2 9+ Mifcellanea Curiofa. 



II H- Y X r -4- y X ? -+• v, which being the whole 

 Number of Chances for three Lives, is com- 

 pounded of the eight Produces following. 

 (0 K r which is the Number of Chances 

 that all three of the Perfbns are Jiving, 

 (a) r ? Y, which is the Number of Chances 

 that the two elder Per/bns are living, and the 

 younger dead. (3; ? y the Number of Chan-? 

 ces that the middle Age is dead, and the youn- 

 ger and elder living. (4) \ r v being the 

 Chances that the two younger are living, and 

 the elder dead. (5-) ? Yy the Chances that 

 the two younger are dead, and the elder Ik 

 ving. (6) r Tv the Chances that the younger 

 and elder are dead, and the middle Age li- 

 ving. (7) I^y «, which are the Chances that 

 the younger is living, and the two other 

 dead. And Laftly and Eighthly, Yy v, which 

 are the Chances that all three are dead. Which 

 latter fubt racked from the whole Number 

 of Chances N n v , leaves N n v — Yy u the 

 Sum of all the other feven Produces ; in all of 

 which one or more of the three Perfbns are 

 furviving. 



To make this yet more evident, I have ad- 

 ded Fig. 8. wherein thcfe eight feveral Pro^ 

 duels are at one view exhibited. Let the 

 re&angled Parallelepipedon MBCDEFGH 

 be conftitured of the fides A B, G H, &c. 

 proportional to N the Number of the youn- 

 ger Age j A C, B D, &c. proportional to n , 

 and A G, C £, &c. proportional to the Num- 

 ber of the elder, or v. And the whole Paral- 

 lelepipedon fhall be as the Producr. N n v 9 or 

 our whole Number of Chances. Let B P be 

 as t{j and A P as Y' 9 let C JL be as r, and L n 



as 



