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).