PROPRIETATE GAVDENTIVM 171 



j— V( 2<7j/H- 2^.v), quac itidcm cft pro cycloide jid 

 ad axcni oblique duftum. Ex quibus pcrfpiciiur quae- 

 ftioni propofitae aliam curu;im non fuihfaccre pnieter 

 cycloidcm j ita vt inter omncs curuas per punda A et M 

 transcuntcs nulhi fit nifi cydois , quac cum fua cuoluta 

 tam exiginun fpatium comprehcndut. 



§. 15. Sit nunc propofitum inter omncs curuas 

 AM dctcrminare eam in qua J-^f fit maximum vel 

 minimum. Ponatur ergo dy~pdx et dp~rdx erit 



--———. Qimre erit L — o, M — o , Nrro, Vr:: 



— dVdx erit dW=:Vdx-\-AdXy hoct^^P^- — 



{x-^pp)l 



^rpdx ^ , -pdp kdp _ 



= 77~T~^7^ + A ^AT rr ,~~-— + -7-. Erit itaquc 



dp~o et j — a A' feu linea quaefita reda ; quac termi- 

 norum defirudio inde oritur, quod fit /Q^rt^x'~ / - ^f^ - 

 integrabile. At fi qu.ieratur curua in qua /j;^"^ fit 

 miximum -vel minimum , fiet Q_— y^J^p^) et dQ_— 

 dr rpdp rdy 



jy{i-i-PP)~jii-^PPrrrn~iTpJ)' '^^ ""^ ^'^ ^ 



— r —rp 



— o M — — ■ V — et W •— 



Y z jY^i 



