Electronic edition published by Cultural Heritage Langauge Technologies (with permission from Charles Scribners and Sons) and funded by the National Science Foundation International Digital Libraries Program. This text has been proofread to a low degree of accuracy. It was converted to electronic form using data entry.

COMMANDINO, FEDERICO (b. Urbino, Italy,
1509; d. Urbino, 3 September 1575), mathematics.

physician in his intellectually stimulating household
in Rome.

Commandino had been translating into Latin and
commenting on Archimedes' Measurement of the Circle
(with Eutocius' commentary), Spirals, Quadrature
of the Parabola, Conoids and Spheroids, and Sand-Reckoner.
Besides the first printed edition of the
Greek text of these five works and an earlier Latin
translation of them (Basel, 1544), he had access also
to a Greek manuscript in Venice, where his patron
was residing when Commandino published this
Archimedes volume in 1558.

During the previous year Commandino had heard
complaints about the difficulty of understanding
Ptolemy's Planisphere, which showed how circles on
the celestial sphere may be stereographically projected
onto the plane of the equator. Although the Greek
text of the Planisphere is lost, it had been translated
into Arabic, and from Arabic into Latin. This Latin
version, done at Toulouse in 1144, and Jordanus
de Nemore's Planisphere, both of which had been
printed at Basel in 1536, were edited by Commandino
and, together with his commentary on Ptolemy's
Planisphere, were published at Venice in 1558.

Ptolemy's Analemma explained how to determine
the position of the sun at a given moment in any
latitude by an orthogonal projection using three mutually
perpendicular planes. Again, as in the case of
Ptolemy's Planisphere, no Greek text was available to
Commandino (a portion was later recovered from a
palimpsest); but an Arabic version had been translated
into Latin. This was edited from the manuscript
by Commandino (Rome, 1562). Besides his customary
commentary, he added his own essay On the Calibration
of Sundials of various types, since he felt that
Ptolemy's discussion was theoretical rather than
practical.

Commandino's only other original work, dealing
with the center of gravity of solid bodies, was published
in 1565 at Bologna, of which his patron had
become bishop on 17 July of the preceding year.
Commandino's interest in this topic was aroused by
Archimedes' Floating Bodies, of which he had no
Greek text, unlike the five other Archimedean works
he had previously translated. Since his time a large part
of the Greek text of Floating Bodies has been recovered,
but he had only a printed Latin translation
(Venice, 1543, 1565), which he commented on and
corrected (Bologna, 1565). In particular the proof of
proposition 2 in book II was incomplete, and Commandino
filled it out. One step required knowing the
location of the center of gravity of any segment of
a parabolic conoid. No ancient treatment of such a
problem was then known, and Commandino's was the
first modern attempt to fill the existing gap.

Archimedes' Floating Bodies assumed the truth of
some propositions for which Commandino searched
in Apollonius' Conics. Of the Conics' eight books only
the first four are extant in Greek, and he had access
to them in manuscript. An earlier Latin translation
(Venice, 1537) was superseded by his own (Bologna,
1566), to which he added Eutocius' commentary, the
relevant discussion in Pappus' Collection (book VII),
the first complete Latin translation (from a Greek
manuscript) of Serenus' Section of a Cylinder and Section
of a Cone, and his own commentary.

Overwork and the death of his patron on 28 October
1565 greatly depressed Commandino; and he
returned to Urbino, where he could live quietly, for
many months on a salt-free diet. He resumed his
former activities, however, after being visited by John
Dee, who gave him a manuscript Latin translation of
an Arabic work related to Euclid's On Divisions (of
figures), of which the Greek original is lost. Commandino
published this Latin translation and added
a short treatise of his own to condense and generalize
the discussion in the manuscript (Pesaro, 1570).

At the request of his ruler's son, Commandino
translated Euclid's Elements into Latin and commented
on it extensively (Pesaro, 1572). Also in 1572
he published at Pesaro his Latin translation of and
commentary on Aristarchus' Sizes and Distances of the
Sun and Moon, with Pappus' explanations (Collection,
book VI, propositions 37-40).

For those of his countrymen who did not know
Latin, Commandino supervised a translation of Euclid's
Elements into Italian by some of his students
(Urbino, 1575). His own Latin translation of Hero's
Pneumatics (Urbino, 1575) was seen through the press
by his son-in-law immediately after his death. From
a nearly complete manuscript, needing three months'
work at most, his faithful pupil Guidobaldo del Monte
published Commandino's Latin translation of and
commentary on Pappus' Collection, books III-VIII
(Pesaro, 1588).

In the sixteenth century, Western mathematics
emerged swiftly from a millennial decline. This rapid
ascent was assisted by Apollonius, Archimedes,
Aristarchus, Euclid, Eutocius, Hero, Pappus, Ptolemy,
and Serenus—as published by Commandino.

BIBLIOGRAPHY

A list of Commandino's publications is available in
Pietro Riccardi, Biblioteca matematica italiana, enl. ed., 2
vols. (Milan, 1952), I, cols. 42, 359-365; II, pt. 1, col. 15;
II, pt. 2, col. 117; II, pt. 5. cols. 9, 49-50; II, pt. 6, col. 189;
II, pt. 7, cols. 25-26. Riccardi omits Conoids and Spheroids
(I, col. 42); misattributes the Italian translation of Euclid's
Elements to Commandino himself (I, col. 364); and misdates