( 6o6 y 
of the Elder Age ; A F } B I the Survivors after the fame term;; 
and CF, DI y thofe of that Age that are dead at that time. 
Then (hall the whole Parallelogram A B C D be Nn 3 or the 
Product of the two Numbers of perfons, representing fuch a 
number of Perfons of the two Ages given ; and by what was 
faid before, after the Term propofed the Re&angle H D /hall 
be as the number of Perfons of the younger Age that furvive, 
and the Rectangle A E as the number of thofe that die. 
So likewife the Re&angles A I, FD /hall be as the Numbers, 
living and dead,, of the other Age. Hence the Re&angle HI 
/hall be as an equal number of both Ages furviving. The 
Re&angle FE being the. Product of the deceafed, or Yy, an 
equal number of both dead. The Redangle G D or Ry, a 
number living of the younger Age, and dead of the Elder : 
And the Re&angle AG or r Y a. number living of the Elder 
Age, but dead of the younger. This being underitood, it 
is obvious, that as the whole Rectangle AD or Nn is to 
the Gnomon FA B D E G or Nn— Yy y fb is the whole num- 
ber of Perfons or Chances, to the number of Chances that 
one of the two Perfons is living : And as A D or N n is to 
FE or Yy y (6 are all the Chances, to the Chances that bcrh 
are deadj whereby may be computed the value of the Re- 
verfion after both Lives. And as A D to G D or Ry y fo the 
whole number of Chances., to the Chances that the younger 
is living -and the other dead ; whereby may be caff up 
what value ought ro be paid for the Reverfion of one Life 
after another, as in the cafe of providing for Clergy-mens 
Widows and others by fuch Reversions. And as A D to A G 
or r Y y fo are all the Chances, to thofe that the Elder furvivos 
the younger. I have been the more particular, and perhaps te- 
dious, in this matter, becaufe it is the Key to the Cafe of 
Three Lives, which of it felf would not have been fo eafie 
ro comprehend. 
VII. If Three Lives are propofed, to find the value of an 
Annuity during the continuance of any of thole three Lives. 
The Paile is,- As the Product of the continual multiplication of tin 
Three Number s y in the,. Table , anfwering to the Ages propofed 3 
is to the difference of that Trcdu£l and of the~ Trodutl of the 
Three Numbers of the deceafed of thofe Ages, in any given, 
term of Years $ So is the prefent value of a Sum of Money 
tn be paid certainly after -fo many Years 3 to the prefent value of the 
