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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 16
# Folio 6r, page id 00068229:0011
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 7v); this page is its right half.
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umeriquadrati progressionis
seia
9.
CEmeticat, se quodem ita ut
difcentia eorum sit data
sint fresquadrate XX yu
ex
- yy = yy -XX
e
 bo B
Ex  aeq. 1. fit ZZ+ XX = 2yy sit X = y - l et Z= y+ m
fiet: (9y) + rym+mm 4 yy - 2yl + U= (29y) seu fiet
yle l+mm : 2 1= m. jat e quam quatton
aequationem 2 jungamus cum aeq. 2. et 4. rtique ex
ag 2 et  freto, Et primus jungamus aequationes etq
extaequ. 4 fit  l=  y -X. (Ergo lG+X = B ex 8 et 2.
en = CB ex seu y4 X = B: l quam componendo
2)
cum aeg. 8 fit 2Ry (1 + B: L quod (per 7 eq. l + tum,: l- m
Ergo fiet (13 = Vn + lB - m B = (13 + lmm seu
mm + I M= B seu per 19 et 11, mm + 2ymL yy =Btgy
6)
B. L
seu me = SB+yy - y. seu
seu m = 1 B+. l: 4 + B. 2 + BB: 4  - l - B. l. seu
(17
s U: 4 + BDg +3AB∞Z = l - B: l
n (8)
Superest tantum, ut faciamus in rationalem
1
seu ut IC: 4 F nm 4 _ HC: 4 + BB: El + 3B:2 sel
sit numerus quadratus su multiplicando per a ad
ut  1 F BB + 6BH sit numerus quadratus.
sit ( 4 BB + 6 BII  BB + 2B nl + nn L
fet 1 +6B = EBn + nn 1 seu fiet
6B - 2 Bn, : nn - 1 = l. Ergo si B ponatur
2
esse datus debet 6B - 2Bn: nn -i esse quadratus
ponatur B esse quadratus. tantum opus est effici
ut 6= 2k; nn-i sit quadratu. Efficiendum
est ergo ut 6- 2n. nn-1 sit quadratus seu ut
6nn - 6 = 214 + 2nn, On ∞rM- 214 +8nn - 6
sit quadentus pro n scribatur p+9 fiet:
p 1
9 12 p9 8p43 294 8p, 16pg184.6
quadratus efficiamus slltem, ut a 24 +80