285:
1382:
306:
336:(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.
1167:
2452:
210:
54:
358:. 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
439:(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
532:
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
410:
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
406:(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.
465:
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
238:
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
234:, 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
275:
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.
246:
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
527:
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
544:
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.
354:, 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
350:
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 (
533:
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."
575:. 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
1143:, 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.).
1209:
2359:
519:, 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.
511:. 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
1600:
1381:
2391:
629:
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
415:, 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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185:. He is referred to as the father of accounting and bookkeeping and he was the first person to publish a work on the
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2488:
1695:
1076:
Gleeson-White, Jane, "Double Entry: How the
Merchants of Venice Created Modern Finance," New York: Norton, 2012.
888:
Piero Della
Francesca's Mathematical Treatises: The Trattato D'abaco and Libellus de Quinque Corporibus Regularibus
17:
1220:
1830:
1234:
1079:
Heeffer, Albrecht, "Algebraic partitioning problems from Luca Paccioli's Perugia manuscript (Vat. Lat. 3129)" in
985:"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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515:. R. Emmett Taylor (1889–1956) said that Pacioli may have had nothing to do with the translated volume
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2528:
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was seen by only a small number of scholars during the Middle Ages. The book was rediscovered after
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1802:
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and was instructed to stop teaching at this level in Sansepolcro in 1491. In 1494, his first book,
59:
2105:
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was rediscovered in 2006, in the 22,000-volume library of Count Guglielmo Coronini-Cronberg in
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that appear in the manuscript or at least designed the chess pieces used in the problems.
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2009:
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Woodcut illustrating the proportions of the human face from the second part of
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367:
366:, respectively. He demonstrated year-end closing entries and proposed that a
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A Napierian logarithm before Napier, John J O'Connor and Edmund F Robertson
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1974:
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259:, was published in Venice. In 1497, he accepted an invitation from Duke
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973:
Times Online: Renaissance chess master and the Da Vinci decode mystery
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267:. There he met, taught mathematics to, collaborated, and lived with
1861:
1463:
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1289:
928:
Smith, L. Murphy (2018). "Luca Pacioli: The Father of Accounting".
447:. It incorporates without credit a translation of the entire book
222:
Luca Pacioli was born between 1446 and 1448 in the Tuscan town of
1763:
1502:
1416:
1294:
572:
198:
2360:
Viewpoints: Mathematical Perspective and Fractal Geometry in Art
1013:"Experts link Leonardo da Vinci to chess puzzles - USATODAY.com"
382:, using an approximation of 100*ln 2 more than 100 years before
27:
15th c. Italian Friar Minor, mathematician and economic theorist
1468:
490:
Summa de arithmetica, geometria. Proportioni et proportionalita
422:
347:
342:
Summa de arithmetica, geometria. Proportioni et proportionalita
271:. In 1499, Pacioli and Leonardo were forced to flee Milan when
255:
Summa de arithmetica, geometria, Proportioni et proportionalita
235:
482:
1453:
1227:
Five Hundred Years of Bookkeeping: A Portrait of Luca Pacioli
554:
537:
264:
749:
MacKinnon, Nick (1993). "The Portrait of Fra Luca Pacioli".
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friar. Thus, he could be referred to as Fra ('Friar') Luca.
1475:
1458:
833:
Chiappetta, Barbara; Larson, Kermit D. (15 November 1995).
645:
The Met Store (Metropolitan Museum of Art shopping catalog)
53:
1050:
Calzoni, Giuseppe and Gianfranco Cavazzoni (eds.) (1996)
836:
Fundamental Accounting Principles: Student Learning Tools
579:, some scholars speculate that Leonardo either drew the
390:. Its exercises were largely copied without credit from
1233:, 1994, vol. XXXIX issue 3 pp. 289–304)
1073:. New York: Garland Publishing, 1996. pp. 445–447.
1063:
History of Accounting: an International Encyclopedia,
948:"Turning the Pages: ICAEW's collection of rare books"
181:, and an early contributor to the field now known as
890:(in English and Italian). Longo Editore. p. 64.
522:
725:
il Falco e il Topo Manualetto di Gestione Aziendale
553:Luca Pacioli also wrote an unpublished treatise on
2257:The Drawing of Geometric Patterns in Saracenic Art
1155:Borgo Sansepolcro. CittĂ di cavalieri e pellegrini
213:A woodcut of Pacioli which appears throughout the
2392:Goudreau Museum of Mathematics in Art and Science
1108:
2470:
832:
461:drew the illustrations of the regular solids in
567:). Long thought to have been lost, a surviving
1052:Tractatus Mathematicus ad Discipulos Perusinos
333:Tractatus mathematicus ad discipulos perusinos
2387:European Society for Mathematics and the Arts
1561:Mathematica: A World of Numbers... and Beyond
1255:
1541:List of works designed with the golden ratio
1036:"Leonardo, Left-Handed Draftsman and Writer"
1199:Luca Paccioli's economic research programme
493:was a slightly rewritten version of one of
488:
483:Translation of Piero della Francesca's work
401:
339:
331:
252:
1262:
1248:
1229:(Tijdschrift voor Economie en Management,
1141:Libellus de quinque corporibus regularibus
1103:No Royal Road: Luca Paccioli and his Times
1081:Sources and Commentaries in Exact Sciences
864:
694:
169:1447 – 19 June 1517) was an Italian
52:
1601:Cathedral of Saint Mary of the Assumption
1157:Pessano con Bornago, Mimep-Docete (2012).
748:
900:
721:
593:List of Roman Catholic scientist-clerics
497:'s works. The third volume of Pacioli's
304:
283:
230:. This was education in the vernacular (
208:
2147:Vier BĂĽcher von Menschlicher Proportion
1269:
1225:Lauwers, Luc & Willekens, Marleen:
1120:MacTutor History of Mathematics Archive
1033:
881:
879:
688:
671:"The Enigma of Luca Pacioli's Portrait"
598:Della mercatura e del mercante perfetto
14:
2471:
1186:The Enigma of Luca Paccioli's Portrait
1038:. New York: Metropolitan Museum of Art
1243:
927:
885:
794:
792:
790:
487:The majority of the second volume of
189:on the continent. He was also called
876:
703:(in Italian). Vol. 80. Treccani
701:Dizionario Biografico degli Italiani
695:Di Teodoro, Francesco Paolo (2014).
288:The first printed illustration of a
2499:16th-century Italian mathematicians
2494:15th-century Italian mathematicians
2332:Journal of Mathematics and the Arts
722:Tarquini, Luca (23 December 2016).
323:Pacioli published several works on
313:, which covers the Vitruvian system
187:double-entry system of book-keeping
24:
2346:Making Mathematics with Needlework
903:"And that's renaissance magic ..."
787:
540:Library's rare book collection at
25:
2560:
2172:I quattro libri dell'architettura
1161:
1059:"Pacioli, Luca (c. 1445-c.1517)."
523:Impact on accounting and business
508:De quinque corporibus regularibus
450:De quinque corporibus regularibus
104:Sansepolcro, Republic of Florence
2451:
2450:
1696:Self-portrait in a Convex Mirror
1380:
901:McDonald, Lucy (10 April 2007).
1005:
991:
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966:
940:
921:
894:
615:
421:(1509), a Latin translation of
2407:National Museum of Mathematics
2159:Regole generali d'architettura
1231:Katholieke Universiteit Leuven
1168:Works by or about Luca Pacioli
826:
817:
742:
715:
663:
501:was an Italian translation of
356:double-entry accounting system
279:
63:, traditionally attributed to
13:
1:
1221:Biblioteca Nacional de España
1208:, Venice, 1509, digitized at
1181:Mathematics Genealogy Project
1094:), (Antonio Capella) Venice:
1054:, CittĂ di Castello, Perugia.
886:Davis, Margaret Daly (1977).
603:
166:
76:
2544:16th-century Italian writers
2539:15th-century Italian writers
1932:Garden of Cosmic Speculation
1210:Biblioteca Digital Hispánica
1083:, (2010), 11, pp. 3–52.
999:"Winnipeg Free Press: Chess"
841:McGraw-Hill Higher Education
152:Luca Bartolomeo de Pacioli,
121:Friar, mathematician, writer
7:
804:www-groups.dcs.st-and.ac.uk
586:
542:Chartered Accountants' Hall
10:
2565:
2524:Catholic clergy scientists
1449:Islamic geometric patterns
1027:
641:"Renaissance 'M' bookmark"
623:Metropolitan Museum of Art
316:
29:
2549:16th-century male writers
2446:
2415:
2369:
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2270:A Mathematician's Apology
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860:– via Google Books.
738:– via Google Books.
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72:
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2382:The Bridges Organization
1125:University of St Andrews
1092:On the Divine Proportion
1034:Bambach, Carmen (2003).
752:The Mathematical Gazette
548:
144:double-entry bookkeeping
60:Portrait of Luca Pacioli
30:Not to be confused with
2489:People from Sansepolcro
2244:The Grammar of Ornament
2196:Nature's Harmonic Unity
2106:De prospectiva pingendi
1017:usatoday30.usatoday.com
443:and its application in
204:
2397:Institute For Figuring
2309:The 'Life' of a Carpet
2134:A Treatise on Painting
489:
408:De viribus quantitatis
403:De viribus quantitatis
402:
340:
332:
314:
302:
253:
219:
193:after his birthplace,
2534:History of accounting
2278:George David Birkhoff
2252:Ernest Hanbury Hankin
2120:De divina proportione
2100:Piero della Francesca
2079:Leon Battista Alberti
1666:Piero della Francesca
1305:Hyperboloid structure
1193:De divina proportione
1135:Catholic Encyclopedia
1088:De divina proportione
1071:Richard Vangermeersch
503:Piero della Francesca
495:Piero della Francesca
468:Piero della Francesca
455:Piero della Francesca
392:Piero della Francesca
317:Further information:
308:
287:
226:where he received an
212:
2203:Frederik Macody Lund
2074:Filippo Brunelleschi
1955:Hamid Naderi Yeganeh
1817:La condition humaine
1111:Robertson, Edmund F.
565:On the Game of Chess
378:. He introduced the
216:Summa de arithmetica
177:, collaborator with
131:Summa de arithmetica
87:Republic of Florence
2519:Italian Franciscans
2509:Italian accountants
2428:Mathematical beauty
2353:Rhythm of Structure
2296:Gödel, Escher, Bach
2092:De re aedificatoria
1723:The Ancient of Days
1342:Projective geometry
1271:Mathematics and art
1109:O'Connor, John J.;
1057:Galassi, Giuseppe.
800:"Pacioli biography"
319:Mathematics and art
290:rhombicuboctahedron
273:Louis XII of France
2433:Patterns in nature
2290:Douglas Hofstadter
1916:Desmond Paul Henry
1906:Bathsheba Grossman
1838:The Swallow's Tail
1759:Giorgio de Chirico
1631:Sydney Opera House
1486:Croatian interlace
1205:Diuina proportione
1153:Varisco, Alessio,
1101:Taylor, Emmet, R.
632:Divina proportione
577:Divina proportione
517:Divina proportione
499:Divina proportione
463:Divina proportione
436:Divina proportione
315:
311:Divina proportione
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299:Divina proportione
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138:Divina proportione
65:Jacopo de' Barbari
2504:Leonardo da Vinci
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2465:
2319:
2318:
2283:Aesthetic Measure
2154:Sebastiano Serlio
2128:Leonardo da Vinci
2018:
2017:
2010:Margaret Wertheim
1671:Leonardo da Vinci
1096:Paganino Paganini
1067:Michael Chatfield
759:(479): 132, 160.
560:De ludo scachorum
459:Leonardo da Vinci
394:'s earlier book,
372:accounting ethics
294:Leonardo da Vinci
269:Leonardo da Vinci
195:Borgo Sansepolcro
179:Leonardo da Vinci
149:
148:
101:(aged 69–70)
16:(Redirected from
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2529:Number theorists
2454:
2453:
2304:Nikos Salingaros
2027:
2026:
1995:Hiroshi Sugimoto
1945:Robert Longhurst
1891:Helaman Ferguson
1846:Crockett Johnson
1775:Circle Limit III
1744:Danseuse au café
1651:
1650:
1621:Pyramid of Khufu
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364:income statement
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228:abbaco education
175:Franciscan friar
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2166:Andrea Palladio
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2055:De architectura
2014:
1970:Antoine Pevsner
1950:Jeanette McLeod
1901:Susan Goldstine
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1397:Algorithmic art
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1372:Wallpaper group
1310:Minimal surface
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843:. p. 209.
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261:Ludovico Sforza
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2324:Publications
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2215:Jay Hambidge
2208:Ad Quadratum
2207:
2195:
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2132:
2118:
2114:Luca Pacioli
2113:
2104:
2090:
2083:
2053:
2041:
1965:Hinke Osinga
1960:István Orosz
1930:
1921:Anthony Hill
1876:Scott Draves
1871:Erik Demaine
1855:Contemporary
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1606:Hagia Sophia
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1429:Computer art
1407:Architecture
1367:Tessellation
1350:Architecture
1300:Golden ratio
1226:
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1177:Luca Pacioli
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1040:. Retrieved
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911:. Retrieved
907:The Guardian
905:
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871:St-and.ac.uk
866:
854:. Retrieved
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807:. Retrieved
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728:. Lulu.com.
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99:(1517-06-19)
97:19 June 1517
58:
36:
32:Luca Pacioni
2484:1517 deaths
2264:G. H. Hardy
2067:Renaissance
2037:Polykleitos
1975:Tony Robbin
1886:John Ernest
1881:Jan Dibbets
1831:Crucifixion
1654:Renaissance
1508:Mathematics
1481:Celtic knot
1444:Fractal art
1346:Proportion
1320:Perspective
1213: [
1042:2 September
856:10 November
325:mathematics
280:Mathematics
263:to work in
249:mathematics
224:Sansepolcro
157:(sometimes
110:Citizenship
83:Sansepolcro
2473:Categories
2238:Owen Jones
2085:De pictura
1990:Oliver Sin
1940:Andy Lomas
1789:Relativity
1520:String art
1434:Fiber arts
1315:Paraboloid
1090:(English:
1065:edited by
913:30 January
707:30 January
680:30 January
604:References
569:manuscript
380:Rule of 72
241:Franciscan
183:accounting
113:Florentine
2049:Vitruvius
2023:Theorists
1803:Waterfall
1708:19th–20th
1636:Taj Mahal
1616:Parthenon
1593:Buildings
1547:Continuum
1515:Sculpture
1491:Interlace
1285:Algorithm
952:ICAEW.com
781:195006163
657:Citations
609:Footnotes
2457:Category
2184:Romantic
1862:Max Bill
1796:Reptiles
1611:Pantheon
1568:Octacube
1534:Artworks
1476:Knotting
1464:Muqarnas
1362:Symmetry
1290:Catenary
1278:Concepts
809:24 March
587:See also
428:Elements
419:Geometry
159:Paccioli
2416:Related
2030:Ancient
1764:Man Ray
1710:Century
1646:Artists
1503:Origami
1417:Pyramid
1295:Fractal
1179:at the
1170:at the
1137:article
1098:(1509).
1028:Sources
958:22 June
954:. ICAEW
934:2320658
773:3619717
573:Gorizia
199:Tuscany
163:Paciolo
2231:Modern
1867:Martin
1730:Newton
1525:Tiling
1469:Zellij
1439:4D art
1147:
1105:(1942)
932:
847:
779:
771:
732:
530:Summa'
474:, and
423:Euclid
388:Briggs
384:Napier
348:Venice
236:Venice
154:O.F.M.
67:, 1495
45:O.F.M.
2042:Canon
1498:Music
1454:Girih
1390:Forms
1355:Human
1217:]
777:S2CID
769:JSTOR
555:chess
549:Chess
538:ICAEW
292:, by
265:Milan
1869:and
1459:Jali
1145:ISBN
1069:and
1044:2006
960:2020
930:SSRN
915:2015
858:2023
845:ISBN
811:2016
730:ISBN
709:2015
682:2015
621:The
536:The
386:and
362:and
352:i.e.
232:i.e.
205:Life
94:Died
79:1447
73:Born
1235:pdf
1061:In
761:doi
637:See
625:in
453:by
425:'s
374:to
161:or
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