340:
33:
230:, developed through exposure to numerous example problems and case studies drawn principally from business and trade. Pacioli's work likewise teaches through examples, but it also develops arguments for the validity of its solutions through reference to general principles, axioms and logical proof. In this way the
393:
contained little or no original mathematical work by
Pacioli, it was the most comprehensive mathematical text ever published at the time. Its thoroughness and clarity (and the lack of any other similar work available in print) generated strong and steady sales to the European merchants who were the
192:
as originally printed consists of ten chapters on a series of mathematical topics, collectively covering essentially all of
Renaissance mathematics. The first seven chapters form a summary of arithmetic in 222 pages. The eighth chapter explains contemporary algebra in 78 pages. The ninth chapter
350:
was composed over a period of decades through
Pacioli's work as a professor of mathematics, and was probably intended as a textbook and reference work for students of mathematics and business, especially among the mercantile middle class of northern Italy. It was written in
290:
that he contributed no original mathematical content to the work, but he also does not specifically attribute any of the material to other sources. Subsequent scholarship has found that much of the work's coverage of geometry is taken almost exactly from
180:. It set a new standard for writing and argumentation about algebra, and its impact upon the subsequent development and standardization of professional accounting methods was so great that Pacioli is sometimes referred to as the "father of accounting".
435:), but none was published before Pacioli's work, and none achieved the same wide influence. The work's role in standardizing and disseminating professional bookkeeping methods has earned Pacioli a reputation as the "father of accounting".
377:, with an identical second edition printed in 1523 in Toscolano. About a thousand copies were originally printed, of which roughly 120 are still extant. In June 2019 an intact first edition sold at auction for
278:
by more than century. These techniques did not originate with
Pacioli, who merely recorded and explained the established best practices of contemporary businesspeople in his region.
450:
that were to become standard in
Italian Renaissance mathematics: 'p' with a tilde above (p̄) for "plus" and 'm' with a tilde (m̄) for minus. Pacioli's (incorrect) assertion in the
417:
represents the first published description of many accounting techniques, including double-entry bookkeeping. Some of the same methods were described in other
308:
303:
297:
539:
312:
594:
507:
327:(and other works). Many of the problems and techniques included in the book are quite directly taken from these earlier works, but the
216:
of contemporary northern Italy, where the children of merchants and the middle class studied arithmetic on the model established by
752:
484:
s publication, depicting
Pacioli surrounded by mathematical and geometric implements. The image on the stamp was inspired by the
427:
784:
339:
868:
667:
792:
438:
The book also marks the beginning of a movement in sixteenth-century algebra toward the use of logical argumentation and
406:, to invite him to serve as a mathematical lecturer in the ducal court, where Pacioli befriended and collaborated with
726:
32:
837:
358:(rather than Latin), reflecting its target audience and its purpose as a teaching text. The work was dedicated to
911:
255:
227:
177:
916:
896:
458:
helped to popularize the problem among contemporary mathematicians, contributing to its subsequent solution by
446:. It is thought to be the first printed work on algebra, and it includes the first printed example of a set of
234:
begins to reintegrate the logical methods of classical Greek geometry into the medieval discipline of algebra.
551:
266:
and various other tools still employed by professional accountants. The business chapter also introduces the
568:
921:
906:
696:
926:
359:
315:. This sort of appropriation has led some historians (notably including sixteenth-century biographer
704:
486:
822:
500:
292:
176:
is the first printed work on algebra, and it contains the first published description of the
626:
447:
254:) describes the accounting methods then in use among northern-Italian merchants, including
459:
205:, in 150 pages. The tenth and final chapter describes practical geometry (including basic
8:
901:
442:
in the study of algebra, following the model of classical Greek geometry established by
432:
105:
818:
814:
407:
374:
198:
80:
635:
560:
355:
169:
56:
331:
generally adds original logical arguments to justify the validity of the methods.
862:
628:
From
Problem Solving to Argumentation: Pacioli's Appropriation of Abbacus Algebra
399:
147:
564:
455:
403:
316:
890:
757:
672:
474:
263:
259:
226:. The emphasis of this tradition was on facility with computation, using the
213:
471:
271:
206:
143:
46:
877:
222:
202:
139:
66:
366:, a patron of the arts whom Pacioli had met in Rome some years earlier.
418:
352:
320:
311:, and a portion of the business chapter is copied from a manuscript by
267:
212:
The book's mathematical content draws heavily on the traditions of the
166:
159:
70:
275:
217:
146:
and first published in 1494. It contains a comprehensive summary of
538:
Sangster, Alan; Stoner, Gregory N; McCarthy, Patricia (June 2008).
193:
discusses various topics relevant to business and trade, including
155:
439:
151:
838:"The Sovietesque Disappearance of Pacioli's Rhombicuboctahedron"
668:"Somma di arithmetica, geometria, proporzioni e proporzionalitĂ "
136:
Summary of arithmetic, geometry, proportions and proportionality
443:
370:
363:
194:
129:
Summa de arithmetica, geometria, proportioni et proportionalita
84:
24:
Summa de arithmetica, geometria, proportioni et proportionalita
398:
earned
Pacioli as a mathematician and intellectual inspired
599:
Il
Contributo italiano alla storia del Pensiero – Scienze
537:
694:
695:
O'Connor, John J; Robertson, Edmund F (March 2006).
162:, written for use as a textbook and reference work.
242:Within the chapter on business, a section entitled
150:mathematics, including practical arithmetic, basic
504:, another influential mathematical work by Pacioli
586:
888:
662:
660:
658:
656:
654:
652:
783:Swetz, Frank J; Katz, Victor J (January 2011).
301:, one of the algebra sections is based on the
649:
394:text's intended audience. The reputation the
244:
127:
22:
835:
753:"A revolutionary treatise goes on the block"
508:List of most expensive books and manuscripts
778:
776:
343:Dedication page of the first (1494) edition
688:
592:
237:
31:
782:
620:
618:
616:
281:
815:"Luca Pacioli: The Father of Accounting"
785:"Mathematical Treasures—Pacioli's Summa"
773:
533:
531:
529:
527:
525:
523:
490:and contains many of the same elements.
338:
428:Della mercatura e del mercante perfetto
37:Title page of the second (1523) edition
889:
880:Particularis de computis et scripturis
871:Particularis de computis et scripturis
613:
477:honoring the 500th anniversary of the
454:that there was no general solution to
274:, anticipating the development of the
246:Particularis de computis et scripturis
812:
724:
697:"A Napierian logarithm before Napier"
520:
733:(in Italian). Vol. 80. Treccani
731:Dizionario Biografico degli Italiani
384:
252:Details of calculation and recording
793:Mathematical Association of America
624:
13:
14:
938:
856:
593:Napolitani, Pier Daniele (2013).
286:Pacioli explicitly states in the
465:
16:Renaissance mathematics textbook
829:
540:"The Market for Luca Pacioli's
369:It was originally published in
270:for predicting an investment's
178:double-entry bookkeeping system
865:(1523 edition) on Google Books
836:John F. Ptak (11 March 2008).
806:
745:
718:
1:
552:Accounting Historians Journal
513:
7:
493:
470:In 1994 Italy issued a 750-
228:Hindu–Arabic numeral system
201:, weights and measures and
183:
10:
943:
565:10.2308/0148-4184.35.1.111
334:
360:Guidobaldo da Montefeltro
111:
101:
91:
76:
62:
52:
42:
30:
840:. JF Ptak Science Booksl
705:University of St Andrews
487:Portrait of Luca Pacioli
256:double-entry bookkeeping
878:English translation of
319:) to accuse Pacioli of
238:Bookkeeping and finance
912:History of mathematics
874:(First (1494) edition)
813:Smith, Murphy (2018).
725:Nuovo, Angela (2014).
601:(in Italian). Treccani
344:
282:Plagiarism controversy
245:
128:
23:
917:History of accounting
897:Mathematics textbooks
869:Digitised edition of
501:De divina proportione
342:
293:Piero della Francesca
727:"PAGANINI, Paganino"
448:plus and minus signs
348:Summa de arithmetica
309:Antonio de Mazzinghi
304:Trattato di Fioretti
190:Summa de arithmetica
922:History of business
907:Medieval literature
625:Heeffer, Albrecht.
27:
574:on 26 January 2018
433:Benedetto Cotrugli
425:(such as the 1458
345:
106:Republic of Venice
21:
542:Summa Arithmetica
460:Niccolò Tartaglia
408:Leonardo da Vinci
385:Impact and legacy
375:Paganino Paganini
199:bills of exchange
123:
122:
102:Publication place
934:
927:Accounting books
850:
849:
847:
845:
833:
827:
826:
810:
804:
803:
801:
799:
780:
771:
770:
768:
766:
749:
743:
742:
740:
738:
722:
716:
715:
713:
711:
692:
686:
685:
683:
681:
664:
647:
646:
644:
642:
636:Ghent University
633:
622:
611:
610:
608:
606:
590:
584:
583:
581:
579:
573:
567:. Archived from
548:
535:
483:
380:
313:Giorgio Chiarini
298:Trattato d’abaco
248:
209:) in 151 pages.
131:
93:Publication date
35:
28:
26:
20:
942:
941:
937:
936:
935:
933:
932:
931:
887:
886:
859:
854:
853:
843:
841:
834:
830:
811:
807:
797:
795:
781:
774:
764:
762:
751:
750:
746:
736:
734:
723:
719:
709:
707:
693:
689:
679:
677:
666:
665:
650:
640:
638:
631:
623:
614:
604:
602:
595:"Pacioli, Luca"
591:
587:
577:
575:
571:
546:
536:
521:
516:
496:
481:
468:
456:cubic equations
400:Ludovico Sforza
387:
378:
337:
284:
240:
186:
138:) is a book on
94:
38:
17:
12:
11:
5:
940:
930:
929:
924:
919:
914:
909:
904:
899:
885:
884:
875:
866:
858:
857:External links
855:
852:
851:
828:
805:
772:
744:
717:
687:
676:. 12 June 2019
648:
612:
585:
559:(1): 111–134.
518:
517:
515:
512:
511:
510:
505:
495:
492:
467:
464:
421:predating the
386:
383:
336:
333:
317:Giorgio Vasari
283:
280:
264:balance sheets
260:trial balances
239:
236:
214:abacus schools
185:
182:
121:
120:
113:
109:
108:
103:
99:
98:
95:
92:
89:
88:
78:
74:
73:
64:
60:
59:
54:
50:
49:
44:
40:
39:
36:
15:
9:
6:
4:
3:
2:
939:
928:
925:
923:
920:
918:
915:
913:
910:
908:
905:
903:
900:
898:
895:
894:
892:
882:
881:
876:
873:
872:
867:
864:
861:
860:
839:
832:
824:
820:
816:
809:
794:
790:
786:
779:
777:
761:. 6 June 2019
760:
759:
758:The Economist
754:
748:
732:
728:
721:
706:
702:
698:
691:
675:
674:
669:
663:
661:
659:
657:
655:
653:
637:
630:
629:
621:
619:
617:
600:
596:
589:
570:
566:
562:
558:
554:
553:
545:
543:
534:
532:
530:
528:
526:
524:
519:
509:
506:
503:
502:
498:
497:
491:
489:
488:
480:
476:
475:postage stamp
473:
466:Commemoration
463:
461:
457:
453:
449:
445:
441:
436:
434:
430:
429:
424:
420:
416:
411:
409:
405:
401:
397:
392:
382:
379:US$ 1,215,000
376:
372:
367:
365:
361:
357:
354:
349:
341:
332:
330:
326:
322:
318:
314:
310:
306:
305:
300:
299:
294:
289:
279:
277:
273:
269:
265:
261:
257:
253:
249:
247:
235:
233:
229:
225:
224:
219:
215:
210:
208:
204:
200:
196:
191:
181:
179:
175:
171:
168:
163:
161:
157:
153:
149:
145:
141:
137:
133:
132:
130:
118:
117:first edition
114:
110:
107:
104:
100:
96:
90:
86:
82:
79:
75:
72:
68:
65:
61:
58:
55:
51:
48:
45:
41:
34:
29:
25:
19:
879:
870:
842:. Retrieved
831:
808:
796:. Retrieved
788:
763:. Retrieved
756:
747:
735:. Retrieved
730:
720:
708:. Retrieved
700:
690:
678:. Retrieved
671:
639:. Retrieved
627:
603:. Retrieved
598:
588:
576:. Retrieved
569:the original
556:
550:
541:
499:
485:
478:
469:
451:
437:
426:
422:
414:
412:
395:
390:
388:
368:
347:
346:
328:
324:
302:
296:
287:
285:
272:future value
251:
243:
241:
231:
221:
211:
207:trigonometry
189:
187:
173:
164:
144:Luca Pacioli
135:
126:
125:
124:
116:
47:Luca Pacioli
18:
419:manuscripts
373:in 1494 by
223:Liber Abaci
203:bookkeeping
165:Written in
148:Renaissance
142:written by
140:mathematics
67:Mathematics
902:1494 books
891:Categories
844:15 January
798:15 January
765:15 January
737:15 January
710:15 January
680:15 January
673:Christie's
641:15 January
634:(Thesis).
605:15 January
578:15 January
514:References
402:, Duke of
389:While the
362:, Duke of
353:vernacular
321:plagiarism
268:rule of 72
167:vernacular
160:accounting
71:Accounting
863:Full text
276:logarithm
218:Fibonacci
77:Publisher
701:MacTutor
494:See also
440:theorems
184:Contents
156:geometry
154:, basic
115:615 pp (
81:Paganini
63:Subjects
53:Language
823:2320658
356:Italian
335:History
323:in the
170:Italian
152:algebra
57:Italian
883:(1994)
821:
444:Euclid
371:Venice
364:Urbino
195:barter
172:, the
85:Venice
43:Author
632:(PDF)
572:(PDF)
547:(PDF)
482:'
479:Summa
452:Summa
423:Summa
415:Summa
404:Milan
396:Summa
391:Summa
329:Summa
325:Summa
288:Summa
232:Summa
174:Summa
112:Pages
846:2020
819:SSRN
800:2020
789:Loci
767:2020
739:2020
712:2020
682:2020
643:2020
607:2020
580:2020
472:lira
413:The
188:The
158:and
97:1494
561:doi
431:by
307:of
295:’s
220:'s
893::
817:.
791:.
787:.
775:^
755:.
729:.
703:.
699:.
670:.
651:^
615:^
597:.
557:35
555:.
549:.
522:^
462:.
410:.
381:.
262:,
258:,
197:,
69:,
848:.
825:.
802:.
769:.
741:.
714:.
684:.
645:.
609:.
582:.
563::
544:"
250:(
134:(
119:)
87:)
83:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
