Cyclomathesis : or, An easy introduction to the several branches of the mathematics; being principally designed for the instruction of young students, before they enter upon the more abtruse and difficult parts thereof . all be two fquares* Let per qu. «j 2+a 3> 4affume 5 = 78 tr. — 2V 9-- 4, io iG I ! X zzX —X tf + V — vv-a —ivy y = X ZZ the number zz yy - b zz zza Ar;yj yy — b zz zz?y zzz — ivy +yy zz zz•b + yy zz vv — ivy + yy= vv -|- b — a vv -j- b — a?iv — b — ti 4VV P R O B. LXVIII. Tofind three numbers (a-, v, z), wboft fum /hall be afquarC) and alfo the fum cf any two to be
Cyclomathesis : or, An easy introduction to the several branches of the mathematics; being principally designed for the instruction of young students, before they enter upon the more abtruse and difficult parts thereof . all be two fquares* Let per qu. «j 2+a 3> 4affume 5 = 78 tr. — 2V 9-- 4, io iG I ! X zzX —X tf + V — vv-a —ivy y = X ZZ the number zz yy - b zz zza Ar;yj yy — b zz zz?y zzz — ivy +yy zz zz•b + yy zz vv — ivy + yy= vv -|- b — a vv -j- b — a?iv — b — ti 4VV P R O B. LXVIII. Tofind three numbers (a-, v, z), wboft fum /hall be afquarC) and alfo the fum cf any two to be a fquare. x +y zz rr x -f z zz ss y+zzztt x 4- y + z zz vv ZW — ix + ly -f- 22 2x 4- iy 4- iz zz rr 4- ss + // zz rr 4- ji 4- * j zz p—V% t zz q — v zvv zz rr 4- pp — ifv 4- vv 4- qq — 2qv 4- V* ipv 4- uppofe 4- 2q *r* * taken at pleafure ; whence s and / are known (ftep 8). X zz <uv ~ tty zz vv — ssz zz vv — rr P R O B. LXIX. To find three fquares in arithmetic 5> 96, 9 i 2 3 4 5e 7S9 IO I i ## —jp zz vv XX xx + y zz zz 2XX ZZ VV + ZZ v zz S X z zz t — x ? 2XX =: SS — 2J# + XX + tt 2tX 4- XX 2S + 2/.ff — JJ + // JJ 4- /* X ZZ . 2S -f- 2/ ji 4- 2St—ttv zz s — sc zz 2S 4- 2t 2St 4- // — ss Z ZZ t X zz is 4- 2t P R O B. LXX. To find two numbers (x, y) fo that xy + x, andxy 4- y, may be flares. per qu. < i~x xy + x zz vv xy 4-jy zz a fquare. J + i = —x 3 — i 38o3 — \ 2. 4 5. 6 9 red. 4, 6, io RATIONAL VV — X B. IL IV- X X x + i a to effed this, let # + i be the fide,then zz # + i w =: ^ + 2Jf z: — x zz. fide,rr— 2rx + xx zz xx + 2xrr X zz .7 = 1 + 2r + 2rr 2r 4- 2 ken at pleafure , where r may be ta- PROB, LXXI. To find two numbers* wbofe fum and difference* jhallbe two Jauares. tf, er qu. < 2 3 2 — e 4 Z* 4 5 Put 6 Si 6 7
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