CVRVILINEO CORvORUM&c, 137 



Tiio maximo pcriicniat int", ducanrur verticalcs Ab 

 tt Cc/atM'JC horizontalcs rt/' et c^l , fmtquc clcmcnta 

 Ar^ et Cc infinitc parun. Dico forc Icmpcr fpatium 

 pcrcurCum AC proportionalc logarithmo latioai» 

 A^ ad C(i" 



Dcmonjlratio. Dcfcendat primo corpus cx A,' 

 peruencritquc in pundum F, moxquc pod tcmpus- 

 culum infmite paruum dt in E, ducantur horizonta- 

 lis FG, ct verticalis GE; ponatur velocitas in 

 pundo Fin-y, \nE,—v-\-dv\ exprimatur adio gra- 

 uitatis corpus fluido fubmcrfum animans pcr|;, nu- 

 mcrusquc illc qui mukiplicatus pcr quadratum velo- 

 citatis dat rcfillcntiam fluidi indicetur pcr n. Sic 



erit vis accelcrans in pundlo Yz:ig^^—nvv, quae mul- 

 tiplicata pcr tempusculum dt dat incremcntum vc>» 

 locitatis dv\ liinc igitur habctur aequatio 



l.[^f~-nvv]dt—dv. 

 quac pofito ^ pro dt abit in hanc aequationem 



II. ^xEG— wy. FE=c'^i'. 



Jam vcro fingamus corpus idem defcenderc incepis- 

 fe cx pun(flo a, rurfusquc pcrucniflc in pundum F 

 moxquc in E-, dicatur rctcntis caetcris pofitionibu* 

 velocitas eius in F— />, ct in E~p-\-dp: ita obtinc- 

 bitur loco fccundae aequationis haec altcra 



III. gEG -nppy¥E—pdp 



fubtrahantiir tcrmini acquationis tcrtiac a terminis 

 acquationib fccundac; fic crit fada ab vtraquc partc 

 diuifionc per pp—v-v 



Tom. IV. 5 Cui 



