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formed by m circles upon HP, with m circles upon 
AGf either by 2 a, or by 2 <2 — i. The number 
of interftices formed by w circles upon each row" 
would be, as hath been fliewn in the preceding cafe, 
2 w — 2. Therefore, the number formed by circles 
upon AG, with’/w— circles upon HP, is either 
2m — 2 — 2a, or 2w — 2^ — i. That Is, ulti- 
mately (when the number m^a is infinitely in- 
creafed) 2 m — 2 a. Now, fuppofe the number of 
circles upon to be m — a — b. The number of 
circles upon the two rows AG, HP, is 2 ;/z a, 
Upon the three rows A G, H P, QJC, the number is 
3 w . — 2 a — b. And if the number of circles upon 
V X, be m — a — b — €, the number of circles upon 
the four rows A G, H P, QJC, r S, will be 
4;;? — 3^ — 2b — c. And, univerfally, the num- 
ber of rows being n, and the number of circles upon 
the feveral rows, m^a — b, m-^a-^b—c, 
m — a — b — c — d, &c. fucceflively, the whole 
number upon all the n rows will be 
<nm — ay^n — i — byn — 2 — cy n — 3, &c. 
But, as it hath been fhewn that circles upon AG, 
with m — a circles upon HP, form 2m — 2a in- 
terftices, if the number m — a be infinite, in the 
fame manner it may be fhewn, that m — a circles 
upon HP, with m' — a — b circles upon Q^X, 
form 2 m — 2 a — 2 b intcrflices, when the number 
m — a — b is infinite. Therefore, the whole num- 
ber of interflices formed by the three rows upon 
AG, H P, QXy is 2tn — 2 ay 2 — 2b, And, in 
like manner, the number of intcrflices, formed by 
the circles of four rows, will be 
2m — 2a y 1 — 2b y 2 — 2 c. And, univerfally, 
n being 
