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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 16
# Folio 16r, page id 00068229:0031
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ss
seq
6h 1 46+ 12)
Esto pp1. et 9n 10, et +-
et ++ fi -. et 1+ p
fiet V poi 2- 20- 100 1ini
F4 =2- 40+61 732
qura +g 12t semper veru est si p. 1. et  +
quantitas major binario; se cunda ergo ut ver succedai necesse
sive 24  1e4 1292 49
1412
18 p 14
130 ep7 11 28
cet (7 (t) ponendo +
Aliter resumta aequatine ponamus r  P
et  V 1 et +, et + F p + f 9. fiet equatio
p. p) - aul + V. 2lp4. P∞ + + 1p4 (2p 7) + apuq- 1q m oprt po
ligo + P
1+9- 1+7+
+41+1
1C1)7)
14 -2p + + 1p al- 19
+ 4l3 + pp + +pgl +6pC
1 + p 12 1 + rp 4 2pgl + + Vqe
414 + + 2p l + apq1 +6p 12
et S7 P, = t.
Sr essiu -. et
51 2. Ergo 2 149+ 497 - 49- 69 + 41 4 ab B es a ex
illude v
 7ath + 10l +P xe videamque au tres conditions
et ex
1 +9.
atee
41 fop multiplic
V do pe aintem, fiet. V + ta + +1Y
ac Y) e t + Cx.
P
P+1 = + P
Xex,
Ergo X - aba ac, est  . e. x -  p (t C   Ct) - Cx) 4. Y + p- p1
sive X. ab - ac p C v - C p - 2 CX.
 ex ex pi at. qua ab. quantidas affirmativa
Ergo C p Y exp, aC = CX. Ergo e p + 2Cx p ac 
ev p e p + 2ex l
c ++ ex p 0.
p
Habeluus ergo tres aequationes determinatucesq a tribus silicet
numeris quibus utimur nempe: CP + ex A Ct. ++1
es
C F + ex p. 0. et e
p CF + 2exH
1 + P + 2
pro et in prima substituatur ejus valor ex secunda) Eo B fr- Bp. 1B
fier er p + ex B 0 = Cx. ergo C F + 2ex pio H(HLS . s +  + L. Poratur
pror ex, substituatur = A 2F,. seu Sp2p..
Ergo vel Ep H 2CX vel 2CX 10.
in Aequatione 3tia  et fiet  + D F ) V
ejus valor inventus, fret: nempe B= e p ergo pro CV pC P + 2CX poms (4 aio
ua
110. quod cum
per se ipsa quantitate constet, quia omnia quadrata sunt affirmativa
H e p + 2 ex. omilti, cum
ideo potest posteria extis e
sua sponte
itm g p et en F
C p + 28X p0. sequatur
+ B +1. fiet:
2+B + - B (+) (FP+t Fb
Pmamus 
eno a p
Rem ergo eo reduximus ut necesse sit vel ep p X sive  p LD) B
vel X p0
Quare si tantum X 1 0. omnibus conditionibus
est satis factum affirmative
ergo C P B+ Ex po- ex
et fier PH i C
Nam si X po. erit etiam p  2CXpO. Fiat Pp D ex ut exaral
Erralum est hic in eo quod conditiones (tem affinuntivam a 
diversasive aequationes diversas inter sejungi
d+ Ex  et  d et LitXYD
. 
2e P+27X+ 
ergo eX  V - X +β. Ego p  Y- 1 . p p + ((DD
ergo e est quantitas affirmaliva. Ergo ep
e + ex P + + e
Ego  oE 
t= +  + + g   P) pro H) sin
p  + 2x 
+ 2x pP+ B.
 2e0
1+ PD + +9 +C
s
(11 14 pr 1 4 + X F
IIs
sine etip  attolem
2.
Ego (Y e (+) 2 B Sp2 18 + 1d ael 2 41. - 2 +2
et pC PV 2rP p
~H () 
V + + 9
2+4+β-B
aemus vatorem ipsius 4. nempe
114 + C - 1
rc tppl- p L
Aliter.
++2
7+1
viBit
pel- p
+2
fiet  eividendo per
et p fiat p et
si apparent tesse quantita
a ( n esptien 
et fiei Aequatio
1en + p 
unde fit:
reeit
D NB. Poneut
scilicet (+) (D 
Ergo V  seu  v2t
l  a)b
a  aV VE