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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 341v, page id 00068196:0678
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quid si sic sint X x+ ab et Xx +  ac aqu. quadralis
x t h 1+ .V 3 = 21+ 20v 8 = 3 lroB
n - (G2. + 148 184 et
XX+ ab = 00 et A O = 1. 40v + 41 + 501h6.
+. 201, 190 = rego d 
20 = 40.50
21 41.50
+ 2. 40. S0
2. 41. 50.
20: 21 = 40:41
0.20 = 50, 10. 30 + 48 ergo 1970. 40.50 - 50.10. 30+40
hinc habetur. 40:50
15291. 50 = 31. 41. 50 + ba =. 11.31. 50 + 4,
hunc habetur 4+. 50
chabetur 41
10+30. 41.50 4 11 +31. 40. 50 = 10. 31. 50 + 1. 30. 58 + 2. 40. 41. hmih 4V
41 = c0. 3F . H35.50 = b, 11451 4850, CH8 1, 50. 10+50 L2. 40
seu
husvalores, ipsius 40 et e substotuendo in aequ
in qua substituendi valores
Restat 4. 41. 50 + 31.4150 + b a = 11. 3150 + 45
per praecedente,
unde lollatur 41
dende 40 per pacedentem, restabit aequalio pro 50
similiter si XX + ac = BG et  = 60v + 61 + 70 st
e similis erit calculus. pero 60,61, 70, ut pro 40, 41, 50.
sit jam  t ab  ag. coto sint y- xrC ergo tabebum
lam ipsum quam quaratum nodn nisi unam cylinet
XXFCX +BCet si sit et yytlly taen. fit Xx +28 + ex fint
= 115. 3 20V 1E
112. 132. 21V
112. 132. 20 = 5
ca non est est p
calione ipsouum
o fue
12. 172. 21 = f. Ergo s2 s. 20 = +: 21
seu 20: 21 =f: t et 112. 12 = 5: 20
I2. 112. 20. 10 + 132.132. 2030 = p se 1 C+ 11276. 104 55, 103
 l 112. 20
seu et BeF. 0. 16. 4+ 132. 26. 30 = p. 20
o ek 20.21 = 5: t. Nam quia 20,21, s
2. 41. 23 +2C+ l. 23
ergo 20+ = 2C +b. Ergo 1= b, ota hypothesia ligores pestangenda ad eum casum
r. 21 et Fu +B2. 51 = r: 21
et f. 1021ruI + 135. 302 - 91
ubi sola r involvit
differentio inter D et 
3E ae jam inventa per 112. sed 12. modudetur per aeu
extitissec
 all aliquam ex his  M. si in aeq. Z et 4 vels,
rursus in absurdum non subtuta I12a habuissemu 12 simperces
sut idem no
 pro 212, annc occo essi 212 et 112
poteren fiet 4D.50 = 60. 70 et  91.50 = 51. 70. quibus prastitis nil ultra superes
melior, ut sit _ a XX + Cx + ab- et 
XX + SX + ag-  quolobet aeq. Clto, et tiat x= 40B + 1+ Hd, ita enim
sed est etiam alia ratio, quae nihi vddetur
et E = 212 ff4 + 232162
2. 40. 23v
12 = 5. M2. 20
sed, non et cun permanus jam emm prodit
sunt cora ipsi C et G etiam + eut coc pdeoque 241. 23 + 2C + B23 =
quo l= b. adeoque revem ad cosum ut gy+ ac ergus+am
-, 40. 400
X763.
sin cquendio se
raru. 11V. 11 F2
et 12. p 25 + 30. 2(11 20 (5] 11.
Porro ad aegu. 3 4, 5, retiacrmus solur ubi 112 o milsa ubi 132,
tc = 1090 W0 n c. pl. 1i
At ex 5q. 3 e A rarsus sut Collendo 112. habetur item aeq. nova ubi jam veniendu ad eplicadem
Ex aeq. 3 et 5 tollumus  112, habelu aequatio nova, quae rusus cois ipsi D et 8 per qua invenietur 20
ipsorum S,t,
valorem, qui fuisset
lamen haec coicident, sed differre possunt sianis.
3 elix 112. simplex