Rectangle HI shall be as an equal number of both Ages surviving. The Rectangle FE being the Product of the Deceased, or Yy , an equal number of both dead. The Rectangle GD or Ry , a number living of the younger Age, and dead of the elder: And the Rectangle AG or rY a number living of the elder Age, but dead of the younger. This being understood, it is obvious, that as the whole Rectangle AD or Nn is to the Gnomon FABDEG or Nn - Yy , so is the whole number of Persons or Chances, to the number of Chances that one of the two Persons is living: And as AD or Nn is to FE or Yy , so are all the Chances, to the Chances that both are dead; whereby may be computed the Value of the Reversion after both Lives. And as AD to GD or Ry , so the whole number of Chances, to the Chances that the younger is living, and the other dead; whereby may be cast up what Value ought to be paid for the Reversion of one Life after another, as in the Case of providing for Clergy-men's Widows, and others, by such Reversions. And as AD to AG , or rY , so are all the Chances, to those that the elder survives the younger. I have been the more particular, and perhaps tedious, in this Matter, because it is the Key to the Case of Three Lives, which of it self would not have been so easie to comprehend.
VII. If Three Lives are proposed, to find the Value of an Annuity during the continuance of any of those three Lives; the Rule is, As the Product of the continual Multiplication of the Three Numbers, in the Table, answering to the Ages proposed, is to the difference of that Product, and of the Product of the Three Numbers of the Deceased of those Ages, in any given Term of Years: So is the present Value of