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 *