t 3^9 ] 
dilute near enough an ifofccles triangle, having the 
angle of a pentagon ; i. e. whole angle at the vertex is 
fubtended by the lide of a pentagon in the circle de- 
fcribed about the triangle. 
Now this will be plain, if it be {hewn, that the 
fquares of the numbers in this feries are alternately 
leifer and greater by an unit, than the product of the 
two numbers next them upon each lide. Thus, in 
the four numbers, y, 8, ig, 21, the fquare of 8 is 
an unit leifer than the product of 5 and 1 g j but the 
fquare of 13 that next follows 8, viz. i6p, is an 
unit greater than 8 times 2 1 , or 168; and fo on con- 
ltantiy. 
Cafe 1 . » 
If a, b y c , be fuch numbers, that \ l - a ■ \~T C 
Then, if d be taken,, fo that d — bfc ; then fhall 
bd -h 1 —c c. 
Becaufe d — b-\-c\ b d -j- 1 llaali be —bb-\-bc-\~ 
i = ac -f-bc [2] which is = afb x c — cc [1]: Ergo 
bd-\- 1 — cc. 
Cafe 2. 
If a y b , c , be fuch that 
Then, if d be taken, fo that d=zbfc ; then fhall 
bd—cc-f- 1 . 
Becaufe bd—bbfbc—asf be f l [.2.] = afb x c-f 1 
1 [ 1 -1 
Problem. 
Having given the number <7, in Cafe 1 . to find 
b and c , i. e. having given a to find b fuch that 
bb- f-i == (ac—) aaf-ab ; then is bb *— ab — aa — 1 : 
A a a and 
1. af b — e 
.2. cc - 4 - 1 — bb 
