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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 157r, page id 00068200:0315
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 156v); this page is its right half.
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et per potetum et. Bavius ve Ex et a hlenf prsiio e eige b p et H. sat pero q. Ct b puo ralitio tacetu X.
Ha arte res velul coguntur ad quidvis
si sit  + 3C +4 (  quadrato,  cuidam fiat  + 2Cd+ dso
4
pN
et ut jam
et c auferri possit, ponatur D e 2 p, et pro 2C dl, fiet 5C, ao pro C ponendo q
eutd  _ 3 pro 2cdl, fiet 3qu12
et stabit
4+ 16 e 451
31aC  + 4l7
(5) -29  1q
’et pro quy ponendo c+ Ece + e
sive C 1 4l4 - 3C= 9l7V
Jam er.
16
i ia
144
256 243
24
g + +IL
B11
256
24
81t
seu 246
48 + 365
+
3216 +20
81 16+12
 2p2, vel 31
 et pro da 91
sive
vr
e
vel 91Va
2 +2d
6
ponendo, omnes indelerminatas esse 1, fiet: 4 - 3 - 9
seu = seu 4, cujus q. est =, et 49 est 256
1627 + 4 debeni aequari quad rato, seu 256 + 27216 + st 4,
2
101a  10
01
e
en1
os
2cC 4ri
=B 1 - 24
C + C seu 4 + 1, - 4 + 1
fiet 16 = 4 ∞4 + 1
64  Error in eo, quod omnes indeterminatas 16 - ~ +1 +6 -24 +9
8
posui  1
Nam inveni hic C p, 414 -3e -91
eaque conferendo : 414 - 3C - 9lY 4 6 ec  + 2ce l + E3
Ista ergo cuncilia:
26
ponendo
E
9l larceliel
et  31c + 4(+ c+ redl + 3  14dl74
d (
+2cd
4c12
+ 2 c dl
ut in hac aequatione habeatur pare valor ipsius m, eud am +8fm + eg + 4f h2
quod ulique feri potest h sumta pro arbitrio, erit que 2m + 2f e h. Sgl + 4f  27
Et resumta aequatione in hitiali, et in ea
A si Hs haec excerpta connescunt restabit subsi
Resumatur Aequatio ipsa, et pro m substituatur ejus valor, caetera sum demta 9, etm
sumantur pro artitrio, fiet: oe Al + e + am + eg  gl- em - 8l 89.
fietque 4- +1 -Eg 510 et 917 3
An brevius ita, debet
et habebimus aequationem:
ia
C
+6l + f 1 Z + 2C + fE, destructisque destruendis, fiet:
61 + fl  2Cl + f c. eritque s 61. 2c (2
+c2 - L
eritque frse
posito c e 1. deber ergo - l, esse quadratus  X  2cd +d
seu C ( = l ~ - d2
2+d
sc
+ 6l + le 5 quadrato     +
n
1+ 3i
253
pr praeterea 6ld t∞d2
_
 quadrato
seu 6d   -d  quad rato quod fut d V Ergo d, debet esse quadratus r
ja
et 6g2 - 12 = g+ erit etiam quadratus g + 69 l f. Gl +29 F etY
Modus efficierdi, ut ex cd + CR + e sint quadratus, pouatur D, CCF Y et dart
et e p, 2 ducatur in se ga Z:, fiet Y a + 2yZ + qu Utbus ex va +Z faciem
une 6 sit (2 +6el + ler ’ a
+ 27 4 2
X
r
2qu 91f27
324
162
452
256
324
1040