On lie USE of NEGATIVE QUANTITIES. 133 



book of his Geometry, where he treats exprefsly of the nature 

 of equations, he takes no notice of thofe which have all their 

 roots negative j and, in the fecond book, where he mentions 

 his new method of confidering curves, he fays nothing of ne- 

 gative abfciflae and ordinates, although the analyfis of curves 

 is, of all the parts of mathematics, that which moil obvioufly 

 fuggefts and requires the ufe of the negative roots. 



IN fact, the ufe of negative quantities appears not to have 

 been, either at this time, or for fome time afterwards, familiar 

 to mathematicians. This is evident from the Elementa Cur- 

 varum of JOHN DE WITT, a work, at that time, of fome me- 

 rit, but which will be confidered, rather as affording a curi- 

 ous piece of information in the life of that great man, than as 

 adding to a fame, which is fo far fuperior to all literary emi- 

 nence. In this work, which is publifhed by SCHOOTEN at the 

 end of his edition of DBS CARTES'S Geometry, no notice is 

 taken of negative abfciflae and ordinates : So that the^author is 

 obliged to confider feparately two or more equations, which 

 every mathematician at prefent, from the view of negative 

 quantities, which is now become familiar, would confider as 

 one fingle equation, denoting for one and the fame line refer- 

 red to the fame axis, the relation between the abfciffse and or- 

 dinates, through all the different cafes of their fituation with re- 

 fpecl to each other, that is, through all the angles of the co- 

 ordinates. Thus, in his fecond book, where he confiders the 

 lines of the firft and fecond order, beyond which he does not 

 go, he demonftrates, in the four firft theorems, that the four 



b x 

 following equations belong to ftraight lines : i. y 



it/ 



bx bx bx 



2. y = -- \-c.; 3- y = -- c s 4-y = --- \- c - But he does 



Q> d Cl 



not fhow, either in this or any other part of the work, that 

 each of thefe equations, by changing the figns of y or , gives 

 the relation between the abfcifs and ordinate, when the one or 



the 



