other dead. And Lastly and Eighthly, Yy υ, which are the Chances that all three are dead. Which latter subtracted from the whole Number of Chances Nn ν, leaves Nn ν - Yy υ the Sum of all the other seven Products; in all of which one or more of the three Persons are surviving.
To make this yet more evident, I have added Fig. 8. wherein these eight several Products are at one view exhibited. Let the rectangled Parallelepipedon ABCDEFGH be constituted of the sides AB , GH , &c. proportional to N the Number of the younger Age; AC , BD , &c. proportional to n ; and AG , CE , &c. proportional to the Number of the elder, or ν. And the whole Parallelepipedon shall be as the Product Nn ν, or our whole Number of Chances. Let BP be as R , and AP as Y ; let CL be as r , and Ln as y ; and GN as ρ, and NA as υ; and let the Plain PRea be made parallel to the Plain ACGE ; the Plain NVbY parallel to ABCD ; and the Plain LXTQ parallel to the Plain ABGH . And our first Product Rr ρ shall be as the Solid STWIFZeb . The Second, or r ρ Y will be as the Solid EYZeQSMI . The Third, R ρ y , as the Solid RHOVWIST . And the Fourth, Rr υ, as the Solid ZabDWXIK . Fifthly, ρ Yy , as the Solid GQRSIMNO . Sixthly, rY υ, as IKLMGYZA . Seventhly, Ry υ, as the Solid IKPOBXVW . And Lastly, AIKLMNOP will be as the Product of the 3 Numbers of Persons dead, or Yy υ. I shall not apply this in all the Cases thereof, for brevity sake; only to shew in one how all the rest may be performed, let it be demanded what is the Value of the Reversion of the younger Life after the two elder proposed. The proportion is as the whole Number