Mifcettanea Curio fa. 81 



the firft Hypothecs; ail the fiiperior ones 

 rriay be reje&ed ; and forming a new Equati- 

 on, by fubftituting a±e=z, J we fhall have (as 

 was faidj ±b=±se± tee. The following Ex- 

 amples will make this more clear. 



Example I. 



Let the Equation ^—3^ + 75 £=10000* 

 bepropos'd. For the firft Hypothefis, let 

 *=io, and fo we have this Equation, 



< dzL*== — da* dae — de~ 

 ~\~czj=r\-ca ce 



=1-10000 4000* -\~6ooee 40* * +e* 

 300 6oe — . $ee 

 + 750 75? 

 —1 0000 



-J-450— 40 1 5* +597**- 40* 3 +*'=o 



j t u 



The Signs + and — with refpeft to the 

 (Quantities e and e 3 , are left as Doubtful, till 

 it be known whether e be Negative or Affir- 

 mative ; which thing creates fome difficulty, 

 fince that in Equations that have feveral 

 Roots, the Hamogenea Comparationis (as they 

 term them/ are oftentimes encreafed by the 

 minute quantity a y and on the contrary, that 

 being increafed, they are diminished. But the 

 Sign of e is determin'd from the Sign of the 

 Quantity b. For taking away the Refolvend 

 from the Homogeneal formed of a } the Sign of 

 *e(and confequently or the prevailing Parts 

 in the compofition of it J will always be con- 



G trary 



