80 DE FNGFLJS CTLINDRORJ^M 



a — r- dx 



y 



^ quac aequAtio integrata fic , vt pofito xzrOy 

 et coufequcnter ^'~/', fiat Sz::o, abit in hanc Srz: 

 cr~.cr y-+- c.a—r.ow. ^ cx quo patct , Qiiadraturam gcnera- 

 lem fpatii vngularis dependerc a rccflificationc arcus cir- 

 cularis OM. Si vero ponatur rurfus fcdio transire 

 per Centrum C , erit ^ — r , ct Z» zr r , quo cafu fit S—cr 

 — cj, et abcunte „v in r , hoc eft , fiKfto j —O^ erit 

 fpatium integrum femi-vngulare ODA~cr~ Reftan- 

 gulo ADxAC; vel deniquc pofito firrr, erit idcm 

 fpatium ODA — r^, id eft, aequalc Qiiadrato radii ; 

 quod Tlicorcma Fajcalio adicribitur in Comment. Acad. 

 Scicnt. Parif Anni 1707 , pag. 330. Edit. Parif occur- 

 rit vcro idem quoque in Gregorii h Sancto l^incentio 

 Tracfl.itu dc Vngulis Cylindricis Prop. LV. Tajcalius 

 quidcm Theorema pronunciauit de fummafinuumomnium 

 redorum totius Qiiadrantis ab arcu AO perpendicula- 

 riter demilforum : fed facile eft demonftrare , f nus hoc 

 modo demiifos fupcrficiem Vngularem modo expHca- 

 tam cfficere in taU Cylindro. 



§. 10. Pro fiiperficie femi-vngulari per axem fe- 

 da, fit iuxta du^ftum §. 8. j/rrV ( 2;\r- .v - ), ct 

 Vidx^dy^)-''^, quare '4^-j-V {dx^- -\-dj^- ) z=z 

 rdx^ et fatfta integratione fic vt abcunte x in 0, 

 et confcquenter j ~o^ fiat j- — , prodit s — 

 ^, atque tahs fuperficies abfokite eft quadrabihs. Po- 

 fito igitur .vzr^, eft fuperficies intcgra zn"!-, ficfla « 

 izr, et conlequentcr Z>— t, eadem fupcrficics eft cr^ 

 et pofito deniquc rizr, eadem cft— r=; hoc eft, ea- 

 dem cum illa , quae exlurgit ex Vngula per ordinatam 

 hoc modo fedvu §. 11. 



