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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 15
# Folio 5v, page id 00068033:0010
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 4r); this page is its left half.
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# Lines: 82 recognised, mean confidence 0.85
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ab + b - a
 aeque
2a
b +b a
+ bb - 2ba +aa
4 aa b6
aab b + 2abb - 2a ab + bb - 2ba + aa a b + b - a
ergo a aequ
L aequ
2 ab
4a a bb
abbrab 2 ab + bb -2ba +aa - 2aab = Xabl
+aabb
 -a bb + bb = 2baH + aa aequ 4 abb + a a bb
seu b - a aequ b s2a +aa. seu b aequ
a aequ
2XX - X
 asrax tgx+8 -x 2 seu baqu
l’aequ.
1- Vrataa
2XX +7X + 6
15 225
2XXa = Xa aequ. 1. Eugo a XX aequ 1 = Xa ( aequ  = X. Rarsus 1XXb + 7Xb + 6b aqu. d
Ergo 2X∞ aequ.  4(- b - 7X sErgo L (x) aequ  - 6 - (dX. Ergo X aequa - L + 1
seu x aequ. b - 4 +6 ab. Ergo a aequ.-
seu
6 ab.
3b a abb
bb -2b a + 12 abb + aa + 12 a ab + 36 a a bb 1b.
36aabb.
bb - 2ba + (2) abb taa (12) aab  36 aa bB 6 abb _ b aat 2qbaabb)
 s
sub
seu bb =2b a + ag aequ36 a bb= 6a bb - 6aab aequ 30 abb-6a ab
ergo necesse est a tb - 6aab cric sempen esse quantitatem
ratio nalem a. b erc. sunt. 4. 3 he 2 etc.
Ergo sia est 1. et b est 2 erit 2a bb ∞6d ab ∞qu.. 30 - 6
aego 
baequ IXXHEFB = X1 2XX+ZKHI
CXK. X
per  erit 2XX aequ. 1+ xa
peraqu. 2. erit 2XX aequ. 1 - 3xb - b. per 3 et 4. erit: b + ab X aequ a = 3b= ab. seu erit
 er
X aequa - b - ab
4 ab et pur3. A etrC
2ab.
29b +34 abX aequ afx - Abx (d gb∞. seu  3 X aequ. 2a
aequanda duos valores ipsius X, ontic 6 e: 8. fiet.
21
ENCL L
aa ab -ab a - b - 3ab 45
Ergo 4abg +4a ab-3aabb semper
(8) a bb aequ. aa - 2ab + bb, ( aab t abb) (3aab (+ 3 abb) + 3aa bb iit quadulu
a et B sint dut
proqessionishujus E. B.
X seu _ 2 ab + 4 abb + 4a ab aequ aa + bb + 3a ct bl.. Et ordinando bb - 4aa. 2a b aqu - aa
G3
aequ (1) + GC + 72
seu bl gaa ora BCs bb - 4aa +2a b. + 9a1+ 4a + aa
1thaa 4a
1+ 3aa-4a
Ergo b aequ 2aa +2 +  a + 8a
 1- 4a +3aa.
1-8a +6a a - 24a + 9at
aequ.
+16aa
1+3aa- +a 1+haa +a
aa +44- 32, 14 ar quta
1- 8a en.
si a sit L. func a + 8a erit = + 8sa
Ergo a + 8a. debet semper esse quadratus posito esse
a terminum seriei. si a sit 1. tunc a +8a erit 9.
seu 1 + 48. seu 49. quod unde patet rem succedere
sed nullum inde video usum nisi ad varia theoremata 3Condenda. 36 possunt quidem hoc modo etiam
occurrere problemata, sed quae raro occurrere solent, ut si quaerat aliquis a me regula
inveniondi infinitor numeros numororum paria, ita ut uno nominato a, altero b sit
4abb + 4 a4b - 3 a abb quaedratus, et A abb - a a + 2 ab - bb + aa bb etiam quadratus
quod alias difficile, quia dua tantum
salie sacient bin quolibet proximi seriei proposilae, a
incognitae et totudem postulata,
X aoqu
 seu  XX aequ aabb fa bb 2aab