274:
1371:
295:
325:(Ms. Vatican Library, Lat. 3129), a nearly 600-page textbook dedicated to his students at the University of Perugia where Pacioli taught from 1477 to 1480. The manuscript was written between December 1477 and 29 April 1478. It contains 16 sections on merchant arithmetic, such as barter, exchange, profit, mixing metals, and algebra, though 25 pages from the chapter on algebra are missing. A modern transcription was published by Calzoni and Cavazzoni (1996) along with a partial translation of the chapter on partitioning problems.
1156:
2441:
199:
43:
347:. The system he published included most of the accounting cycle as we know it today. He described the use of journals and ledgers and warned that a person should not go to sleep at night until the debits equalled the credits. His ledger had accounts for assets (including receivables and inventories), liabilities, capital, income, and expenses – the account categories that are reported on an organization's
428:(written in Milan in 1496–1498, published in Venice in 1509). Two versions of the original manuscript are extant, one in the Biblioteca Ambrosiana in Milan, the other in the Bibliothèque Publique et Universitaire in Geneva. The subject was mathematical and artistic proportion, especially the mathematics of the
521:
s section on accounting was used internationally as an accounting textbook up to the mid-16th century. The essentials of double-entry accounting have for the most part remained unchanged for over 500 years. "Accounting practitioners in public accounting, industry, and not-for-profit organizations, as
399:
is divided into three sections: Mathematical problems, puzzles, and tricks, along with a collection of proverbs and verses. The book has been described as the "Foundation of modern magic and numerical puzzles," but it was never published and sat in the archives of the
University of Bologna, where it
395:(Ms. Università degli Studi di Bologna, 1496–1508), a treatise on mathematics and magic. Written between 1496 and 1508, it contains the first reference to card tricks as well as guidance on how to juggle, eat fire, and make coins dance. It is the first work to note that Leonardo was left-handed.
454:
while he lived with and took mathematics lessons from
Pacioli. Leonardo's drawings are probably the first illustrations of skeletal solids, which allowed an easy distinction between front and back. The work also discusses the use of perspective by painters such as
227:
around 1464, where he continued his own education while working as a tutor to the three sons of a merchant. It was during this period that he wrote his first book, a treatise on arithmetic for the boys he was tutoring. Between 1472 and 1475, he became a
223:, the local tongue) rather than Latin and focused on the knowledge required of merchants. His father was Bartolomeo Pacioli; however, Luca Pacioli was said to have lived with the Befolci family as a child in his birth town Sansepolcro. He moved to
264:
seized the city and drove out their patron. Their paths appear to have finally separated around 1506. Pacioli died at about the age of 70 on 19 June 1517, most likely in
Sansepolcro, where it is thought that he had spent much of his final years.
235:
In 1475, he started teaching in
Perugia as a private teacher before becoming first chair in mathematics in 1477. During this time, he wrote a comprehensive textbook in the vernacular for his students. He continued to work as a private tutor of
516:
Pacioli dramatically affected the practice of accounting by describing the double-entry accounting method used in parts of Italy. This revolutionized how businesses oversaw their operations, enabling improved efficiency and profitability. The
533:
holds the complete published works of Luca
Pacioli. Sections of two of Pacioli's books, 'Summa de arithmetica' and 'Divina proportione' can be viewed online using Turning the Pages, an interactive tool developed by the British Library.
343:, the spoken language of the day). It is also notable for including one of the first published descriptions of the bookkeeping method that Venetian merchants used during the Italian Renaissance, known as the
339:
1494), a textbook for use in the schools of
Northern Italy. It was a synthesis of the mathematical knowledge of his time and contained the first printed work on algebra written in the vernacular (
522:
well as investors, lending institutions, business firms, and all other users for financial information are indebted to Luca
Pacioli for his monumental role in the development of accounting."
564:. A facsimile edition of the book was published in Pacioli's home town of Sansepolcro in 2008. Based on Leonardo da Vinci's long association with the author and his having illustrated
1132:, corredato della versione volgare di Luca Paccioli ; eds. Cecil Grayson,... Marisa Dalai Emiliani, Carlo Maccagni. Firenze, Giunti, 1995. 3 vol. (68 ff., XLIV-213, XXII-223 pp.).
1198:
2348:
508:, and that it may just have been appended to his work. However, no such defense can be presented concerning the inclusion of Piero della Francesca's material in Pacioli's Summa.
500:. In neither case did Pacioli include an attribution to Piero. He was severely criticized for this and accused of plagiarism by sixteenth-century art historian and biographer
1589:
1370:
2380:
618:
claims that the "M" logo it uses to decorate souvenir items (which the museum calls "the
Renaissance M") is from an illustration originally in the
404:, a mathematician, came across a reference to it in a 19th-century manuscript. An English translation was published for the first time in 2007.
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438:
174:. He is referred to as the father of accounting and bookkeeping and he was the first person to publish a work on the
629:
2477:
1684:
1065:
Gleeson-White, Jane, "Double Entry: How the
Merchants of Venice Created Modern Finance," New York: Norton, 2012.
877:
Piero Della
Francesca's Mathematical Treatises: The Trattato D'abaco and Libellus de Quinque Corporibus Regularibus
1209:
1819:
1223:
1068:
Heeffer, Albrecht, "Algebraic partitioning problems from Luca Paccioli's Perugia manuscript (Vat. Lat. 3129)" in
974:"International Herald Tribune: Experts link Leonardo da Vinci to chess puzzles in long-lost Renaissance treatise"
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be used to prove a balanced ledger. Additionally, his treatise touches on a wide range of related topics from
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273:
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504:. R. Emmett Taylor (1889–1956) said that Pacioli may have had nothing to do with the translated volume
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2517:
1777:
1338:
987:
1179:
400:
was seen by only a small number of scholars during the Middle Ages. The book was rediscovered after
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1791:
1113:
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and was instructed to stop teaching at this level in Sansepolcro in 1491. In 1494, his first book,
48:
2094:
1784:
1427:
1308:
1103:
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2385:
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2122:
1503:
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was rediscovered in 2006, in the 22,000-volume library of Count Guglielmo Coronini-Cronberg in
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922:
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2240:
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2067:
1909:
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1059:
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142:
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33:
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330:
243:
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119:
75:
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that appear in the manuscript or at least designed the chess pieces used in the problems.
8:
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307:
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1732:
460:
2421:
2278:
2108:
1904:
1894:
1747:
1619:
1474:
765:
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620:
424:
287:
126:
1614:
2142:
2116:
1998:
1659:
1133:
1084:
1055:
918:
833:
769:
718:
548:
447:
360:
282:
257:
167:
2130:
1673:
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1983:
1933:
1879:
1834:
1763:
1563:
1343:
1160:
749:
464:
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1988:
1813:
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1479:
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Woodcut illustrating the proportions of the human face from the second part of
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1973:
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1325:
1313:
1165:
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615:
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356:
355:, respectively. He demonstrated year-end closing entries and proposed that a
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1953:
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1355:
1288:
895:
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A Napierian logarithm before Napier, John J O'Connor and Edmund F Robertson
433:
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20:
2252:
2025:
1963:
1874:
1869:
1469:
1432:
372:
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71:
248:, was published in Venice. In 1497, he accepted an invitation from Duke
2073:
1978:
1928:
1508:
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761:
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368:
229:
171:
1228:
962:
Times Online: Renaissance chess master and the Da Vinci decode mystery
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1624:
1604:
1273:
753:
256:. There he met, taught mathematics to, collaborated, and lived with
1850:
1452:
1350:
1278:
917:
Smith, L. Murphy (2018). "Luca Pacioli: The Father of Accounting".
436:. It incorporates without credit a translation of the entire book
211:
Luca Pacioli was born between 1446 and 1448 in the Tuscan town of
1752:
1491:
1405:
1283:
561:
187:
2349:
Viewpoints: Mathematical Perspective and Fractal Geometry in Art
1002:"Experts link Leonardo da Vinci to chess puzzles - USATODAY.com"
371:, using an approximation of 100*ln 2 more than 100 years before
16:
15th c. Italian Friar Minor, mathematician and economic theorist
1457:
479:
Summa de arithmetica, geometria. Proportioni et proportionalita
411:
336:
331:
Summa de arithmetica, geometria. Proportioni et proportionalita
260:. In 1499, Pacioli and Leonardo were forced to flee Milan when
244:
Summa de arithmetica, geometria, Proportioni et proportionalita
224:
471:
1442:
1216:
Five Hundred Years of Bookkeeping: A Portrait of Luca Pacioli
543:
526:
253:
738:
MacKinnon, Nick (1993). "The Portrait of Fra Luca Pacioli".
232:
friar. Thus, he could be referred to as Fra ('Friar') Luca.
1464:
1447:
822:
Chiappetta, Barbara; Larson, Kermit D. (15 November 1995).
634:
The Met Store (Metropolitan Museum of Art shopping catalog)
42:
1039:
Calzoni, Giuseppe and Gianfranco Cavazzoni (eds.) (1996)
825:
Fundamental Accounting Principles: Student Learning Tools
568:, some scholars speculate that Leonardo either drew the
379:. Its exercises were largely copied without credit from
1222:, 1994, vol. XXXIX issue 3 pp. 289–304)
1062:. New York: Garland Publishing, 1996. pp. 445–447.
1052:
History of Accounting: an International Encyclopedia,
937:"Turning the Pages: ICAEW's collection of rare books"
170:, and an early contributor to the field now known as
879:(in English and Italian). Longo Editore. p. 64.
511:
714:
il Falco e il Topo Manualetto di Gestione Aziendale
542:Luca Pacioli also wrote an unpublished treatise on
2246:The Drawing of Geometric Patterns in Saracenic Art
1144:Borgo Sansepolcro. CittĂ di cavalieri e pellegrini
202:A woodcut of Pacioli which appears throughout the
2381:Goudreau Museum of Mathematics in Art and Science
1097:
2459:
821:
450:drew the illustrations of the regular solids in
556:). Long thought to have been lost, a surviving
1041:Tractatus Mathematicus ad Discipulos Perusinos
322:Tractatus mathematicus ad discipulos perusinos
2376:European Society for Mathematics and the Arts
1550:Mathematica: A World of Numbers... and Beyond
1244:
1530:List of works designed with the golden ratio
1025:"Leonardo, Left-Handed Draftsman and Writer"
1188:Luca Paccioli's economic research programme
482:was a slightly rewritten version of one of
477:
472:Translation of Piero della Francesca's work
390:
328:
320:
241:
1251:
1237:
1218:(Tijdschrift voor Economie en Management,
1130:Libellus de quinque corporibus regularibus
1092:No Royal Road: Luca Paccioli and his Times
1070:Sources and Commentaries in Exact Sciences
853:
683:
158:1447 – 19 June 1517) was an Italian
41:
1590:Cathedral of Saint Mary of the Assumption
1146:Pessano con Bornago, Mimep-Docete (2012).
737:
889:
710:
582:List of Roman Catholic scientist-clerics
486:'s works. The third volume of Pacioli's
293:
272:
219:. This was education in the vernacular (
197:
2136:Vier BĂĽcher von Menschlicher Proportion
1258:
1214:Lauwers, Luc & Willekens, Marleen:
1109:MacTutor History of Mathematics Archive
1022:
870:
868:
677:
660:"The Enigma of Luca Pacioli's Portrait"
587:Della mercatura e del mercante perfetto
2460:
1175:The Enigma of Luca Paccioli's Portrait
1027:. New York: Metropolitan Museum of Art
1232:
916:
874:
783:
781:
779:
476:The majority of the second volume of
178:on the continent. He was also called
865:
692:(in Italian). Vol. 80. Treccani
690:Dizionario Biografico degli Italiani
684:Di Teodoro, Francesco Paolo (2014).
277:The first printed illustration of a
2488:16th-century Italian mathematicians
2483:15th-century Italian mathematicians
2321:Journal of Mathematics and the Arts
711:Tarquini, Luca (23 December 2016).
312:Pacioli published several works on
302:, which covers the Vitruvian system
176:double-entry system of book-keeping
13:
2335:Making Mathematics with Needlework
892:"And that's renaissance magic ..."
776:
529:Library's rare book collection at
14:
2549:
2161:I quattro libri dell'architettura
1150:
1048:"Pacioli, Luca (c. 1445-c.1517)."
512:Impact on accounting and business
497:De quinque corporibus regularibus
439:De quinque corporibus regularibus
93:Sansepolcro, Republic of Florence
2440:
2439:
1685:Self-portrait in a Convex Mirror
1369:
890:McDonald, Lucy (10 April 2007).
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980:
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955:
929:
910:
883:
604:
410:(1509), a Latin translation of
2396:National Museum of Mathematics
2148:Regole generali d'architettura
1220:Katholieke Universiteit Leuven
1157:Works by or about Luca Pacioli
815:
806:
731:
704:
652:
490:was an Italian translation of
345:double-entry accounting system
268:
52:, traditionally attributed to
1:
1210:Biblioteca Nacional de España
1197:, Venice, 1509, digitized at
1170:Mathematics Genealogy Project
1083:), (Antonio Capella) Venice:
1043:, CittĂ di Castello, Perugia.
875:Davis, Margaret Daly (1977).
592:
155:
65:
2533:16th-century Italian writers
2528:15th-century Italian writers
1921:Garden of Cosmic Speculation
1199:Biblioteca Digital Hispánica
1072:, (2010), 11, pp. 3–52.
988:"Winnipeg Free Press: Chess"
830:McGraw-Hill Higher Education
141:Luca Bartolomeo de Pacioli,
110:Friar, mathematician, writer
7:
793:www-groups.dcs.st-and.ac.uk
575:
531:Chartered Accountants' Hall
10:
2554:
2513:Catholic clergy scientists
1438:Islamic geometric patterns
1016:
630:"Renaissance 'M' bookmark"
612:Metropolitan Museum of Art
305:
18:
2538:16th-century male writers
2435:
2404:
2358:
2312:
2259:A Mathematician's Apology
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2018:
2011:
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849:– via Google Books.
727:– via Google Books.
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61:
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2371:The Bridges Organization
1114:University of St Andrews
1081:On the Divine Proportion
1023:Bambach, Carmen (2003).
741:The Mathematical Gazette
537:
133:double-entry bookkeeping
49:Portrait of Luca Pacioli
19:Not to be confused with
2478:People from Sansepolcro
2233:The Grammar of Ornament
2185:Nature's Harmonic Unity
2095:De prospectiva pingendi
1006:usatoday30.usatoday.com
432:and its application in
193:
2386:Institute For Figuring
2298:The 'Life' of a Carpet
2123:A Treatise on Painting
478:
397:De viribus quantitatis
392:De viribus quantitatis
391:
329:
321:
303:
291:
242:
208:
182:after his birthplace,
2523:History of accounting
2267:George David Birkhoff
2241:Ernest Hanbury Hankin
2109:De divina proportione
2089:Piero della Francesca
2068:Leon Battista Alberti
1655:Piero della Francesca
1294:Hyperboloid structure
1182:De divina proportione
1124:Catholic Encyclopedia
1077:De divina proportione
1060:Richard Vangermeersch
492:Piero della Francesca
484:Piero della Francesca
457:Piero della Francesca
444:Piero della Francesca
381:Piero della Francesca
306:Further information:
297:
276:
215:where he received an
201:
2192:Frederik Macody Lund
2063:Filippo Brunelleschi
1944:Hamid Naderi Yeganeh
1806:La condition humaine
1100:Robertson, Edmund F.
554:On the Game of Chess
367:. He introduced the
205:Summa de arithmetica
166:, collaborator with
120:Summa de arithmetica
76:Republic of Florence
2508:Italian Franciscans
2498:Italian accountants
2417:Mathematical beauty
2342:Rhythm of Structure
2285:Gödel, Escher, Bach
2081:De re aedificatoria
1712:The Ancient of Days
1331:Projective geometry
1260:Mathematics and art
1098:O'Connor, John J.;
1046:Galassi, Giuseppe.
789:"Pacioli biography"
308:Mathematics and art
279:rhombicuboctahedron
262:Louis XII of France
2422:Patterns in nature
2279:Douglas Hofstadter
1905:Desmond Paul Henry
1895:Bathsheba Grossman
1827:The Swallow's Tail
1748:Giorgio de Chirico
1620:Sydney Opera House
1475:Croatian interlace
1194:Diuina proportione
1142:Varisco, Alessio,
1090:Taylor, Emmet, R.
621:Divina proportione
566:Divina proportione
506:Divina proportione
488:Divina proportione
452:Divina proportione
425:Divina proportione
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300:Divina proportione
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288:Divina proportione
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127:Divina proportione
54:Jacopo de' Barbari
2493:Leonardo da Vinci
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2454:
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2272:Aesthetic Measure
2143:Sebastiano Serlio
2117:Leonardo da Vinci
2007:
2006:
1999:Margaret Wertheim
1660:Leonardo da Vinci
1085:Paganino Paganini
1056:Michael Chatfield
748:(479): 132, 160.
549:De ludo scachorum
448:Leonardo da Vinci
383:'s earlier book,
361:accounting ethics
283:Leonardo da Vinci
258:Leonardo da Vinci
184:Borgo Sansepolcro
168:Leonardo da Vinci
138:
137:
90:(aged 69–70)
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2518:Number theorists
2443:
2442:
2293:Nikos Salingaros
2016:
2015:
1984:Hiroshi Sugimoto
1934:Robert Longhurst
1880:Helaman Ferguson
1835:Crockett Johnson
1764:Circle Limit III
1733:Danseuse au café
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1610:Pyramid of Khufu
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2155:Andrea Palladio
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2044:De architectura
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1959:Antoine Pevsner
1939:Jeanette McLeod
1890:Susan Goldstine
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1386:Algorithmic art
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1299:Minimal surface
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2204:Jay Hambidge
2197:Ad Quadratum
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2103:Luca Pacioli
2102:
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1954:Hinke Osinga
1949:István Orosz
1919:
1910:Anthony Hill
1865:Scott Draves
1860:Erik Demaine
1844:Contemporary
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1356:Tessellation
1339:Architecture
1289:Golden ratio
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1166:Luca Pacioli
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843:. Retrieved
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88:(1517-06-19)
86:19 June 1517
47:
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21:Luca Pacioni
2473:1517 deaths
2253:G. H. Hardy
2056:Renaissance
2026:Polykleitos
1964:Tony Robbin
1875:John Ernest
1870:Jan Dibbets
1820:Crucifixion
1643:Renaissance
1497:Mathematics
1470:Celtic knot
1433:Fractal art
1335:Proportion
1309:Perspective
1202: [
1031:2 September
845:10 November
314:mathematics
269:Mathematics
252:to work in
238:mathematics
213:Sansepolcro
146:(sometimes
99:Citizenship
72:Sansepolcro
2462:Categories
2227:Owen Jones
2074:De pictura
1979:Oliver Sin
1929:Andy Lomas
1778:Relativity
1509:String art
1423:Fiber arts
1304:Paraboloid
1079:(English:
1054:edited by
902:30 January
696:30 January
669:30 January
593:References
558:manuscript
369:Rule of 72
230:Franciscan
172:accounting
102:Florentine
2038:Vitruvius
2012:Theorists
1792:Waterfall
1697:19th–20th
1625:Taj Mahal
1605:Parthenon
1582:Buildings
1536:Continuum
1504:Sculpture
1480:Interlace
1274:Algorithm
941:ICAEW.com
770:195006163
646:Citations
598:Footnotes
2446:Category
2173:Romantic
1851:Max Bill
1785:Reptiles
1600:Pantheon
1557:Octacube
1523:Artworks
1465:Knotting
1453:Muqarnas
1351:Symmetry
1279:Catenary
1267:Concepts
798:24 March
576:See also
417:Elements
408:Geometry
148:Paccioli
2405:Related
2019:Ancient
1753:Man Ray
1699:Century
1635:Artists
1492:Origami
1406:Pyramid
1284:Fractal
1168:at the
1159:at the
1126:article
1087:(1509).
1017:Sources
947:22 June
943:. ICAEW
923:2320658
762:3619717
562:Gorizia
188:Tuscany
152:Paciolo
2220:Modern
1856:Martin
1719:Newton
1514:Tiling
1458:Zellij
1428:4D art
1136:
1094:(1942)
921:
836:
768:
760:
721:
519:Summa'
463:, and
412:Euclid
377:Briggs
373:Napier
337:Venice
225:Venice
143:O.F.M.
56:, 1495
34:O.F.M.
2031:Canon
1487:Music
1443:Girih
1379:Forms
1344:Human
1206:]
766:S2CID
758:JSTOR
544:chess
538:Chess
527:ICAEW
281:, by
254:Milan
1858:and
1448:Jali
1134:ISBN
1058:and
1033:2006
949:2020
919:SSRN
904:2015
847:2023
834:ISBN
800:2016
719:ISBN
698:2015
671:2015
610:The
525:The
375:and
351:and
341:i.e.
221:i.e.
194:Life
83:Died
68:1447
62:Born
1224:pdf
1050:In
750:doi
626:See
614:in
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