:
1547:
1545:Vat. gr. 190
1544:
1540:
1537:
1534:4th century,
1533:
1532:
1528:
1524:
1520:
1517:Proof of the
1515:
1502:
1497:
1493:
1489:
1485:
1482:
1479:
1474:
1467:
1465:
1463:
1458:
1445:
1439:
1433:
1428:
1425:
1418:
1406:
1401:
1398:
1392:
1388:
1377:
1373:
1369:
1365:
1361:
1357:
1349:
1347:
1345:
1340:
1338:
1332:
1329:
1321:
1319:
1317:
1313:
1312:
1306:
1302:
1300:
1294:
1292:
1288:
1283:
1281:
1276:
1274:
1270:
1263:
1259:
1254:
1247:
1242:
1237:
1234:
1227:
1210:
1207:
1204:
1201:
1198:
1195:
1192:
1189:
1186:
1183:
1180:
1177:
1174:
1171:
1169:Propositions
1168:
1167:
1163:
1160:
1157:
1154:
1151:
1148:
1145:
1142:
1139:
1136:
1133:
1130:
1127:
1124:
1121:
1120:
1116:
1113:
1110:
1107:
1104:
1101:
1098:
1095:
1092:
1089:
1086:
1083:
1080:
1077:
1074:
1073:
1069:
1066:
1063:
1060:
1057:
1054:
1051:
1048:
1045:
1042:
1039:
1036:
1033:
1030:
1027:
1026:
1022:
1019:
1016:
1013:
1010:
1007:
1004:
1001:
998:
995:
992:
989:
986:
983:
980:
979:
976:
967:
963:
960:
956:
952:
948:
944:
940:
936:
933:
929:
926:
922:
918:
914:
896:
886:
883:
879:
875:
872:
868:
865:
861:
857:
853:
849:
848:prime numbers
845:
841:
838:
834:
831:
827:
823:
819:
815:
811:
807:
803:
799:
795:
791:
788:
784:
780:
776:
773:
769:
765:
761:
758:
754:
750:
746:
743:
739:
735:
731:
730:
726:
724:
722:
718:
714:
710:
700:
695:
694:
692:
688:
684:
677:
675:
667:
665:
663:
659:
654:
649:
647:
643:
639:
635:
630:
625:
623:
619:
615:
611:
610:Thomas Hobbes
607:
603:
599:
595:
591:
587:
584:. Scientists
583:
579:
575:
571:
563:
560:, printed by
559:
554:
547:
545:
543:
538:
536:
532:
531:J. L. Heiberg
528:
523:
520:
516:
511:
509:
505:
501:
492:
487:
483:
480:
476:
472:
468:
463:
461:
456:
452:
448:
440:
436:
432:
428:
424:
419:
417:
413:
409:
405:
401:
393:
391:
389:
385:
381:
373:
369:
361:
353:
349:
347:
343:
339:
335:
331:
327:
325:
317:
309:
305:
300:
293:
289:
285:
281:
277:
272:
266:
262:
257:
250:
248:
245:
241:
237:
233:
229:
225:
220:
218:
214:
210:
206:
202:
201:number theory
199:, elementary
198:
194:
190:
189:constructions
186:
182:
178:
171:
168:
164:
161:
156:
146:
142:
141:
130:
126:
119:
113:
109:
105:
101:
97:
96:number theory
93:
89:
86:
82:
79:
78:Ancient Greek
76:
72:
69:
66:
62:
57:
53:
50:, Euclid was
49:
45:
39:
34:
19:
5409:
5396:
5238:Thomas Heath
5229:
5112:
5096:Law of sines
4952:
4884:Golden ratio
4749:
4742:
4733:
4727:(Theodosius)
4723:
4715:
4708:
4701:
4694:
4685:
4675:
4669:(Hipparchus)
4665:
4655:
4647:
4640:
4631:
4630:
4621:
4613:
4608:(Apollonius)
4604:
4596:
4584:
4559:Zeno of Elea
4319:Eratosthenes
4309:Dionysodorus
4088:Thomas Heath
4033:
4026:
4020:
4019:
4012:
3962:Siku Quanshu
3961:
3955:
3946:
3940:
3928:
3917:
3903:
3866:
3847:Oliver Byrne
3788:. Retrieved
3775:
3760:
3734:
3728:. Routledge.
3725:
3705:
3671:(3): 12–24.
3668:
3664:
3642:
3637:
3623:
3618:
3601:. Springer.
3597:
3569:
3545:
3535:
3530:
3516:
3495:
3473:
3453:
3433:
3408:New York, NY
3403:
3383:
3369:
3348:
3338:
3317:
3302:
3283:
3263:
3259:
3219:
3207:
3195:
3183:. Retrieved
3179:the original
3174:
3165:
3153:
3141:
3130:. Retrieved
3126:
3117:
3106:. Retrieved
3102:
3093:
3081:
3069:
3057:
3045:
3033:
3021:
3009:
2983:
2952:
2928:
2918:
2906:. Retrieved
2897:
2887:
2875:the original
2858:
2847:
2840:Ketcham 1901
2835:
2826:
2816:
2807:
2797:
2778:
2772:
2763:
2754:
2749:, p. 1.
2742:
2716:. Retrieved
2712:
2709:"DigiVatLib"
2702:
2689:
2682:
2670:
2629:
2625:
2615:
2590:
2586:
2580:
2564:
2552:
2529:
2516:
2503:
2487:
2456:
2449:Russell 2013
2427:
2351:
2343:
2335:
2331:
2321:
2313:
2309:
2305:
2301:
2293:
2285:
2280:
2276:
2268:
2260:
2256:
2248:
2236:
2203:
2197:
2180:
2175:
2160:
2146:
2126:
2096:
2082:
2068:
1960:
1824:Matteo Ricci
1806:
1642:Isaac Barrow
1618:Translations
1572:
1563:
1555:(incomplete)
1526:
1501:Jīhé yuánběn
1495:
1484:Matteo Ricci
1459:
1372:dodecahedron
1359:
1353:
1341:
1333:
1327:
1325:
1315:
1309:
1307:
1303:
1295:
1284:
1277:
1266:
1245:
1232:
1231:Euclid,
1229:
1223:
1028:Definitions
974:
873:of integers.
844:divisibility
829:
825:
821:
817:
813:
809:
805:
801:
783:circumcircle
757:golden ratio
705:
691:right angles
683:line segment
680:
679:
671:
661:
657:
652:
650:
645:
626:
605:
602:Isaac Newton
569:
567:
557:
539:
526:
524:
512:
496:
490:
464:
450:
430:
420:
397:
379:
350:
337:
333:
328:
323:
321:
315:
307:
279:
260:
243:
223:
221:
208:
181:propositions
160:mathematical
139:
138:
136:
43:
5305:mathematics
5113:Arithmetica
4710:Ostomachion
4679:(Autolycus)
4598:Arithmetica
4374:Hippocrates
4304:Dinostratus
4289:Dicaearchus
4219:Aristarchus
3843:archive.org
3832:vol. 3 c. 2
3630:(in Czech).
3589:Sarma, K.V.
3224:Sertöz 2019
3212:Euklid 1999
3200:Servít 1907
3062:Heath 1956a
3050:Heath 1956a
3038:Heath 1956a
2747:Busard 2005
2718:20 November
2675:Busard 2005
2593:: 249–302.
2573:p. 165
2547:of one page
2241:Wilson 2006
2185:Kickstarter
2004:(Hungarian)
1814:Jean Errard
1786:Commandinus
1775: [
1770:1564–1566,
1738: [
1636:Thomas Rudd
1610:1883–1888,
1599:Commandinus
1588: [
1494:edition of
1376:icosahedron
1075:Postulates
955:integration
923:to produce
634:Springfield
578:mathematics
215:and modern
110:Mathematics
48:Renaissance
5432:Categories
5357:Babylonian
5257:arithmetic
5223:History of
5052:Apollonius
4737:(Menelaus)
4696:On Spirals
4615:Catoptrics
4554:Xenocrates
4549:Thymaridas
4534:Theodosius
4519:Theaetetus
4499:Simplicius
4489:Pythagoras
4474:Posidonius
4459:Philonides
4419:Nicomachus
4414:Metrodorus
4404:Menaechmus
4359:Hipparchus
4349:Heliodorus
4299:Diophantus
4284:Democritus
4264:Chrysippus
4234:Archimedes
4229:Apollonius
4199:Anaxagoras
4191:(timeline)
4035:Phaenomena
3908:Greek HTML
3888:manuscript
3790:2006-08-30
3785:"Elements"
3175:huji.ac.il
3158:Sarma 1997
3132:2023-07-28
3108:2023-07-28
3074:Boyer 1991
3014:Heath 1963
2976:p. 55
2496:p. 38
2480:p. 54
2432:Boyer 1991
2348:Boyer 1991
2273:Boyer 1991
2253:Boyer 1991
2223:References
2155:3836517752
2115:(vol. 2),
2107:(vol. 1),
2034:Portuguese
1828:Xu Guangqi
1717:'s edition
1663:John Keill
1568:(in Latin)
1562:(Venice),
1509:) in 1607.
1488:Xu Guangqi
1368:Apollonius
1356:apocryphal
794:magnitudes
352:Pythagoras
346:Theaetetus
240:quadrivium
177:postulates
4818:Inscribed
4578:Treatises
4569:Zenodorus
4529:Theodorus
4504:Sosigenes
4449:Philolaus
4434:Oenopides
4429:Nicoteles
4424:Nicomedes
4384:Hypsicles
4279:Ctesibius
4269:Cleomedes
4254:Callippus
4239:Autolycus
4224:Aristotle
4204:Anthemius
4052:Namesakes
3939:Euclid's
3685:0343-6993
3482:929205858
3472:(1956c).
3452:(1956b).
3442:22193354M
3432:(1956a).
3300:(1915) .
2988:Ball 1915
2972:Ball 1915
2808:The Verge
2662:144172844
2646:0007-0874
2569:Ball 1915
2492:Ball 1915
2476:Ball 1915
2420:Citations
2385:−
2014:(Russian)
1976:(Italian)
1918:(Swedish)
1837:(Italian)
1830:(Chinese)
1798:(Spanish)
1751:(Italian)
1402:−
1364:Hypsicles
1350:Apocrypha
1337:congruent
1322:Criticism
1267:Euclid's
947:cylinders
824: ::
808: ::
764:inscribed
548:Influence
222:Euclid's
155:Stoikheîa
31:Elements
5382:Japanese
5367:Egyptian
5310:timeline
5298:timeline
5286:timeline
5281:geometry
5274:timeline
5269:calculus
5262:timeline
5250:timeline
4953:Elements
4799:Concepts
4761:Problems
4734:Spherics
4724:Spherics
4689:(Euclid)
4635:(Euclid)
4632:Elements
4625:(Euclid)
4586:Almagest
4494:Serenus
4469:Porphyry
4409:Menelaus
4364:Hippasus
4339:Eutocius
4314:Domninus
4209:Archytas
4137:Category
4081:Scholars
4021:Elements
3947:Elements
3941:Elements
3929:Elements
3918:Elements
3904:Elements
3867:Elements
3776:Elementa
3761:Elements
3703:(1975).
3693:26811463
3591:(1997).
3567:(2013).
3528:(1594).
3493:(1963).
3462:7650092M
3412:Springer
3341:. Dover.
3185:29 April
3088:, p. 163
2908:29 April
2902:Archived
2728:cite web
2541:Archived
2352:Elements
2310:Elements
2306:Elements
2302:Elements
2286:Elements
2281:Elements
2277:Elements
2261:Stoichia
2257:Elements
2211:See also
2181:Elements
2123:(vol. 3)
1946:(Hebrew)
1892:(German)
1870:(French)
1857:(French)
1844:(French)
1761:(German)
1468:Editions
1360:Elements
1328:Elements
1316:Elements
1246:Elements
1233:Elements
975:Elements
943:pyramids
839:figures.
828: :
820: :
812: :
804: :
779:incircle
768:tangents
766:angles,
727:Contents
662:Elements
658:Elements
653:Elements
646:Elements
606:Elements
600:and Sir
570:Elements
558:Elements
533:and Sir
527:Elements
517:and the
504:John Dee
491:Elements
460:Almagest
451:Elements
431:Elements
427:Boethius
380:Elements
338:Elements
334:Elements
324:Elements
316:Elements
308:Elements
286:, 1270.
280:Elements
261:Elements
244:Elements
228:textbook
224:Elements
209:Elements
185:theorems
163:treatise
150:Στοιχεῖα
140:Elements
131:13 books
74:Language
44:Elements
5362:Chinese
5317:numbers
5245:algebra
5173:Related
5147:Centers
4943:Results
4813:Central
4484:Ptolemy
4479:Proclus
4444:Perseus
4399:Marinus
4379:Hypatia
4369:Hippias
4344:Geminus
4334:Eudoxus
4324:Eudemus
4294:Diocles
4112:Related
3902:Euclid
3595:(ed.).
3248:Sources
2764:maa.org
2654:4026757
1901:1720s,
1788:(Latin)
1744:(Latin)
1623:English
1551:1460s,
1543:Peyrard
1492:Chinese
1478:Italian
1023:Totals
921:formula
837:similar
816:, then
798:Eudoxus
582:science
564:in 1482
542:scholia
447:Arethas
412:Heiberg
408:Vatican
342:Eudoxus
330:Proclus
251:History
217:science
207:lines.
191:), and
158:) is a
84:Subject
5377:Indian
5154:Cyrene
4686:Optics
4605:Conics
4524:Theano
4514:Thales
4509:Sporus
4454:Philon
4439:Pappus
4329:Euclid
4259:Carpus
4249:Bryson
4045:Topics
4028:Optics
3999:Euclid
3828:vol. 3
3824:vol. 2
3820:vol. 1
3805:
3741:
3713:
3691:
3683:
3649:
3626:]
3605:
3577:
3553:
3503:
3480:
3460:
3440:
3418:
3391:
3356:
3326:
3290:
2993:pp. 54
2785:
2660:
2652:
2644:
2607:310767
2605:
2167:
2153:
2133:
2119:
2111:
2103:
2089:
2075:
2010:1880,
2000:1865,
1972:1818,
1955:1804,
1942:1780,
1914:1744,
1888:1697,
1866:1672,
1853:1639,
1840:1615,
1833:1613,
1822:1607,
1812:1604,
1801:1594,
1794:1576,
1784:1572,
1757:1558,
1747:1543,
1733:1505,
1720:1939,
1709:1908,
1703:1862,
1697:1833,
1691:1828,
1682:1795,
1670:1756,
1661:1708,
1655:1705,
1649:1685,
1640:1660,
1634:1651,
1628:1570,
1604:1574,
1597:1572,
1571:1533,
1558:1482,
1481:Jesuit
959:sphere
945:, and
749:lemmas
620:, and
437:under
435:Arabic
423:Cicero
203:, and
170:Euclid
123:300 BC
68:Euclid
64:Author
5372:Incan
5293:logic
5069:Other
4837:Chord
4830:Axiom
4808:Angle
4464:Plato
4354:Heron
4274:Conon
4006:Works
3960:, or
3943:Redux
3689:S2CID
3641:[
3628:(PDF)
3622:[
3534:[
2878:(PDF)
2871:(PDF)
2694:(PDF)
2658:S2CID
2650:JSTOR
2603:JSTOR
2538:image
2536:; an
2314:Bible
2228:Notes
1779:]
1742:]
1592:]
1523:Byrne
1291:Theon
1287:proof
1020:XIII
1005:VIII
981:Book
939:cones
742:areas
687:lines
681:If a
574:logic
236:Bible
213:logic
145:Greek
128:Pages
107:Genre
102:lines
88:plane
5334:list
4622:Data
4394:Leon
4244:Bion
4014:Data
3803:ISBN
3739:ISBN
3711:ISBN
3681:ISSN
3647:ISBN
3603:ISBN
3575:ISBN
3551:ISBN
3501:ISBN
3478:OCLC
3416:ISBN
3389:ISBN
3354:ISBN
3324:ISBN
3288:ISBN
3187:2018
2910:2018
2783:ISBN
2734:link
2720:2023
2642:ISSN
2165:ISBN
2151:ISBN
2131:ISBN
2117:ISBN
2109:ISBN
2101:ISBN
2087:ISBN
2073:ISBN
1506:幾何原本
1476:The
1374:and
1311:Data
1271:and
1211:465
1070:131
1017:XII
1002:VII
990:III
781:and
568:The
388:Leon
284:Iraq
187:and
137:The
90:and
5236:by
4950:In
3895:by
3886:'s
3673:doi
3268:doi
3001:127
2634:doi
2595:doi
1525:'s
1521:in
1199:115
1014:XI
1008:IX
999:VI
993:IV
987:II
576:to
5434::
3830:,
3826:,
3822:,
3687:.
3679:.
3669:15
3667:.
3458:OL
3438:OL
3414:.
3410::
3282::
3264:49
3231:^
3173:.
3125:.
3101:.
2999:,
2997:58
2995:,
2990:,
2974:,
2964:^
2937:^
2927:,
2900:.
2896:.
2866:.
2825:.
2806:.
2762:.
2730:}}
2726:{{
2711:.
2656:.
2648:.
2640:.
2630:23
2628:.
2624:.
2601:.
2591:71
2589:.
2571:,
2494:,
2478:,
2468:^
2439:^
2365:10
2288:".
1826:,
1777:fr
1740:de
1590:fr
1389:10
1301:.
1208:18
1205:18
1202:39
1196:36
1193:27
1190:39
1187:33
1184:25
1181:16
1178:37
1175:14
1172:48
1164:5
1117:5
1061:28
1058:16
1049:22
1043:18
1037:11
1031:23
1011:X
996:V
984:I
941:,
854:,
846:,
832:).
723:.
616:,
612:,
596:,
592:,
588:,
510:.
443:c.
386:,
376:c.
364:c.
356:c.
312:c.
310:,
282:.
179:,
173:c.
147::
121:c.
98:,
94:,
4171:e
4164:t
4157:v
3991:e
3984:t
3977:v
3964:.
3935:.
3874:.
3809:)
3793:.
3747:.
3719:.
3695:.
3675::
3655:.
3611:.
3583:.
3559:.
3509:.
3484:.
3464:.
3444:.
3424:.
3397:.
3373:.
3362:.
3332:.
3270::
3241:.
3226:.
3214:.
3202:.
3189:.
3148:.
3135:.
3111:.
3004:.
2978:.
2912:.
2842:.
2829:.
2810:.
2791:.
2766:.
2736:)
2722:.
2677:.
2664:.
2636::
2609:.
2597::
2575:.
2498:.
2482:.
2398:]
2395:)
2390:5
2382:5
2379:(
2376:3
2373:[
2369:/
2259:(
2187:.
2093:.
2079:.
2036:)
1809:)
1498:(
1446:.
1440:6
1434:5
1429:+
1426:5
1419:=
1412:)
1407:5
1399:5
1396:(
1393:3
1161:–
1158:–
1155:–
1152:–
1149:–
1146:–
1143:–
1140:–
1137:–
1134:–
1131:–
1128:–
1125:5
1114:–
1111:–
1108:–
1105:–
1102:–
1099:–
1096:–
1093:–
1090:–
1087:–
1084:–
1081:–
1078:5
1067:–
1064:–
1055:–
1052:–
1046:4
1040:7
1034:2
934:.
927:.
897:2
884:.
866:.
830:d
826:b
822:c
818:a
814:d
810:c
806:b
802:a
774:.
441:(
374:(
362:(
354:(
183:(
143:(
58:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
