300 DE MOTV TArrOCHROMO 



§. 24. Aequatio aut^m pro curua tantochrona ia« 

 Tcnta : ^"^ = '^ =1 '-^-' conarucflu cft difficil- 

 lima , neque variabilcs vllo modo a (c nuiccm feparare 

 licet. Qiiamuis enim radius olculi r pcr binas rciitjuis 

 variabiles x et z definiri queat , ( crit cnim , fi applicata 

 QG —j ponatur , r =: '^ z^ "£55^ , pofitc) d x con- 

 ftiuite , vel r :=: ^^l pofito d z conllunc , ct d y — V 

 { d z — d X* )) \ tamcn hinc acquatio tantopere pcrturbarc- 

 tur , vt nihil prorfus cx ca concludi poflct. Sin autcm 

 cx ca vcl .V vcl z cxtcrminctur in multo maiores tricas 

 delabcrcmur. Cum igitur pro pcndiilo fimplici conrtruiftio 

 curuae tautochronae fit ficillima , pro pcndulo compofi- 

 to tantis laborat difficultatibus , vt cas nulio ctiam nunc 

 pa<fto fupcrare potucrim. 



§. 25. Si quidem loco quantitatum .v ct z intro- 

 ducatur angulus variabihs (p , non folum acquatio ad du- 

 as variabiles rcducctur , fcd ctiam a ditfcrcntialibus (c- 

 cundi gradus libcrabitur ; ncque tamcn ad (cparationcm 

 variabilium pcrtingerc licct. Cum cnim fit d (\i — -^, 

 crit dzz^r d (^ , ct dx — {a-s)d(^ fin. —rd<^ 

 fin. CP , hincquc .v m/r <^(J) fin. (|). Subllituantur lii 

 vaiorcs pro d z ct d x in acquationc inucnta , prodibit- 

 que. 



Vikk-^rr)-^-^'^ 



vndc fit % a X z=: - ^^^H^ tf^* • quac diflcrcntiata 

 dabit : 



adx=z 



