"He rendered no less service to sci ence, by treating, in a clear and geome trical manner, the doctrine of motion, which has been justly called the key of nature. The rational part of mechanics had been so much neglected, that scarce ly any improvement was made in it for al most 2000 years ; but Galileo has given as fully the theory of equable motions, and of such as are uniformly accelerated or retarded, and of these two compound ed together. He first demonstrated, that the spaces described by heavy bodies, from the beginning of their descent, are as the squares of the times ; and that a body, projected in any direction that is not perpendicular to the horizon, de scribes a parabola. These were the be ginnings of the doctrine of the motion of heavy bodies, which has been since car ried to so great a height by Sir Isaac Newton. In geometry, he invented the cycloid, or trochoid, though the proper ties of it were afterwards chiefly demon strated by his pupil TorrIcelli. lie hi* vented the simple pendulum, and 'made use of it in his astronomical experiments: he had also thoughts of applying it to clocks, but did not execute that design. The glory of that invention was reserv ed for his son Vincenzo, who made the experiment at Venice in 1649; and Huygens afterwards carried the inven tion to perfection. Of Galileo's inven tion also was the machine with which the Venetians render their laguna fluid and navigable.
" He also discovered the gravity of the air, and endeavoured to compare it with that of water ; and opened several other inquiries in natural philosophy. He was not esteemed and followed by philoso phers only ; but was honoured by per sons of the greatest distinction of all na tions. Galileo had scholars worthy of so great a master, by whom the gravitation of the atmosphere was fully established, and its varying ,pressure accurately and conveniently measured, by the column of quicksilver of equal weight sustained by it in the barometrical tube. The elas ticity of the air, by which it perpetua'ly endeavours to expand itself, and while tt admits of condensation, resists in propor tion to its density, was a phenomenon of a new kind, (the common fluids having no such property,) and of the utmost im portance to philosophy. These princi ples opened a vast field of new and use ful knowledge, and explained a great va riety of phenomena, which had been ac counted for in an absurd manner before that time. It seemed as if the air, the fluid in which men lived from the begin ning, had been then first discovered. Philosophers were every where busy, enquiring into the various properties and their effects ; and valuable discoveries rewarded their industry. Of the great number who distinguished themselvs on this occasion, we cannotbut mention Tor xicelli and Viviani, in Italy ; Pascal, in France ; Otto Guricke, in Germany ; and Boyle. in England." Galileo wrote a number of treatises, of which the principal, published during his life-time, besides his" Mechanics," " Ba lance," and " Dialogues," already men tioned, were, " The Operations of the Compass, geometrical and military," 1606 ; " A Discourse, addressed to the Most Serene Cosmo II. Grand Duke of
Tuscany, concerning the swimming of Bodies upon, and their submersion in, Water," 1612: " Nuncius Sidereus," 1610, of which a Continuation," or " An Essay on the History of Galileo's last Observations on Saturn, Mars, Venul, and the Sun, &c."w as afterwards collected from letters between Galileo and his cor respondents ; " A Letter concerning the Trepidation of the Moon, lately disco vered, inscribed to Alphonso Antonini, with Antonini's Answer," 1638 , " A Dis course of the Solar Spots, &c. with Pre dictions and Ephemerides of the Medi cean Planets," 1613 ; the famous Italian: piece, entitled, II Saggiatore," written in defence of Guiducci's " Discourse oh Comets," and containing a complete ac count of the physiology and astronomy of our author, printed in 1623 ; " A Letter to Prince Leopold of Tuscany, examin ing the fiftieth chapter of Licetus's Le theosphoros;" " A Letter to Christopher Greinhergerus, concerning the Montuo sity of the Moon," 1611 ; " Mathematical Discourses and Demonstrations concern ing two new Sciences, relating to Me chanics and local Motions, together with an Appendix concerning the Centre of Gravity in some Solids," 1638, &c.
The preceding articles, together with some other treatises, written either b'y Galileo, or by some of his disciples, in defence of his doctrines and observations, were collected and published by Aleno lessi, in 1656, under the title of" l'Opere de Galileo Galilei Lynceo, nohile Fioren tino," &c. in two volumes quarto. Seve ral of these pieces were translated into English, and published by Thomas Salis bury, in his " Mathematical Collections," in two vols. folio.
A volume also of his "Letters," to se veral learned men, and solutions of a va riety of problems, was published at Bo logna, in quarto. Hislast disciple, Vincen zo Viviani, who proved a very eminent mathematician, methodised a piece of his master's, and published it under the title of" Quinto I.ibro de gli Elementi d'Eu cfid," &c.1674, quarto ; and be also pub lished some other pieces of Galileo, in cluding extracts from his " Letters to a learned Frenchman," in which the au thor gives an account of the works which he intended to have published, and an extract of a letter to John Camillo, a ma-. thematician of Naples, concerning the angle of contact. Many other of Gali leo's writings were unfortunately lost to the world, owing to the superstition of one of his ignorant nephews ; who, con sidering that his uncle died a prisoner of the holy office,though permitted to reside in his own house, suspected that his pa pers mightcontain dangerous heresies,and therefore committed them to the flames; Sir John Finch, in a letter to Thomas Salisbury, attributes the destruction of Galileo's MSS. to his widow's devotion, and the fanaticism of her confessor : but the best authorities maintain that our phi losopher was never married. His son Vincenzo Galilei, who, as we have alrea dy seen, honourably supported his fa ther's reputation, by first applying his in vention of the pendulum to clock-work, was of illegitimate birth.