1 68 MifceUanea Curiofa. 



^ Theorem concerning the Tropr- 

 tion of the Time that a heavy 

 Body [fends in descending thro 

 a rip'ht Line joining two given 

 Toints, to the (fhorteft) Time, 

 in which it fajfes from the one 

 to the other of thefe Toints, by 

 the Arch of a Cycloid. 



THEOREM. 



(Fig. z-j.) ; 



IN the Cycloid AVD, whofe Balis AD is 

 parallel to the Horizon, and the Vertex 

 V turn'd downwards, if from A be drawn 

 the right Line AB meeting the Cycloid in 

 any point as B, from whence is drawn BG 

 perpendicular to the Curve of the Cycloid 

 in B, and AC be let fall perpendicular to 

 BC from the point A : Then the Time that 

 a Body at reft in A 7 fpends in defcending 

 thro' AB (by the force of its Gravity) is to 

 the Time that it fpends in falling thro 7 the 

 Curve AVB, as AB to AC 



Thro' B draw BL parallel to the Axis of 

 the Cycloid VE, and BK parallel to the Ba- 

 lis AD, meeting the Axis in G, and the 

 Circle (whofe Diameter is EV) in F and H, 

 and the Cycloid |t felf in K; Draw the 



