$. ap. Jam quoque spatii plani A M Q, af ea , sive cur- 

 vae quadratura in potestate erit. Habemus nempe differentiale 

 areae P N M A — u 3,i; — l^ZZjIllzz^ll , quo sic integrato , ut 

 casu rmo 5cuii— ^ ev:anes3cat, invenimus aream ARM::::iliH!i:5lH 



3 



Areae mt^ A <XM idiffereiitiale .es.t zz: 



Pos.teriu:s autem intejjrale Iqgarithmicum reperitur :zi: 



ubi si substituitur 



o log. "-/(^^'-^') rr .2 1; _ ^ / a* - a*) , 

 ideni integrale nanciscitur formam 



I, y uiV[u'^ — a'^) — y4+j2'T- »' — ^^agM - /(v» — n») — ^^a^ 



■■ ^aiu — V *u2 — a2)~) 



3 



U 1) — ^ ^^^ — "'^^ ^^" '^^^ ~ "'^' ~' ' ''*'~ "''^^ Zi: U y (i/« ~a»f ^ 



•^a iu — V [u- — u- ; j 2 a 



Ji 



Quamobrem ob /•"^"^^-^-g') — l5l-£i\, obtinemus aream 



3 



Aa.M — ui;— i^— '^' — ay 



3a 



unde resultat summa A R M -^ A CLM — (u — ^) y zi: rectan- 

 gulo ACLMR, 



§. 30. Spatium solidum , vei volumen Acorporis, quod e 

 revolutipne curvae A M circum axem P N oritur , etiam alge- 

 braice exprimere licet. Repraesentante etenim P A M N sectio- 

 nem sc^idi per ,axem , basis illius circulus erit radio N M zir u 

 descriptus, ideoqxie basis area zz: u* tt. Elementum itaque solidi 

 tanquam cylindrum considerare licel , cujus basis zz: u* tt , alti- 

 tudo ~5i;, unde reperitur lioc elementum ~ — — j/(u'- a'^), 



cu- 



