116 



of it. Vietus extended it stifl further, in expressing 

 by those general characters, not only unknown num. 

 beis and proportions, but such as are known ; doing 

 that by figures, which Euclid does by reasoning." And 

 Descartes hath extended it to geometry, in marking by 

 equations (he proportions of lines. Yet, even since 

 the discovery of our modern algebra, M. Bouillaud, 

 \vhom I was acquainted with at Paris, and who was 

 without all doubt an excellent geometrician, never 

 could reflect, but with astonishment, on the ddmon- 

 strations of Archimedes concerning the properties of 

 the spiral tine, and could not conceive how that great 

 man hit upon the applying the tangent of that line 

 to the commensuration of the circulation of the cir- 

 cle. N unes is of the same opinion with the former ; 

 and in his history of algebra, regrets that the ancients 

 concealed from us, a method which they themselves 

 used ; and says, u that we are not to think that the 

 greater part of the propositions of Enclid and Archi- 

 medes, were founded by those great men in that way 

 of reasoning, in which they have thought proper to 

 transmit them to us." 



G, This method of thdrt, w^iich rci^mblcd our al- 

 gebra, sometimes however discovers itself in their re. 

 searches, We meet with traces of it sufficiently 

 strong in the thirteenth book of Eurlrd ; especially if 

 \\G make use of the 'Greek text, or the old Latin trans- 

 lation, And although Wallis imagines, that they may 

 belong to some other scholiasts, yet. the antiquity of 

 the swence itself will still be the same. Some indeed 

 make it mount much higher, -who, led by the authority 

 of some able mathematicians among the ancients, as; 

 the first invention, of it to Plato. WiifewwrfedtfW to 

 enter info a more exact examination of this,'- will /md 

 in Wallis a guide and monitor, whose authority may 

 be acquiesced in, he having set this matter in the 

 clean, st light,as vvcll asmade the first and noblest efforts 

 in our time, to raise algebra to the state of perfection 

 W:hich it hath now attained. Now, according to this 



