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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 3
# Folio 34v, page id 00068000:0068
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 XX: gy integer sit X = WZ: a et y = vZ: a
fiet WWoZZ:aa; : vvZZ: aa = WW: VV, AF
sed 20 et V sunt primi inter se, ergo necessano V = a
ac proinde si sit XX: yu integer, debet etiam
X: y esse integer. item est in X: g quocunque. Etsit X= Wyia + XX. yy = WW: aa
X: yy. Erit Xxrgu integer integer. Ergo X.y est
integer, sit X = H92Z: a et y = 1 8Z: a, et
X: 9 = 8u973: a et sunt _ AetZ, H et3, 8 etZ
primi inter se. jam debet 8EEZ: a, rursus dividi per y
seu per 138E: a, fiet a2Z3: X38 = sunt autem
polaerediptin sub finem pau. idae
DAV:m tab lm =app sit N- 11. 12. B. 14. 15: +
 et E primi inter se, (33: H3 est integer, et quia
gler Aut primi intrse, aetiam e est integer
II et 13, 1 et 14,  et 15, 12 et 14, 12 et 15, 13 et 15 sunt
primi inter de n eset 12, 13, 14, 1, et 15-1. 
sed A et Z sunt primi inter se, ergo X = a et fit X. gy-
esit
ut  sunt pimi inter se est E:  integer
ergo 8 = 8: a, seu 2.8 = 4: a. Ergo
Et quia
cum est X3: qu integer, fiet X - G5Z a =.  123. .
=(aby.a e y -1 V: ab et x
2 sin x = d4dL: a
XA. gy = 96ip3 23: 6 qu seu X. y9 - 1 Z: aa
seu 
itaque si sit _ x: gy integer, Debet esse X = es 1Z a
et y = 8 Yp: a, et X. gy, = 2pZ3: a, et sunt
et Z primi inter se. Aliquae ex his literis assiuntis
sossunt esse aequales unitati, a
et 11 = 1: l et fit H = a3: A et M = CN: 1
h=a, p= 2a 6 = 2a:
Z= a: Il f = Cghglraa =) 2ga : 13.
q= fZ = q zaagE:
FL9g. a
Y. 77a=) glda= adE: 1 sed hoc
non prodesset, nam fieret q:r Reu y: a
no n= (H GP: a= 
etfiet nor= 1 et clacalaetus quadem probus
sed res non prodesset
sivsset 1. 13.13. 14 = 14 5.g +b l t 2
r_+ ab=  fficZ
lit - + a: tin = ataE sit - d.
B s
a ffZ (a +a
eosset posi assasse= a +Z:
et aZ = AH
Aff- aa
fta= bv: m
H f+207
 ff. (1 2nt + ZX   Z2
itq ia-4, .  29
X HH. a b
45= 2 um + abq = m Z + a
fint aZum + 2 ab = 2nm Z + 2 m a 2ma
seu: Z mat eele ab mim
HT: a
et m = 15. 12. 15. 14: a et n n- 1s. 143 a
=I2. B2. 14. 15a. adeoque fit tandem:
at2. 13. 1c. B.g 4 fOC H. 1. 15. 14 = a pp, ubi