31:
376:
116:, Jordanus of Saxony (d. 1237) wrote two mathematical texts with titles similar to two by Jordanus de Nemore, but this late suggestion is more likely a confusion on the part of Trivet, rather than any proof of identity. Jordanus of Saxony never uses the name âde Nemoreâ and is nowhere else credited with mathematical writings â in fact he had lectured in theology at the
489:
352:, Nuremberg, 1543) â was the heading under which all the treatises were grouped. Eneström thought it highly unlikely, however, that this version was the work of Jordanus since no manuscript ascribes it to him (if they give an author, it is generally a Magister Gernarus, or Gerhardus or Gernandus). The first part of this treatise (also known as the
446:. Jordanus used a system similar to that of ViĂšte (although couched on non-symbolic terms) of formulating the equation (setting out the problem in terms of what is known and of what is to be found), of transforming the initial given equation into a solution, and the introduction of specific numbers that fulfil the conditions set by the problem.
507:). The first and historically the most important proposition proves for all cases that circles on the surface of a sphere when projected stereographically on a plane remain circles (or a circle of infinite radius, i.e., a straight line). While this property was known long before Jordanus, it had never been proved.
389:
contains over 400 propositions divided into ten books. There are three versions or editions in manuscript form, the second one with different or expanded proofs than found in the first, and a number of propositions added at the end; the third version inserts the added propositions into their logical
465:
at its best. It contains propositions on such topics as the ratios of sides and angles of triangles; the division of straight lines, triangles, and quadrangles under different conditions; the ratio of arcs and plane segments in the same or in different circles; trisecting an angle; the area of
477:) which divides the text into books, re-arranges and expands book 2, and adds propositions 4-12 to 4-28. This latter set of 17 propositions also circulated separately. While the longer version may not be by Jordanus, it was certainly complete by the end of the thirteenth century.
510:
There are three versions of the treatise: the basic text, a second version with an introduction and a much expanded text, and a third, only slightly expanded. The introduction is sometimes found with version 1 and 3, but it was obviously written by someone else.
405:. Definitions, axioms and postulates lead to propositions with proofs which are somewhat sketchy at times, leaving the reader to complete the argument. Here also Jordanus uses letters to represent numbers, but numerical examples, of the type found in the
578:, ed. Ernest A. Moody and Marshall Clagett (Madison: University of Wisconsin Press, 1952). The commentaries are also found in Joseph E. Brown, âThe âScientia de ponderibusâ in the Later Middle Ages,â PhD. Dissertation, University of Wisconsin, 1967. The
88:
No biographical details are known about
Jordanus de Nemore. Cited in the early manuscripts simply as âJordanusâ, he was later given the sobriquet of âde Nemoreâ (âof the Forest,â âForesterâ) which does not add any firm biographical information. In the
255:
Related to these treatises is an anonymous set of comments, each of which begins with the words âAliud commentumâ (and thus known as the âAliud commentumâ version). This commentary surpasses all others, especially the commentary on
Proposition 1.
424:, Barnabas Hughes, has found two sets of manuscripts for this text, one containing 95 propositions, the other, 113. As well some of the common propositions have different proofs. There are also 4 digests or revisions in manuscript form.
120:. Likewise the name of Jordanus of Saxony is never found with a mathematical text. This identity, popular among some in the nineteenth and twentieth centuries, has been for the most part abandoned.
634:
5. Geometry: "De triangulis" was first published by M.Curtze in "Mittheilungen des
Copernicusvereins fĂŒr Wissenschaft und Kunst" Heft VI - Thorn, 1887. See in Kujawsko-Pomorska Digital Library:
108:, but the text in question was not written by Jordanus and this possible association is without foundation. A fourteenth-century chronicle of the Order of Preachers by the Englishman
601:
treatises: The articles by Gustaf Eneström, which contain the Latin text of the introductions, definitions and propositions, but only some of the proofs, were published in
199:
seems to be the one work which can definitely be ascribed to
Jordanus; and the first of the series. Jordanus took what Joseph Brown has called the "Logicianâs Abstract of
252:. This is usually ascribed to Jordanus, but more likely it is the work of an unidentified mathematician because the citations by Jordanus of his other works are deleted.
30:
616:(1455â1536) published a version (with his own demonstrations and comments) in Paris in 1496; this was reprinted Paris, 1514. The modern edition is: H. L. L. Busard,
123:
It is assumed that
Jordanus did work in the first part of the thirteenth century (or even in the late twelfth) since his works are contained in a booklist, the
871:
803:
A discussion of the various texts, and a list of the manuscripts and printed editions (to 1976), are found in
Thomson, âJordanus de Nemore: Opera,â 97-144.
657:
and the introduction were published in the sixteenth century â Basel, 1536 and Venice, 1558. All versions are edited and translated in: Ron B. Thomson,
342:
is a spurious attribution although for a long time this item was ascribed to
Jordanus. Up until Eneström began to sort out the various treatises, the
431:
was the first treatise in advanced algebra composed in
Western Europe, building on elementary algebra provided in twelfth-century translations from
827:
876:
881:
778:
For a list of these dubious and spurious items, plus false attributions and ghost editions, see Ron B. Thomson, âJordanus de Nemore: Opera,â
184:
also proves the conditions of equilibrium of unequal weights on planes inclined at different angles â long before it was re-established by
390:
position in the text, and again changed some of the proofs. Jordanusâ aim was to write a complete summary of arithmetic, similar to what
60:. He wrote treatises on at least 6 different important mathematical subjects: the science of weights; âalgorismiâ treatises on practical
765:
Published by H. L. L. Busard, âDer
Traktat De isoperimetris, der unmittelbar aus dem Griechischen ins Lateinische ĂŒbersetz worden ist,â
211:) and created a new treatise (7 axioms and 9 propositions) in order to establish a mathematical basis for the four propositions on the
402:
176:
in his discussion of "virtual" displacements (this being another interpretation of Duhem) of objects in equilibrium. He proves the
222:. An early commentary on this (which also contains a necessary correction to Proposition 9) is the âCorpus Christi Commentaryâ.
375:
360:) contains definitions and 42 propositions. Eneström shows that while different from the algorismi treatises of Jordanus, the
650:(Philadelphia: American Philosophical Society, 1984), 5: 196-293 and 346-477, which is much improved over Curtze's edition.
97:
792:
591:
677:
832:
500:
73:
605:, ser 3, vol. 7 (1906â07), 24-37; 8 (1907â08), 135-153; 13 (1912â13), 289-332; 14 (1913â14) 41-54 and 99-149.
574:
1. Mechanics: The three main treatises and the âAliud commentumâ version (Latin and
English) are published in
56:
and scientist. The literal translation of Jordanus de Nemore (Giordano of Nemi) would indicate that he was an
344:
543:(âa short introductory exerciseâ?) are dubiously ascribed to Jordanus. A number of other texts including a
401:
Jordanus collected and organized the whole field of arithmetic, based both on Euclidâs work and on that of
105:
53:
839:
627:): The text was published in the 19th century, but a critical edition now exists: Jordanus de Nemore,
286:(its opening words) appears to be the earliest form of the work, closely related to the much expanded
436:
177:
128:
730:(Toronto: Pontifical Institute of Mediaeval Studies, 1978), chapter 1: âJordanus the Mathematician.â
818:
349:
204:
117:
822:
852:
845:
613:
563:
is a fiction, in italian, based on historical research, around the life of Jordanus de Nemore.
272:
571:
Most of Jordanus' works have been published in critical editions in the twentieth century.
189:
113:
109:
469:
Again there are two versions of this text: the shorter and presumably first edition (the
618:
Jordanus de Nemore, De elementis arithmetice artis. A Medieval Treatise on Number Theory
583:
215:
865:
305:, made either by Jordanus himself or by some other thirteenth-century mathematician.
301:
contains 21 definitions and 34 propositions. This is probably a later version of the
80:. We know nothing about him personally, other than the approximate date of his work.
560:
212:
185:
165:
17:
635:
720:âą Barnabas B. Hughes, âBiographical Information on Jordanus de Nemore to Date,â
443:
440:
172:, 1905) thought that Jordanus also introduces infinitesimal considerations into
90:
77:
435:
sources. It anticipates by 350 years the introduction of algebraic analysis by
241:
which improve some of the demonstrations and better integrate the two sources.
504:
488:
386:
276:
61:
536:
313:
149:
631:, ed. Barnabas B. Hughes (Berkeley: University of California Press, 1981).
76:. Most of these treatises exist in several versions or reworkings from the
462:
395:
356:) contains definitions, axioms and 43 propositions. The second part (the
268:
69:
248:
is a skillfully corrected and expanded version (45 propositions) of the
112:(or Triveth, 1258â1328) suggested that the second master-general of the
421:
188:(with his clootcrans -- "wreath of spheres" experiment) and later by
173:
157:
101:
65:
718:, ed. Thomas Glick, et al. (New York: Routledge, 2005), pp. 294-295;
693:
Ron B. Thomson, âJordanus de Nemore and the University of Toulouse.â
524:
432:
391:
161:
93:
his name was often given as "Jordanus Nemorarius", an improper form.
728:
Jordanus de Nemore and the Mathematics of Astrolabes: De Plana Spera
712:, ed. Charles C. Gillispie (New York: Scribners, 1973), 7: 171-179;
659:
Jordanus de Nemore and the Mathematics of Astrolabes: De Plana Spera
646:
have been critically edited and translated in: Marshall Clagett,
487:
374:
57:
29:
499:
This treatise of five propositions deals with various aspects of
96:
An entry in the nineteenth-century manuscript catalogue for the
466:
triangles given the length of the sides; squaring the circle.
152:) owes much of its importance to the work of Jordanus. In the
791:
Eresia Pura, by Adriano Petta, Publisher "La Lepre", (2012)
661:(Toronto: Pontifical Institute of Mediaeval Studies, 1978).
716:
Medieval Science, Technology, and Medicine. An Encyclopedia
854:
Sphaerae atque astrorum coelestium ratio, natura, et motus
653:
6. Stereographic projection: The text of version 3 of the
35:
Sphaerae atque astrorum coelestium ratio, natura, et motus
331:, and contains and expands the propositions found in the
275:
early in the twentieth century, dealing with practical
237:. There are at least two commentary traditions to the
582:
and the âAliud commentumâ version were published by
320:â they are often found together in the manuscripts.
229:
fuses the seven axioms and nine propositions of the
754:Jordanus de Nemore, De elementis Arithmetice Artis
741:Jordanus de Nemore, De elementis Arithmetice Artis
620:(Stuttgart: Franz Steiner Verlag, 1991), 2 parts.
743:(Stuttgart: Franz Steiner, 1991), Part I, p. 12.
586:(= Peter Bienewitz) in Nuremberg, 1533; and the
203:" (a skillful compression of the conclusions of
636:http://kpbc.umk.pl/dlibra/docmetadata?id=39881
8:
348:â since it was the only one published (ed.
335:â again a re-edition of the original text.
156:, he introduces the concept of âpositional
695:British Journal for the History of Science
714:âą Edward Grant, âJordanus de Nemore,â in
708:âą Edward Grant, âJordanus de Nemore,â in
148:The medieval âscience of weightsâ (i.e.,
54:thirteenth-century European mathematician
27:Thirteenth-century European mathematician
531:(on figures with equal perimeters), the
271:treatises in this category, examined by
828:MacTutor History of Mathematics Archive
670:
197:Elementa super demonstrationem ponderum
180:by means of the principle of work. The
154:Elementa super demonstrationem ponderum
104:suggested that Jordanus taught at the
7:
872:13th-century Italian mathematicians
851:Jordanus : Nemorarius (1536).
710:Dictionary of Scientific Biography
706:For biographical information, see:
471:Liber philotegni Iordani de Nemore
364:is still closely related to them.
131:, compiled between 1246 and 1260.
44:(fl. 13th century), also known as
25:
857:(in Latin). Basel: Johann Walder.
316:seems to be a second part of the
841:De ponderibus propositiones XIII
682:Les ingénieurs de la Renaissance
233:to the four propositions of the
576:The Medieval Science of Weights
420:The editor of this treatise on
610:De elementis arithmetice artis
533:Demonstrationes pro astrolapsu
380:Demonstrationes in Arithmetica
1:
877:13th-century writers in Latin
844:- digital facsimile from the
648:Archimedes in the Middle Ages
370:De elementis arismetice artis
290:. Eneström believed that the
882:13th-century Italian writers
838:Nemorarius Jordanus (1553)
655:Demonstratio de plana spera
644:Liber de triangulis Iordani
567:Editions of Jordanusâ works
559:The book "Eresia Pura", by
483:Demonstratio de plana spera
475:Liber de triangulis Iordani
294:was certainly by Jordanus.
160:â and the use of component
98:SĂ€chsische Landesbibliothek
898:
551:are spurious ascriptions.
515:Dubious and spurious works
481:Stereographic projection:
327:likewise is linked to the
793:Eresia pura on www.ibs.it
614:Jacques LefĂšvre dâĂtaples
329:Demonstratio de algorismo
325:Demonstratio de minutiius
299:Demonstratio de algorismo
288:Demonstratio de algorismo
833:University of St Andrews
640:Liber philotegni Iordani
501:stereographic projection
473:) and a longer version (
144:(the science of weights)
74:stereographic projection
362:Algorismus demonstratus
345:Algorismus demonstratus
340:Algorismus demonstratus
170:Origines de la statique
603:Biblioteca Mathematica
503:(used in planispheric
496:
382:
358:Algorismus de minutiis
354:Algorismus de integris
142:scientia de ponderibus
106:University of Toulouse
38:
823:"Jordanus Nemorarius"
638:. More recently, the
549:Compositum astrolabii
491:
378:
318:Communis et consuetus
303:Communis et consuetus
292:Communis et consuetus
284:Communis et consuetus
33:
819:Robertson, Edmund F.
724:62 (1975), 151-156;
539:engraving), and the
333:Tractatus minutiarum
310:Tractatus minutiarum
129:Richard de Fournival
817:O'Connor, John J.;
608:3. Arithmetic (the
588:De ratione ponderis
580:Liber de ponderibus
495:, geometric drawing
246:De ratione ponderis
239:Liber de ponderibus
227:Liber de ponderibus
182:De ratione ponderis
118:University of Paris
64:; pure arithmetic;
46:Jordanus Nemorarius
18:Jordanus Nemorarius
846:Linda Hall Library
726:âą Ron B. Thomson,
697:7 (1974), 163-165.
555:Historical fiction
497:
383:
42:Jordanus de Nemore
39:
782:38 (1976)124-133.
780:Mediaeval Studies
769:42 (1980), 61-88.
767:Mediaeval Studies
739:H. L. L. Busard,
594:in Venice, 1565.
590:was published by
545:Liber de speculis
521:De proportionibus
461:This is medieval
409:, are not given.
385:This treatise on
16:(Redirected from
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858:
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629:De numeris datis
592:NicolĂČ Tartaglia
541:Pre-exercitamina
452:Liber philotegni
429:De numeris datis
415:De numeris datis
407:De numeris datis
368:Arithmetic: The
350:Johannes Schöner
220:Liber de canonio
209:Liber karastonis
205:ThÄbit ibn Qurra
178:law of the lever
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34:
444:mathematics
441:Renaissance
218:called the
140:Mechanics:
125:Biblionomia
91:Renaissance
78:Middle Ages
866:Categories
505:astrolabes
450:Geometry:
427:Jordanusâ
387:arithmetic
297:The later
277:arithmetic
235:De canonio
62:arithmetic
599:Algorismi
537:astrolabe
314:fractions
269:algorismi
263:treatises
261:Algorismi
150:mechanics
752:Busard,
642:and the
463:geometry
454:and the
403:Boethius
396:geometry
250:Elementa
231:Elementa
168:(in his
135:Writings
70:geometry
52:, was a
597:2. The
527:), the
422:algebra
216:balance
190:Galileo
174:statics
158:gravity
102:Dresden
66:algebra
58:Italian
547:and a
525:ratios
433:Arabic
392:Euclid
162:forces
72:; and
37:, 1536
722:Janus
665:Notes
439:into
213:Roman
535:(on
523:(on
519:The
338:The
323:The
308:The
282:The
244:The
225:The
195:The
84:Life
48:and
612:):
312:on
207:âs
127:of
100:in
868::
831:,
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398:.
279:.
192:.
164:.
68:;
684:.
20:)
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