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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 69v, page id 00068049:0138
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 68r); this page is its left half.
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# Lines: 85 recognised, mean confidence 0.77
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nam est =
dZ. summuri potest conice
Atque adeo videndum quomodo secudata summanda secundum Z,
possit reduci ad hanc forman praesertim cum etam f et g. possint
esse indelinitae, seu continere Z, pro lubitu. Unde licet faciamus Z7. 221Z H2 etram extralioilem
necape si sit n. 31+ 1L. 2 C et possumus quidem ipsi F et g dare tommunem vilorem
divisorem qui  ita ut soccedat extractio aliqua, e verb. a. si is etiam sit divisor cois ipsius 27 - 2. 21Z - 1. 31
et m ductus dende in 627 - 2. 1 Z - 2. 11. 31, det a aliquid, quod se serviat vel e+ 3
tollendum vel ad deprimendum nominatorem, de pripere ossumus ine hac extractione, sed sollere
non nisi per lipsam. sed, 22 = 2. 21 - 1131 non este aliblis debet reddi extrahibilis, hisi velimus
etam a 102 et i 16 2 aliquid disse extrahibile
sed alia jam cogilatio est, ut haec methudus serviat analytice magis pro dati reolatione
sit scil data s quaecunque secundum Z. continens irrationalem. YH. Z it et ut inogie seu
bevins (8. fiet 5Z = 5, - 1 y per 12. seut  - -
+102 +
1162
505, dx: 106
ex 7 fiet Z= fXX + x + si = X Z = (06 -x p 6  sam si propositasit
summaada V8dZ erit sumuada i - 1Z f s02 +9184, 0+6 - s0s d,: (06
quod utique per quadcaturam sanicam praestari potest. Poniam per 17 et 19 res ad extractione
reducta est. Nam (8 
= y +x - 06 f 102 +9 162
quoniam ergo de non cotinet nisi 05 irrationalem, ideo si detur summanda
8 du po 7 utcunque Yationabiter dari ex Z, dabitur itique
per curvam sonicam per quadraturas sonicas seu rationales.
(∞ HBB1
dEtar
Esantum ergo opus ope datae s Z N  _Z + n Z 7 41ZZ + 43Z+ 44, invenic C, 6 et 2
hau suum resolvamus in duas AX LAX 27 + 51Z + 52 et 2Z+ 61Z+62, et his unam co
et 22+51Z +51 oparemu cum 55   4 99 Z. 3i f 2f9 - 74 2 11 2 - 191), et fiet
fZ3 ∞  - 2f6. 11 Z + ff 11. 11
-28931
+2f9. 11
L259.31
+ fglI. 31
(27
27+513+52 fil f rg 1 f + g )1. et porro hinc facili habebsu, 1, et 31
Nx
 haberumu non solumn 2t ad et ad huc  alteritum extr quo supersunt foclus
+)931 - 2993
si + esset  et (4) esset + fieret - 21 + (, 11 - 4 993) sed si   esset +
et fi = 931 = 152 possem tamen et novas
431 = 4 89 11
habere arbitrarias pro 2 sumendo BW
et (4) esset + fiere C. 31 -49931 -5
quo anglius si 2sset 53+
ei
mul siplicam per arbitrariam 7+. et ta risus faculio eut conparatio. Itaque de successa nx vndetur pos dibitari.
jam video nc nihil agi quia admscetur exhactio et vex 12 fil y = 177- 2. 0.
4 f 1O4 + gV64 = y sic H D  +29
fit 5102+ 9984 + 2592 106 = y
sit O= roderna S ox rua 6 hox 13ca.
jam 106 aequemus quadrato fiet (iocex roaX + 1. 2G aa  (o 3 XB + 2. Ao. Lo XaZ  + aa 23
faciamus 10 et 3oesse t. et sit O = x+ a
quadiglo fiet ( + 1 X +
= 23-2. 11
jam dx
u
F11.39
et ( ox 2 per 8, 9, 10. fiet
ff Z11
5= X + 31 et
Jam C6 aequemus
et similiter 6 = 22= 2. 31Z (= 11. 311, :, 11 + 31 - 22
A 11. 21 3 :  31 - 22
L+1. 31
2912  hn 7
1058X+ 2) hi
9093 St   ff Z  + gg 2 + 2f9
9E.3 + 259- 1 = 3. 2 un, 2E- 2NZ F . 2
il2l17
f. Z- 11 +997
2L+ 2
Vs ∞D + 2x Z + 27 seu X= 22 - 1131,:, 11431 - 2Z. et ft  et fiet
: 11+31 - 27
et fia
0
5. X I3- 2
Z 13, 
5i - 22
)22
fl. 31 2 a
d106 - O A +
XtZ = (Z- 1131 -272+57
1Z +;, 2Z 11. 31