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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 210v, page id 00068196:0416
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 209r); this page is its left half.
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biL
c ac aac, seu compendio
302Z+ 314Z + 32 aa, et A0ZZ + 41 aZ +42 aa debent habere divisorem
communem, A30. 402Z+ 31. 40aZ + 32. quaa. Ent hic divisor communis
frat (- 30.4077) = 30. 41 a Z = 30. 42aa
30. 2Z +31 aZ +32 aa sividendus per 131. 4047 + 32. 40a
1+ 11 4b3 F3 2qua
- 39. 41 2 -30. 42a
3072+ 31aZ +32 ad
+31.407 +32.40a
=30: 41 = = 30. 42a
sed brevius b Z
fiet Dandem 32le 
30. 41Z - 30. 42 a
+ 36. 31. G1 - 31. 31. 40 (. 30. 32. 40 + 30.30. 42 a
qu (31.40 - 30. 41
(30. 31. 41 - ete) (32. 40- 30. 42)
qu (31. 40 -30. 41)
sn qu. (31. 40 = 30. 41) 3E (30. 31. 91 - etc) (32. 40 - 30. 42)
+ 3t aZ + 32aa, fit  2h+ 3 aZ + 31 11 aa = 31. 31 - 4. 30. 31, aa
y L E 4 - C31 = (31.31 = 4. 30. 32 a
41 + + (41. 41 - 4. 40. 37)
En his radieibus una alteri hebet e
sunt binae radices prioris formule
sunt binae radices posterioris
39 = 10a 20  et 31 = naa. vabay na
fiet 11. 11 a =  2. 1. 21 a b + 21. 31 Jaabb = 4. 10. p2a + 10. 22ab 20. 2raab b
114a = 21 ab = - 2. 21b + 2( (tagi praeceo fin. Q habetur B) + 42 20ab
et 21 = 210 - 216,: bAc et hic 10 21ab -   bEB 4 b (1C - se
 eta firi 4 bb  S + G - 216G = 4. 10. 12 - 4. 10. 229( + 4. 20. 22 abb
sengo. 12 aol 0. 22 aclb. F 410. t2 aabbt 10. 2t abb  abb 186 -..
4.20. 22 bCbb. 12. 20
42022 bbbb a12. 20
- 41220.9a
sedb Haec ubi tamen rursus adhuc quadrare; necesse erit, quod paulo prolixins
sed in casu praesenti speciali rem breavius consequemur
4 st D- -
Z et O. = 2 et b+C = , fiet b +c = cub -C = t
214( 8F 2r aff + 162 2 = 0 et 21. 51 - Bt 2 2f + 16th = 16 16b t - 1622
seu 2. 21 f.= At +at (ab + 4 (tB 22)
ergo tk. 27 = AOD pe fit 21 21f =, d +2 D + 2 15
Pt 21 9+ t = 10 spersunt jam binae formulae
quaquae deberent habere communem divissrem
sirahatur ab alterafit nova formula 2
0 + 3) + +00 60
+10a Z3 + inlaZ + 12 a, onZZ + naa Z + 12a
-20b7+ =216Z = 22ab 630c2Z= uacz Fu2MC
que +arae Z  20873+ 21
eigdem divisorem debet habere cum altentra priorum
debet etidem habere dvisorem cum altentra pross
Ergo omisso eta
dividendot fit (10. ) 410(a: (Z  ua . 6) aZ + 12 (a: 6) aa. Habelmu ugo fret fommalest ex orima
=2022 =2147
secundafit +10A: L)LL
= 22aa 11 diviendoper C 420 y
+28 a2 T23 aa
 quas cnvicem addendo prodibit 10CZZ + 1C aZ + 22 aa e, et considerando formulas
EC t aequaliones fit 1027 + 1aZ + 22aa, formula quarta. Ergo si a binae pria
ced plinabae habent digisorem communem Etiam 1022 binae posteriones
in a IZZ + Uaz f2raa, et 20Z2+ uiaz +. naa didissiem commupen
a5 1e harebunt contra hypothesin. Ergo non licet efficere, ut binae ex formalis 
et eut unae binae ex formulis quatuor, quae prodeunt ex X + b, Xb XtC, XuC
habeant livisorem communem. poperest ergo ut quaeramus an tres ex his formulis possint
aaquan quadratis. duas jam aequabimus et habuimus valores. it et 21, aequemus et tertiam
e= de alet velu rioa, 2Z + unqZ + n~,, et fet na= 
214b2 = 22a a
20. 22bb 12. 28. seu nab224 2b - 28- 2b,
E sit et fit b9 + C - b2 -c4 = (210 - 2b16 et fit (C- D) 10 seu 2 = Y4 ~41: ) L supra 2G. 2C,
20, 2266 - 12. 20 ac
4 = 10. 12 aa = 10. 2 al.
20. 22 bb = 12. 20 ab
 (b+927-268
sit bic = h irt et b b+c = c.
anQ + ec 4   b08 + 2H 192 = +bb 8 et h94 7 e24 + ahhec 9q hiet
es e
 sit Au (hhQ = ect AAOV∞ (htQ teC H)
V tis htr 9- ee
hns ioces = rbor.ebB  bcel abgu 
sed th  e  (bbr cdB= 4bc
28 + C4 = 2b15
Catilbrec btra euborces sa nbe (ribest bbitca) (  vorce V_2b. BBrBV) - 2etorus sabeC
Aal 10. 12a
abe + 
bc p . o rabi ur , teicer B. b) a  rabbC
sit 2 = +)
0. 22 bb F1. 2
am dt
et hho = eeq = abb, a ion
 11. 8) aZ T1a) aa