-o SOLVTIO SINGVLARIS CASVS 



§.5. Ad tempus derccnfus per curuiim MB in- 

 uciiiendum, elt ceieritas in Y -zzV {a — x) ct elemen- 

 tiim tcmporis — i/jiV (^ — .v). Huius integrale ita af- 

 fumtum, vt fiat =ro fi X — o dabit tcmpus dcfcenfus 

 perYB, in quo ergo fi ponitur x — a prodibit de- 

 fcenfus tempus per M B , qiiod cum priorc conflantem 

 quantitatem ab a liberam coniicere debet. Si puncflum 

 M incidit in pundtam B, i. e. fi ^euancfcit, intcgrum 

 tejBipus dcfjcnfus crit tempus defccnfus per curuam BMA, 

 quod ex fupcriore formula euadit rr/;. Hanc ob rem 

 ctiam tempus dcfcenfus pcr MBNA dcbet efle —k. 

 Proindc tempus per MB debebit elfc -—aa-^-^a^-^ 

 y<?'-hetc. 'i-^Va-j-yiay a~]-$a-Va-+-ctc. 



§. 6. Koc Yt fiat afliimo pro curua quacfita fe- 

 quentcm aequationem dsznAdxV x-^Bx^xV x-i- 

 Cx-dxV X -t- etc . H- E dx -+- F x dx -f- G .v = ^.v-f- etc . 

 Tempus ergo defcenfus per arcum MB erit — /v(£^* 



, /-BxdxVJC ■ fC x'dx^Jx . f E_dx . r Vxdx , ^ 



-r-7 vT^^ ~T~J V(a-a} -T- ttC. -Jr-J V(a— X) ~T~J V ( a—x ) ~^ 



/y^^^) -i- etc. lcilicet li intcgralibus his ita iumtis vt 

 fiant ~o li X — o ponatur vbique x—a. Determi- 

 nentur ergo coefficientes A,B,C, etc. ita, vt fint 



—^^a-J^f—^^—yiaVa-J^^^^-^^a^^Va etc. Af- 

 fumfi vero ilUim loco ds valorem, vt litterae A,B,C, 

 etc. non ab a pendentes determinentur. 



§. 7. Intcgratio huius 7(^z^ pcndet a quadratu- 

 ya circuli \ At fi ope logarithmorum imaginariorum in- 



tcgre- 



