132 On tie USE of NEGATIVE 



changed its fign in the equation. It is evident how vaft an ac- 

 ceffion was thus gained to the elegance and univerfality of al- 

 gebraical folutions. 



ALBERT GIRARD appears to have been the firft who obferved 

 this ufe of negative roots. In his work, publifhed in the year 

 1629, entitled, Invention nouvelle en Algebre, he mentions it with 

 great diftindnefs, and as a matter unknown before *. 



MONTUCLA, who acknowledges that he never faw the work 

 of GIRARD, infills very ftrenuoufly that DES CARTES was the 

 perfon, to whom we owe our knowledge of the nature and ufe 

 of negative roots ', that it was he, who firft introduced them 

 into geometry and algebra f. But without derogating from 

 the very extraordinary merit of that philofopher, we muft beg 

 leave, in this matter, to differ fomewhat from MONTUCLA. 

 For, according to his own account, the work of GIRARD 

 was publifhed in 1629, whereas the Geometry of DES CARTES 

 was not publifhed till feven or eight years afterwards, in 



163? t- 



WE may, perhaps, go farther, and add, that although DES 

 CARTES indeed obferved, that the fhifting of a line or point 

 from one fide of a given line or point to the other, made no 

 change in the equation, except in the figns + and , yet he 

 did not fee, in its full extent, all the advantage to be derived 

 from the ufe of negative quantities. This will appear not altoge- 

 ther improbable from the following circumftances : In the third 



book 



* I HAVE not been able to procure the book ; but the following paflage, quoted by Dr 

 HORSELEY, feems to warrant what has been aflerted : " Jufques icy nous n'avons encore 

 " explique a quoy fervent Us folutions par mains, quand il y en a. La folution par 

 " moins s'explique en geometric en retrogradant, et le moins recule la oil le + avance." 

 And, after giving an inftance, he adds ; " Et ainfi faudrd-t-il entendre de toutes fblu- 

 " tions par moins ; qui eft une chofe de confequence en geometric incognue aupara- 

 41 vant." HORSELEV'S NEWTON, vol. 1.^.171. note () 



f MONTDCLA Hift. de Math. vol. 2. p. 85. 



J MONTUCLA Hift. de Math. vol. 2. p. 82. & 84. 



