20 LECTURE II. 



of going round the figure, destroy each other, and the body remains at 

 rest. We may understand the truth of this proposition by imagining each 

 motion to take place in succession for an equal small interval of time ; 

 then the point would describe a small polygon similar to the original one, and 

 would be found, at the end of every such interval, in its original situation. 

 When the motions to be combined are numerous and diversified, it is 

 often convenient to resolve each motion into three parts, reduced to the 

 directions of three given lines perpendicular to each other. It is easy to 

 find in this manner, by addition and subtraction only, the general result of 

 any number of motions. We may describe the flight of a bird ascending 

 in an oblique direction, by estimating its progress northwards or south- 

 wards, eastwards or westwards, and at the same time upwards, and we may 

 thus determine its place as accurately as by ascertaining the immediate 

 bearing and angular elevation of its path, and its velocity in the direction 

 of its motion. 



LECT. II. ADDITIONAL AUTHORITIES. 



Wjallis's Ph. Tr. iii. 864. Mechanica, 4to, Lon. 1670. Opera, 3 vols. fol. Oxf. 1713, 

 i. 571. Varignon, Nouvelle Mecanique, 2 vols. 4to, Paris, 1725 (Posthumous). Hist, et 

 Mem. de 1'Acad. de Paris, 1714, p. 280, H. 87 ; 1733, x. 301. Roberval, ibid. vi. 

 1,68. Joh. Bernoulli, Opera, 4 vols. 4to, Lausanne, 1 742, iii. 1. Hermann, Phoro- 

 nomia, 4to, Amst. 1716. Courtivron's Researches, Hist, et Mem. de Paris, 1748, 

 p. 304 ; 1749, p. 15. Kraftii Mechanik, 2 vols. 4to, Soroe, 1762-4 ; also, 4to, Bat. 

 1772, and Dresd. 1787. See also LECT. XIX. 



Elementary Treatises on Mechanics. Qflohaulti, Physica Clarkii, 2 vols. Lond. 

 1799. Ferguson's Mechanics, 1799. Bossut, Traite de Mec. Paris, 1800. Eytelwein 

 ETaridbuch der Mechanik, Berl. 1801. Carnot, Principes Fondamentaux, Par. 

 1803. Bezout, Cours deMath. Gregory's Mechanics, 2 vols. plates, 1806. LePriol, 

 Introduction, Strasburg, 1806. Foucoeur, Mec. 1800. Gamier, Lefons, 1811. Emer- 

 son's Mech. Venturoli, Element! di Meccanica, 2 vols. Milan, 1817 ; translation by 

 Creswell, Camb. 1822. Vega Vorlesungen iiber die Mathematik, 4 vols. Wien. 

 1818-19. Farrar, Mech. Camb. U.S. 1825. Boucharlat, Mec. 1827. Leslie's Ele- 

 ments of Natural Philosophy, Edin. 1829. Biot, Notions Elementaires de Statique, 

 1829. Hachette (translation of Young} Resume Complet de Mecanique, 32, Par. 

 1829. Dandelin, Cours de Statique, Liege, 1830. Prichard's Theory of Statical 

 Couples, Camb. 1831. Renwick's Mechanics, New York, 1832. Poinsot, Elem. de 

 Statique, Monge, TraitS Elem. de Statique, 1834. Together with treatises by the 

 following authors, most of which have passed through several editions, and are well 

 known : 



Bridge, Wood, Whewell Mechanical Euclid, Statics, Dynamics, fyc. Earn- 

 shaw's Statics, Dynamics. Walker, Young (J. R.), Lardner (Library of Useful 

 Knowledge}. Lardner and Kater (Cabinet Cyclopaedia), Eland's Mechanical Pro- 

 blems. Walton's Do. Moseley's Illustrations of Mechanics, and Mechanics applied 

 to the Arts. 



Treatises which embrace a wider range Laplace, Traite de Mecanique Celeste, 

 5 vols. 4to, Paris, 1799-1825. Bowditch's Translation of Laplace's Celestial Mecha- 

 nics, with a Commentary, 3 vols. 4to, Boston, U.S. 1829-34./\Lagrange, Mecanique 

 Analytique, 2 vols. 4to, Paris, 1815. Prony, Legons de Mecanique analytique, 2 vols. 

 4to, Paris, 1815. Poisson, Traite de Mecanique, 2 vols. Paris, 1833. Harte's Trans- 

 lation of Poisson's Mechanics, 2 vols. Lond. 1843. Pontecoulant, Theorie Analytique 

 du Systeme du Monde, 3 vols. Paris, 1829-34. Somerville's (Mrs.) Mechanism of the 

 Heavens, Lond. 1831. Pratt, The Mathematical Principles of Mechanical Philoso- 

 phy, Camb. 1836. 



