COMPOSITIO FORMARUM.
243
Sint determinantes formarum F, f s f' resp. D, d, d'\ divisores communes
maximi numerorum A, 2B, C; a, 2 b, c; a, 2V, c resp. M, m, m (quos omnes
positive acceptos supponimus). Porro determinentur sex numeri integri 2i, 23, (£,
2123', (£' ita ut sit
2ia + 2236 + (£c = m, 2tV-f-223 'b'-\-<gc' = m
Denique designentur numeri
pq—qp, pq — qp"> pq'"—qp'"> pq—q'p"> p'f—qp"> p"f—qp"
resp. per P, Q, R, S, T, U, sitque ipsorum divisor communis maximus positive
acceptus = k. — lam ponendo
App"'-\- B {p q'"-f- qp) -f- Cq q" r = b b'-f- A . . . . [10]
iit ex aequ. 9
App^\- B ijfiq-p qp") •+• Cqq" = bb'—A . . . . [11]
Ex his undecim aequationibus 1... 11, sequentes novas evolvimus *):
DPP — d'aa [12]
DP{R — S) — 2 d'ab [13] .
DPU = d'ac — (A A — dd') [14]
D [R— S) 2 = Ad'bb-\-2{/\/\ — dd') [15]
D{R — 8) U = 2 d'bc [16]
DUU = d'cc [17]
DQQ = da a , . [18]
DQ{R+S) = 2 dab’ [19]
DQT = ddc — (A A — dd') [20]
U{RA-Sf = 4d6'6'+2(AA —d<T) [21]
D{R + S)T = 2 ddc [22]
DTT == d c c [23]
Hinc rursus deducuntur hae duae:
• *) Origo harum aequationum haec est: 12 ex 5.5 —1.2; 13 ex 5.9 — 1.7 —2.6; 14 ex 10.11 — 6.7;
15 6X 5.8 4- 5.8 + 10.10 + 1 1.1 1 — 1.4 — 2.3 — 6.7 — 6.7; 16 ex 8.9 — 3.7—4.6; 176X8.8—3.4. Deductio
sex reliquarum eodem modo adornatur, si modo aequationes 2,5,7 cum aequationibus 3,6,8 resp. commu
tantur, et reliquae 1,4, 9, io, li eodem loco deinceps retinentur, puta 18 ex 6.0— 1.3 etc.
31 *