) CIf 87 



EH & GH iifdem aequales , ad fequentia erit attenden- 

 dum. 



Dudis nim. in Fig. 3. doabus Tranfverfis angulum in- 

 finite exiguum conftituentibus LHM , IHK, quse habeant In- 

 crementum IN partis HL acquale Decremento OM partis HM ; 

 atque defcriptis centro H radiis HL HK arcubus LN , KO 

 differentias IN & OM modo didas abfcindentibus , manife- 

 ftum eft ex natura infinite parvorum , quod Lineariini EL & 

 El, HL & HI , GK & GM, HK & HM; nec non triangu- 

 lorum HLE &HIE, ut &GHK &GHM poffit unum prò al- 

 tero promifcuè accipi ; adeoque triangula ambo HLE & HIE 

 ipfis GHK & GHM iìmilia haberi ; quapropter erit LH : HK = 

 lE: HG. Sed eft etiam, ob triangulorum LHN & HKO fi- 

 niilitudinem LH:HK = LN:KO, unde JE: HG^LN:KO 



HGxLN 

 & K0 = — j-; — . Porrò, quia triang. KOM fimile ipfis 



HGM & lEH, erit lE : EH = KO : OM, vel fubftituendo prò 



HC xT N 



KO valorem ante inventum lE : EH = : OM, adeo- 



lE 

 ^,, EHxHGxLN 



que Decrementum OM = Praeterea, quia 



lE quad. 



triang. ILN fimile ipfi lEH & propterea EH : lE — LN : NI, 



. , lExLN 



erjt Incrementum NI = . Sed Decrementum OM eft 



EH 



EHxHGxLN lExLN 



iTicremento NI acquale ; Ergo eft etiam =z — 



lEquad. EH 



feu EH quad. xHG = cubo IE,vel R.cub. (EH quad. x HG)=IE. 

 Tandemque, cùm fìt lE : EH = HG : GK, erit K. cub. (EH quad. 



EHxHG 



xHG): EH=HG: GK. adeoque GK= 



^ R.cub. (EHquad.xHG; 



^ R.cub, (EHcub. xHGciibJ 



feu .-^ id eft R.cub. (EHxHGquad.); 



R. cub. (EH quad. X HG) ^ ^ 



Unde 



