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# Title: An Introduction To Algebra (shelfmark Leibn. Marg. 87)
# Folio 155, page id 827130880:0171
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Resolution of Problemes.
ASche lesser limit helped as 1o 1, 4, 8 For common Divilors OF A. B
Sochis ercater limir givesus 2, 3. IE chese mulripls thole FOrmer, we 
tave 3. 12. 24. And (0 we are again Fallen upon che six Divisors
(2. 3. 4. 8. 22. 24) Pa8, 252. liV. 26.
The Reason oF thac ACultiplication is ehis
X.) When(OeVeF = -- 3y - 3C OF 37 + 3C, ic maties A. B. K. D. div
by 3. IF che same Z BC aI(O 27 - + 4h (28 7 = 7. 2 = 28. p =- 27. 2 -
ic makres them divisible by 8. Andcheretore cheir grearest common Divis
3 cimes 8, that15 24.
2.) ButiEche same Z DC (BOF 27 .t AB, buE) 27 F 2B, it makes therr
divisible by 43 and cherecore cheir grearest common Divilor I5 3 cimes 4
thac is 12. A5 When p =- 5. 2 = 12. OFY = 7. Z =24.
3.) BucIF Z = 37 - 30 Or Z =3y + 36, DC al(027. 1 some odd number,
it makes them noc divisible by any number Greater than F. S0 chat cheir
creacelt common Dirilor is 3 times X chac is 3. AS When Y = 4, 2 =9. O
Wten y = 1O, Z = 33.
4.) Wrhen = is noc cqual 10 37 - or - some cripled Inteoer then it
makes HOC A. B. R. D divisible by any muniber greater than P. S0 chae cheir
common Dirilor is no ocher chen was deligned betore Dy Z = - 2Y t h, 27 1 2b.
2y + 4h, a5 IB P2G, 253.
Whieretore nom chere is no place lese For that suspicion (pa3. F52 lin. 28
Chat A. B. K. D con have Come orter orearest common DivilOES chan one Ot
chose siX 24, 22, 8, 4. 3, 7.
Lec the rationes OF y ro = be distinguistred by chese six Divisors into (X
Rantes, Whose Lcaders may be Found by chese 3 last PaBes, supPOsingB =2. 2
c = F Or 0, and chen lagine
ad
242 =- 27 + 4 -- 3p - 3,. y = 7.. 2 = 18)I
T2 2 = 2y 1 2 =37 - 3..) =5.. 2 =12 II
8 2 = 27 1 4 = 37 1 1.. ) =3 ,. 2 =20 IIL
42 = 27 1 2 -37 - 2.. 7 = 3.. 2 = 8 IV
3
2 = 27 1 F =-37 - 0.. 7 =T.. Z = 3
V
2 2 = 27 F 1-37- 2,. 7 =2,. 2 = 5IVI
u   cact Rank reguires muchi more work to tind it.
E2