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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 122v, page id 00068200:0246
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 121r); this page is its left half.
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# Lines: 111 recognised, mean confidence 0.75
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Tres numeri inventi sunt al.
al - X
in
usa
al = X
rCX X
+C
quadralum primi, a l. quodrul Ergo al Na- ralX + X quadrato
ito
secundi, pro  W po Wl, pons 1 (e
x
1487 (4, 4d X+
4 df
none 
seu - 1212
et 2a lX + X+
et ponendo Wl 1. X - dl fiet - W 2(2
r
iase
 - 2alX +X
 X7 - 2dlX + al modo scilicet
quod sedulo notandum est, et habebinius idque
ostendam fieu posse erit enim 2d (X +e X  + d
 30eo- fl3 ergo X - ol 5 Sd  f (3, cujus possibilitasermanifesta,
quia f pro arbitrio assumi potest. quare si differentia inter X et d, p
minor esit quam d, seu si si X minor dupla dl,. seu X 52dl.
Hinc jam aequati fiet:- 2d CX +d (
_. 1 d1
Fal +2dF
vel ponendo X d , e + N 2al  2al + 2dl
Et quaeritur Ratix ex 2al + 2dl, Ergo 
eritque
Ego 2al + 2dI ( _  v et erit d B  v - 2al, eritue
X e
v0 - 2al
ax
. Quadratum
Ergo Terminus secundus est al 
ita
+ al V
+v
2C
secundi est ergo est a
4au2
et quadratum ejus
aQuadratum termini tertii est s ut habeamus pro Z adhibearus loco
asat
16c a l
=8C alX-gal valoris ejus inventi, fietque
a(2
opo
 =a l + 2atX + 2alZ  +2427 ~ 94
5) X + 2flX + s et differentia quad ratorum termini secundi et tertui
L
entque tal +-
2(M)
fiet t al = yV
( XfX + ( (ponendoque
E
+
+ 29Z, ponendo + D + hZ. perit GY Z + AY
L
 dil a
L + 2dhl Z + h 1
vyr
dl 102 4(2
v4
erit +2alZ1 + 29V X
L SI W=
17
t
eridque
u
L e 
q + hl et g, erit
d + do 2l
I2
Z, HAZ, eutue
1 1 est itd non hab ut sed ita d vix habebitur sine fracte ne,
ergo suiditate; Ergo potius ponamus al-
se contnet n.. sic ergo
=h umo non succedit, quia g. in
rectius effidemus ut h eva- 2
evanesent, faciendo 2 al ye q - fX = p qtfX 2f  al, et
pionendo
X 1 5 + f
sive f
z2
X pu va ral
pone
2 V
fiet y
e
2 N +f∞ 2al, sive f
45  et X ( 5 + Z X 2al. et supra
fiet 8V7 16 als p(65 V + 2vZ aV al
S( 2V + L, fiet 16 et _ ponentoque prBy e ponendo BV W ponendo scilice tp Z
et pro 5) ponendo v + L pro W 2 P +4, pet 8v +8rt cb 7.. 8r Fvr 18r
6p 15
jatum ponennde Y H 3
at, pone set Y +al, fiet al, t  22 al
ces pone s Z 2al + vel. ponendoque
+ dl fiet f
et
5
S 1 = 24 +292 - 9, et pro -g, ponendo  = Z- 2hZ - h
fiet al - qu
H - Z2
aesu
h
vet