And that therefore In the firft fericss half theiirft term is gfeafer than the fum of 
the two next, andlMf this furaof ihe ftcond a>nd third greater than the fum of the 
four raxn -and haft the fum of thofe|bur greater than the fum of the next eight, &cl 
in infinitum. For -~ dP ==; bt bk \ but hn >> therefore L dD > £r -*-fGi &c. 
And in the/efW feries half the firft term is lefs then the fum of the two next, and 
half this fum lefs then the fum of the four next, &c. in infinitum. 
That the" firft feries are the even terms, viz,, the 2 d , 4 th , 6 th , 8\ 10 th , &c. and the 
fecond x the odd, viz. the i\ $\ 5% 7 \ g\&c* of the following feries,™*. 4 ^ 
j_ _l • -L_ jl . <4r. in infinitum = i W hereof <z being put for the number of terms 
3x4 * 4X5 5*6 Cx 7 j a 
taken at pleafure, ^7 is the laft, — t ,is the fum of all thofe terms from the begin- 
n j n g^ an d -p^ the fum of the reft to the end. 
That — of the firft terme in the third feries is lefs than the fum of the two next, and 
a quarter of this fum, lefs than the fum of the four next, and one fourth of this laft 
fum lefs than the next eight, I thus demonftrate. 
Let a— the 3 d or laft number of any term of the firft Column,™*: of Divifors, 
j 1 1 6a 3 - 48a 2 -*r .$6%-? 24^. : , j . 
TT7~a^2 ^ a ? — 3a*~f~2a ~~ 16a 6 — 9 < >a s -t-2paa 4 — 288 a 5 -i-i 84 a 2 --- 48a I 
2 a 2 a- 1 2_a : 2 -8a ? ~i2a*-i-4a 
-x- x- ^ . i6aV4 fe'rHg(g%^.24 :,,; 
64a <f -38i|al4 88oaV9iQ£?^496a^6 p 
aa-2 2a-3 2a^4 ^ ? -3^ ^5 2a ' 2 ^ 
f — x — -x 1 . - : : 
64-a 6 — 384a 5 ^93#ay n?2a» +-73<fo*---io2a / - ; — " . 
6^ tf — 384a^tfaSt^ 06o.i 3 -t- 496a* —| 9^a ^ ^ 6 ^'; 0 i 
And 48a 4 — • 1 92a 5 '-+- 2401 s — 961 = Excefs ofithetiutofrMoz. Sovs Detiomh* - 
i But — The affirm. > the Negat. } 
; : ihatts y 48a*4-240a a > 192^96 a ^> 2 ^ / 
IBecaufe a^ 5 a 2 > 4a 3 2^ : ^ ec5e ^°^< 
.. *xi£lfc 5 a 4a 2 -ir z " j: 
Therefore B > \K 
Therefore \ of any number of A. or Terms \ is lefs than their fo 
many refpeftiveB. that is , than twice fo'many oPthe next 
Terms, jgupd, &c, 
Aaaa % By 
