VI 



THE PROGRESS OF 



statical principles, which lie consigned in the 

 first book of his treatise de Insidentibus in Fluido. 

 The second book of that treatise is occupied with 

 various difficult questions respecting the situation 

 and stability of certain bodies immersed in a 

 fluid. 



The ancients ascribe to him the invention of 

 forty remarkable mechanical contrivances ; but 

 nothing more than some obscure notices of two 

 or three of them have come down to us. His 

 sphere, a machine by which he represented the 

 movements of the stars and planets , is one of the 

 most celebrated. It has been noticed by grave 

 philosophers, and sung by poets, as may be seen 

 in the following epigram of'Claudian : 



Jupiter, in parvo cum cerneret acthera vitro, 

 Ki-it, et ad cuperos talia verba dedit : 



Huccine mortalii progreisa potentia cure; 

 Ecce Syracusii ludimur arte senis. 



Archimedes wrote a description of this machine, 

 under the name of Sphasropceia ; but it is lost, 

 .-mil with it every thing respecting the nature of 

 the sphere has perished. 



The burning mirrors, by which he is said to 

 have set fire to the Roman vessels in the harbour 

 of Syracuse, were long considered as fabulous. 

 But Buffon showed how, by placing a number of 

 small mirrors so that every one of them should 

 reflect the image of the sun to the same point, 

 heat enough might be produced to kindle wood 

 at the distance of 140 feet 



The protracted defence of Syracuse against 

 the Romans, chiefly in consequence of the won- 

 derful mechanical inventions of Archimedes, is 

 too well known to be enlarged on here. 



If we except the discoveries of Archimedes in 

 statics and hydrostatics, hardly any other branch 

 of physical science was much cultivated by the 

 ancients. They had made, indeed, considerable 

 progress in the knowledge of acoustics, so far as 

 music is concerned. In optics they can scarcely 

 be said to have made any progress of conse- 

 quence ; and, in astronomy, very little till the 

 time of Hipparchus, who may be considered as, 

 in some measure, the founder of that sublime 

 science. 



After these preliminary remarks on the pro- 

 gress of physical science among the ancients, we 

 shall proceed to take a brief view of the ad- 

 vances which have been made in it since the 

 revival of letters, and to describe the present state 

 of the various branches into which it has been 

 divided, as far at least as is consistent with the 

 very limited length to which our observations 

 can be permitted to extend. 



There are only two methods by which the physi- 

 cal sciences can be advanced. These are, I. Obser- 

 vation and experiment ; 2. The application of 



mathematical reasoning to deduce new truths 

 from facts already established. AVe shall take a 

 brief view of these two instruments of investiga- 

 tion in the first place ; beginning with malhf- 

 matics; because they were first employed. 



OF MATHEMATICS. 



The object of mathematics is the measurement 

 or comparison of quantity. Now, there are two 

 kinds of quantity, namely, number and surface. 

 That branch of mathematics which treats of num- 

 bers is called arithmetic, that which treats of 

 surfaces, or rather of space, is called geometry. 

 There is a third branch of mathematics, which 

 treats of quantity in a general way, and which, 

 therefore, applies equally to arithmetic and geo- 

 metry. To this branch, the name of algebra has 

 been given. 



I. ARITHMETIC. 



The ancients employed the letters of the alpha- 

 bet io represent numbers. This method seems 

 to have originated with the Egyptians or Pheni. 

 cians, or, at any rate, the Greek mode of ex- 

 pressing numbers was obviously borrowed from 

 the Hebrew. 



The decimal mode of numeration has been 

 adopted by almost all nations, evidently because 

 man has ten fingers, and because men were in 

 the habit at first of reckoning on the fingers, and 

 after coming to an end, they began again. If 

 the number of the fingers had been twelve instead 

 often, the mode of numeration would certainly 

 have been duodecimal instead of decimal and 

 this mode would have had its conveniences, 

 which the decimal mode wants. 



The Hebrew alphabet has twenty-two letters. 

 The first nine of these letters denoted the nine 

 digits; thus, N, 1 ; 1, 2 ; J, 3 ; -f, 4 ; n, 5; 1, 6 ; 

 T, 7 ; H, 8 ; 10, 9 : the next nine letters denote 

 the nine tens ; thus, , 10 ; 3, 20 ; '*?, 30 ; Q, 40 ; 

 3, 50; D, 60; y, 70; 3, 80; 90. The rest 

 of the alphabet consisted only of four letters ; but 

 there are five of the letters that have a different 

 form when at the end of a word. These are, 3, Q, 

 3, 3, ik? which are then written *], D, ) *)> V' ^Y 

 means of the last four letters, and these five final 

 letters, they expressed the nine hundreds : thus, 

 p, 100; -), 200; fc, 300; f], 400; f, 500; D, 

 GOO ; ], 700 ; t), 800 ; y, 900. 



The Hebrews wrote from right to left, contrary 

 to our method. Hence, when two numbers are 

 placed together, that on the right hand stands 

 for tens, and that on the left for units. Thus, 31 

 is 12; Hp is 105, and so on. 



