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.

MONTE, GUIDOBALDO, MARCHESE DEL (b.
Pesaro, Italy, 11 January 1545; d. Montebaroccio,
6 January 1607), mechanics, mathematics, astronomy.

does the power which sustains to the weight sustained.
Consequently, the same principle and proportions
cannot hold good for both moving and sustaining.

Galileo overcame this objection to a unified
mechanics by positing that an insensibly greater
amount of power was needed to move, than to
sustain, a given weight. Guidobaldo had scorned the
use of insensibilia in mechanics, probably because they
were not susceptible of precise mathematical definition.
Like his contemporary Benedetti, Guidobaldo
attacked Jordanus, Cardano, and Tartaglia for
assuming that the lines of descent of heavy bodies were
parallel rather than convergent to the center of the
earth. The answer of both Tartaglia and Galileo to
this demand for unreasonable exactitude in mechanics
was that, at a great distance from the center, the
difference between the parallel and convergent
descents was insensible.

This extreme concern for precision led Guidobaldo
to reject the valid inclined-plane theorem of Jordanus
in favor of the erroneous theorem of Pappus. Pappus'
premise that a definite amount of force was needed to
move a body horizontally was in accord with the view
of Guidobaldo that more power was required to move
than to sustain the body. Moreover, Jordanus'
theorem seemed vitiated by its neglect of the angle of
convergence of the descents. By supposing against
Pappus (whom he named) and Guidobaldo (whom he
did not name) that an insensible amount of power was
required to move a body horizontally, Galileo was
able to apply the principle of virtual displacements to
both static and dynamic cases and was able to frame
useful principles of virtual work and inertia.
Guidobaldo's quest for mathematical rigor may have
barred such imaginative concepts from his mind.

The most fruitful section of the Liber mechanicorum
deals with pulleys, reducing them to the lever. This
analysis--which is far superior to that of Benedetti--was
adopted by Galileo. In two subsequent mechanical
works Guidobaldo developed other ideas of this first
book. These works were the Paraphrase of Archimedes:
Equilibrium of Planes (1588), a copy of which was sent
to Galileo, and the posthumous De cochlea (1615).

Guidobaldo was Galileo's patron and friend for
twenty years and was possibly the greatest single
influence on the mechanics of Galileo. In addition to
giving Galileo advice on statics, Guidobaldo discussed
projectile motion with him, and both scientists
reportedly conducted experiments together on the
trajectories of cannonballs. In Guidobaldo's notebook
(Paris MS 10246), written before 1607, it is asserted
that projectiles follow parabolic paths; that this path
is similar to the inverted parabola (actually a catenary)
which is formed by the slack of a rope held horizontally;
and that an inked ball that is rolled sideways
over a near perpendicular plane will mark out such a
parabola. Remarkably the same two examples are
cited by Galileo at the end of the Two New Sciences,
although only as postscripts to his main proof--which
is based on the law of free fall--of the parabolic
trajectory.

Among Guidobaldo's nonmechanical works are
three manuscript treatises on proportion and Euclid;
two astronomical books, the Planisphaeriorum (1579)
and the posthumous Problematum astronomicorum
(1609); and the best Renaissance study of perspective
(1600).

Guidobaldo helped to develop a number of
mathematical instruments, including the proportional
compass, the elliptical compass, and a device for
dividing the circle into degrees, minutes, and seconds.

BIBLIOGRAPHY

I. ORIGINAL WORKS.

Guidobaldo's published works are
Liber mechanicorum (Pesaro, 1577; repr. Venice, 1615);
Italian trans. by Filippo Pigafetta, Le mechanice (Venice,
1581; repr. Venice, 1615); Planisphaeriorum universalium
theorica (Pesaro, 1579; repr. Cologne, 1581); De ecclesiastici
kalendarii restitutione opusculum (Pesaro, 1580); In duos
Archimedis aequeponderantium libros paraphrasis (Pesaro,
1588); Perspectivae libri sex (Pesaro, 1600); Problematum
astronomicorum libri septem (Venice, 1609); and De
cochlea libri quatuor (Venice, 1615).

MS works of Guidobaldo are the Meditatiunculae,
Bibliothèque Nationale (Paris), MS Lat. 10246; In quintum
Euclidis elementorum commentarius and De proportione
composita opusculum, Biblioteca Oliveriana (Pesaro),
respectively MSS 630 and 631; and a treatise on the reform
of the calendar, Biblioteca Vaticana, MS Vat. Lat. 7058.
A collection of drawings of machines by Francesco di
Giorgio Martini in the Biblioteca Marciana (Venice), MS
Lat. VIII 87(3048), was formerly owned by Guidobaldo.
The present location of the MS In nonnulla Euclidis
elementorum expositiones (item 194 bis in the Boncompagni
Sale Catalogue of 1898) is not known.

Guidobaldo's letters (some are copies) are scattered:
Biblioteca Nazionale Centrale (Florence), MSS Galileo 15,
16, 88; Biblioteca Comunale “A. Saffi” (Forlì), MSS
Autografi Piancastelli Nos. 755, 1508; Archivio di Stato
(Mantua), Corrispondenza Estera, E.XXVIII, 3; Biblioteca
Ambrosiana (Milan), MSS D.34 inf., J.231 inf.,
R.121 sup.; Bodleian Library (Oxford), MS Canon.
Ital. 145; Bibliothèque Nationale (Paris), MS 7218 Lat.;
Biblioteca Oliveriana (Pesaro), MSS 193 Ter.; 211/ii; 426;
1580 (MS 1538 = Tasso to Guidobaldo); Archivum
Pontificiae Universitatis Gregorianae (Rome), Cassetta 1,
MSS 529-530; Biblioteca Comunale degli Intronati
(Siena), MS K.XI.52; Biblioteca Universitaria (Urbino),
MS Carità Busta 47, Fasc. 6; and Biblioteca Nazionale
Marciana (Venice), MS Ital. IV, 63 (Rari V.259).