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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 16
# Folio 8v, page id 00068229:0016
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Effuriendum ee semper ut tot ia qua obfineantur aequationes simplices quor sunt occurrentes
eninque in finem, etiam ipsas varie in ter se componere licet.
30nO 00000 1
301300660
000
vlbo vllv
D V
V vD
qV
Ergo b
pa
 X 16
(1X + I8X 1(X), 2bX + b
2XF + 11 X H c23)
3X + 12 X ( d-  +
(4X, + 13 X ((4X) + aXC + e2
6 X + 14 X _ fux+
. pone es . Ego, fa
Inveniae duas quadratos, quorum summ  numorus ous
lb p
X + qV
12
pro 16 ponc 2Z fiet PX H X X+ Z p0. eti n
2Z I6B ∞ = Z2, pone pro lb, ponc X p. pro Z, pone X Y fiet
lb PXp L + XY, sive p p X + XV. at idem pp L. Ergo X + X 1 , lb
a
ne ponendo X ⊓ sZ, fiei P= R F1 Z
quaeritur. Multipicetiu, fery, fiet yt + ly + my +n datur
25 + 9 p (34
es summa omnium st +(y + my, quin i summae omnium re
quae datuo datur et summa omnium y+, + lyr, ergo
differentia omnium y H + ly + mX p - n
exhamitur dissia Y IY etiam exhamitur
etiam sun diffra omnum  et ergo
et diffra omnium my cxhaurituo;
22
.cuborum dcincess ab unitate
552 + 473
H bc.
e + lf. fer
2c
y +ly +m + n 0
+ 1x L F ++ Z (t Z +- o quci na l. et n. dam summi omnum in, quopipe varcentae
fiei pZ - 72 X fiei P = Z A
ai idem X pX F lb. fier: 1bp 1+ 5. Ergo debet 105 420
Nluncus datus ponntu v + d, p X 1Z per ∞4 dl V4 NC  c + _ q Ergo fB N
1b - 7V p X, pone lbp 1Z
 10
fet (X2pX + V et, ponend r. p PX, fei pX ⊓ 1 + 5
hac methodo Ib -, esse quadiatus
PX Y ( b + 5, sive (12
sed et hoc nihil quae d deplicanda
iisdem
e
1
si jam Ib sit quadratus, et E site quadatus aeie ud aoditus ad 1. fuccet quadralum,
quod facile est extrahi potest radinhobii et socutum est problema
Esto PX +, X + X X
pone X + 2 F +2 +Z ppo
x 1
s
10l - b r 11 - 4b5 ∞64 23 - 8029 + 1625
Habetm ego d. cujus valor inferatur
aequationi X b
1ol-b
ergo X lb + Z p0. sed hinc nihil si munerus datussit quadiatus clia metaodo
res facile procedir:
eg
1b cZ 1 X aZ
2
eropr summ 42 quadiatus
radi
2
553
+ 52 4 33
503 +2
(3 +2 +42 + 33
3+ 2
c. jem pone X 5 e + f. Item fxp, fl +C
fui fet 8 a 2ef +5 + Z
Xe+ fe +lf
py C. pore Zp e. fiet:
+e 4 2ef 4 f +C, C - pro e ponc fr l. fier:
eisenis
2
1
C. 9. v. +
101 - 1b Y 131 - 40
est
honc b,
s600
qu 
datur et summa ometium ny
x
Xealf 1