6i OBSERVATIONES DE COMPARATIONE 



erit n — nxx<^i — nxx ideoque «>>i, abfciffa ergo 

 CQ femi axem CA fuperaret , eiquc propterea arcus 

 imuginarius refponderet ; ita vt hinc nulla condufio con- 

 formis deduci poffet. 



5. Tentemus ergo alias formulas , fitque tam 



T£==-f. qiBm/rlf^l, vnde ob aa-aaxx 

 — uu~\-nxxuuzzio et act — aauu — xx-+-nxxuuzzz 

 colligimus azzzi, ita vt fit 1 — uu-xx + nxxuuzzzo, 

 ideoque uzzzVj— gj. Hinc autem prodit BM-f-BN 



/dx tdu rxdx-*-udu \j 

 ™-\-J™z-J S • Verum aequatio uu-+-xx 



zzz 1 -j- nxxuu differentiata dat : 



xdx-\-udu zzz nxu (xdu-\-udx) feu * x x "t* - - n {xdu~\udx 



vnde concludimus B M -J- B N — nj{xdu -+- udx) zzr nxu 



-4-Conft. 



6. Haec folutio nullo incommodo laborat, cuiti enim 

 fit w<^i, erit i-nxx^> 1 -xx, ideoque u<z\i; vti na- 

 tura rei poftulat. Sumta ergo abfcifTa quacunque C? ~x t 

 capiatur altera CQjzuz^V ~ki£ ? eritque fumma ar- 

 cuum BM4-BN-»*a+ Conft. Ad quam con- 

 ftantem definiendam fit #— o, vt fiat BM~ o; erit- 

 que uzzzi, et arcus BN abit in quadrantem BMNA; 

 vnde fit 0+BMNA-0+ Conft. ficque haec con- 

 ftans erit -BMNA. Quo valore eius loco fubftituto 

 habemus BM + BNr»Ji-a-r-BMNA, ideoque 



BM-AN-»h:(i -u)xuzzzBN-AM 



7. Dato ergo in quadrante elliptico ACB pun- 

 &o quocunque M , affignare valemus alterum pun- 



&um 



