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JORDANUS DE NEMORE (fl. ca. 1220), mechanics,
mathematics.
BIBLIOGRAPHY
As yet there is no ed. of the ten-book Arithmetica,
although the enunciations of the propositions were published
by Jacques Lefèvre d'Étaples (Jacobus Faber Stapulensis),
who supplied his own demonstrations and comments
in Arithmetica (Iordani Nemorarii) decem libris
demonstrata (Paris, 1496, 1503, 1507, 1510, 1514). At least
sixteen complete or partial MSS of it are presently known,
among which are two excellent and complete thirteenth-century
MSS: Paris, BN 16644, 2r-93v; and Vat. lat.,
Ottoboni MS 2069, 1r-51v.
The Latin text of the definitions and enunciations of the
34 propositions of the Demonstratio Jordani de algorismo
were published by G. Eneström, “Über die ‘Demonstratio
Jordani de algorismo,’ ” in Bibliotheca mathematica,
3rd ser., 7 (1906-1907), 24-37, from MSS Berlin, lat. 4?
510, 72v-77r (Königliche Bibliothek, renamed Preussische
Staatsbibliothek in 1918; the fate of this codex after
World War II, when the basic collection was divided
between East and West Germany, is unknown to me) and
Dresden Db 86, 169r-175r. The Demonstratio appears to
be an altered version of a similar and earlier work beginning
with the words “Communis et consuetus ...,” which
Eneström called Opus numerorum. The Latin text of its
introduction and a comparison of its propositions with
those of the Demonstratio Jordani were published by Eneström
as “Über eine dem Jordanus Nemorarius zugeschriebene
kurze Algorismusschrift,” in Bibliotheca mathematica,
3rd ser., 8 (1907-1908), 135-153. He relied primarily on
MS Vat. lat. Ottob. 309, 114r-117r, supplemented by MSS
Vat. lat. Reg. Suev. 1268, 69r-71r; Florence, Bibl. Naz.
Centr., Conv. Soppr. J.V. 18 (cited by Eneström as San
Marco 216, its previous designation), 37r-39r; and Paris,
Mazarin 3642, 96r and 105r. Since the Demonstratio Jordani
was definitely ascribed to Jordanus, and the Opus
numerorum seemed an earlier version of it, Eneström conjectured
that the Opus was a more likely candidate for
Jordanus' original work, while the Demonstratio Jordani,
which omits most of the introduction but expands the
text itself, may have been revised by Jordanus or someone
else.
Each of these two treatises has associated with it a brief
work, attributed in some MSS to Jordanus, on arithmetic
operations with fractions. The treatise associated with the
Opus numerorum, which Eneström calls Tractatus
minutiarum,
contains an introduction and 26 highly abbreviated
propositions; the work on fractions associated with the
Demonstratio Jordani de algorismo, which Eneström calls
Demonstratio de minutiis, consists of an introduction and
35 propositions. Although the introductions differ, all
26 propositions of the Tractatus minutiarum have, according
to Eneström, identical counterparts in the longer
Demonstratio de minutiis. In “Das Bruchrechnen des Jordanus
Nemorarius,” in Bibliotheca mathematica, 3rd ser.,
14 (1913-1914), 41-54, Eneström includes a list of MSS
for both treatises (pp. 41-42), the Latin texts of the introductions,
the texts of the enunciations of the propositions,
and analytic representations of the propositions. By analogy
with his reasoning about the relations obtaining
between the Opus numerorum and Demonstratio Jordani
de algorismo, Eneström conjectures that Jordanus is the
author of the Tractatus minutiarum, the briefer treatise
associated with the Opus numerorum. One of the MSS is
Bibl. Naz. Centr., Conv. Soppr. J.V. 18, 39r-42v, which
follows immediately after the Opus numerorum in the same
codex cited above; correspondingly, MS Berlin, lat. 4? 510,
72v-77r, of the Demonstratio Jordani de algorismo is followed
immediately by a version of the Demonstratio de
minutiis on fols. 77r-81v, a relation which also seems to
obtain in Bibl. Naz. Centr., Conv. Soppr. J.I. 32, 113r-118v,
118v-124r. Whether the two algorithm treatises and
the two associated treatises on fractions bear any relation
to works (5), (6), (7), or (10), cited above from the
Biblionomia, has yet to be determined and may, indeed, be
impossible to determine. The Algorismus demonstratus published
in 1534 by J. Schöner and formerly ascribed to Jordanus,
was composed by a Master Gernardus, who is
perhaps identical with Gerard of Brussels.
The Liber de proportionibus, mentioned in the Biblionomia,
is probably a brief work by Jordanus beginning with
the words “Proportio est rei ad rem determinata secundum
quantitatem habitudo ....” A seemingly complete MS of
it is Florence, Bibl. Naz. Centr., Conv. Soppr. J.V. 30,
8r-9v. Other MSS are listed in L. Thorndike and P. Kibre,
A Catalogue of Incipits of Mediaeval Scientific Writings in
Latin, rev. ed. (Cambridge, Mass., 1963), col. 1139. The
Suppletiones plane spere of the Biblionomia is probably a
commentary on Ptolemy's Planisphaerium. According to
G. Sarton, Introduction to the History of Science, 3 vols.
in 5 pts., II, pt. 2 (Baltimore, 1931), 614, it is “a treatise on
mathematical astronomy, which contains the first general
demonstration of the fundamental property of stereographic
projection--i.e., that circles are projected as circles
(Ptolemy had proved it only in special cases).” In Thorndike
and Kibre, op. cit., Jordanus' Planisphaerium is listed
under three separate and different incipits (see cols. 1119,
1524, and 1525, where MSS are listed for each). An edition
appeared at Venice in 1558, under the title Ptolemaei
Planisphaerium: Iordani Planisphaerium; Federici Commandi
Urbinatis in Ptolemaei Planisphaerium commentarius. A
work on isoperimetric figures, De figuris ysoperimetris, is
also attributed to Jordanus: MSS Florence, Bibl. Naz.
Centr., Conv. Soppr. J.V. 30, 12v (a fragment) and
Vienna 5203, 142r-146r, the latter actually copied by
Regiomontanus, who was also acquainted with Jordanus'
De triangulis, Planisphaerium, Arithmetica, De numeris
datis, and De proportionibus; the enunciations of the eight
propositions in the Vienna MS were published by Maximilian
Curtze, “Eine Studienreise,” in Zentralblatt für
Bibliothekswesen, 16 (1899), 264-265.
II. SECONDARY LITERATURE.
The most significant studies
on Jordanus are monographic in character and have been
cited above, since they are associated with editions and
translations of his works. No general appraisal and evaluation
of his scientific works has yet been published. To
what has already been cited, the following may be added:
O. Klein, “Who Was Jordanus Nemorarius?,” in Nuclear
Physics, 57 (1964), 345-350; Benjamin Ginzberg, “Duhem
and Jordanus Nemorarius,” in Isis, 25 (1936), 341-362,