145 DE LINEA CELERRIMI BESCENSVS 



poCxto dx conft:inte (§. 14.)- Ex quibns aeqiwtionibiis 

 coniiincftis exterminata littera v prodibit aequatio pro 

 ciirua brachyltochrona quaefita. 



§. 24. Propter dx conftans erit ddy~^-~~ ideoque 



V — idKdUl- ^^?P "^ — zdxdds' -"IS 



valoribus fubftitutis in aequatione dv—gdx — —;^ ha- 



gdsdy'd's-:^gdfdds^ ^ ds""-^' df-'' 

 bebitur "-7^7^7 -iWa^'^^'"'^' 



^z . ^fj ci e \ 'L . Hacc aequatio , fi 



medium refiftcns fit infinite rarum feu in vacuum trans- 

 mutatur, quo cafu fit c — c^^ abit in ds d'' S— ^^dds- ^ 

 cuius integralis eft adxdds — ds\ Qnxo. quod fit ad 

 cydoidem §. ::ii. oftendimus. 



§. i^. Ad aequationem autem generalem conftru- 

 endam pono dsz=:pdx, vt fit ddszzdpdx et d\^ — 

 dxddp. Hinc erlt ^j - dx V (/)^ - i ) et c» - ^-^^^^f^. 

 Ipfi autem aequatio abibit in Iwnc pddp— :^dp' — 



-5 i.^_— ^-^^ — . Ponatur porro dx—qdp, 



dpdq ^ - , ,• pdq-:iqdp 



critque ddpzz- - .Qiio lubftituto prodibit- - 



,,-3 .n-H. ( ft^-l )"— ^p 



;;2i '^ — ^ K—, "^; • MultipUcctur hacc ac- 



nuatio per 72 />""'""' ; quo fido habebitur ■ 



