7(J CURVA TAUTOCHRONA 



' —ns — ns ^iJH — ^^ 



^(i-c''^'')o--'^''ds=etft feu mac-^^^ds-mac^ ds~nedt. 



Eft vero fc^/i,"^^x , trgo dt—Vi^c^^^dx. Quo- 

 circa ejedo /, habcbitur aequatio inter s tt Xy haec 



— ns —ns — ns 



mmac-^^^^ds—mmac "'•'^ ds—{m—n)nec '^^- dx. Qiiac mul- 



71S 71? 



tiplicata per t""^ abit in hanc mmac-^^^ds—mmads— 

 {m~-n)7iedx. 



§. 16. Aequatio difFerentialis inuenta efi: ite- 



ns 



rum integrabilis •, integrata vero dat , '-a^iic-'^'^— 

 mmas-t:!!^—{m-7i)nex , poilquam debita conftans 

 'J^^ ablata eft. Quae magis accommodatur hoc 



ns 



2771 a a 2771 aa 



Haec quidem aequatio fufliceret ad curuam conflru- 

 cndam ; fed commodior euadet liberata ab expo- 

 nentiahbus. Hanc ob rem fumantur logarithmi, 

 eritque ~—I{m'nns-\- zm ' aa-^-Qn—nyi-ex^—lzm^^aa. 



_^. , . ,-v~ - 1 ■ • nds m nads->-(m—n'n edx 



Hmcditterentiandoacquiritur^~-^ ~ 



m nas-^2m. aa-i-[m—n]n ex 



> ct ex hac ordinando ?n-n^asds-i-i.m—H)fi'^exds:zz 

 -x^m—nymn^^aedx. Quae diuifa per nn praebet fequen- 

 tem acquationem finalcm pro curua quaefita, 

 m"asds-\-{m—n nexds—^(m—n)maedx. 



^. 17. Si itaque curua AME eam habuerit pro- 

 pri etatem, vt fit ?n^asds-\-(m~n)nexds—2{m—n)waedx 



ea 



