De la coupïdes Poutres également resist. 4S9 



eandem efle quje recflanguli fub lineis I H , C N ad rec- 

 tangulum fub lineis Z C , H K. Nam , ut fupra , oftende- 

 tur rationern momentorum componi ex rationibus qua- 

 dracorum C N ad H K,plus redangulorum A H B ad ACB. 

 Sed ex proprietate hyperboles redangulum A H B ad rec- 

 tangulum A C B , eft uc redangulum I H K ad redangu- 

 lum Z C N : Eric ergo ratio momenti in C ad momentum 

 in H compolîta ex rationibus quadrari C N ad quadratum 

 H K , ôc redanguli I H K ad redangulum Z C N. Rursùs 

 demonftratum eftab aliis idem effe eompofitum rationum, 

 quadrati C N ad quadratum H K , & redanguli I H K ad 

 redangulum Z C N,quod eompofitum rationum quadrati 

 C N ad reclangulum Z C N , id eft , linea: C N ad lineam 

 ZC, & redanguli IHK ad quadratum HK,id eft, lineae 

 I H ad lineam H K : Eft ergo ratio momenti refiftentix So- 

 lidi liyperbolici in C ad momentum refiftentis ejufdeni 

 in H , compofita ex ratione linex C N ad Z C , plus ra- 

 tione linex I H ad HK j quibus etiam componitur ratio 

 redanguli I H ^ C N ad reftangulum fub lineis Z C j HK. 

 Qiiod erat demonftrandum. 



PROPOSJTJO UNHI-CIMA. 



Denique , fi Trabs A E per femiliyperbolam F K N B ''^•'•^''*- '"* 

 fecetur , cujus Axis A F , tranfverfa diameter F V , & op- 

 pofira fedio V I Z , oriaturque alter Cuneus hyperbolicus 

 AFN BG LD -, erit intricatiffima ratio momentorum 

 refiftentixejufdemindiverfispuna:rsC&.H. Nam fî ex- 

 tendanturline^CN , HK, utinfuperioripropoiltione, 

 donec occurrant oppofitae fedioni in Z & I , erit ratio mo - 

 menti refiftentix Cunei hyperbolici in C ad momentum 

 ejufdemin H, com-pofita ex rationibus redanguli fub li- 

 neis 1 H & C N ad redangulum fub lineis Z C , H K , plus 

 redanguli fub compofita ex tota AB & parte A Cm li- 

 neam A H , ad redangulum fub compofita ex eadem A B 

 & parte A Hin lineam A C. Sit AC^a;qualis AB oftende- 



Z z z iij 



