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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folio 34r, page id 00068255:0067
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 33v); this page is its right half.
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# Lines: 108 recognised, mean confidence 0.79
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at
Invenire tres Numeros, ita su ut summma duorum
duorum
quorum vis sit quadratus, et summa quadsulorum ab ipsis quorumvis
 sit etiam quadratis
La qx + ly = fusi
1x+ 1Z= gg ly +Z = R
yy+22 = pp
I XX + Gy =msa XX +ZZ =  nn
ly = ff lx = hh Z (Z = gg - lx = hh -ly fit ly = ges hh- g9 + 12
= ff- lX et fit 2lx = ff + gy - hh et Ely = ff + hh =gg 2tZ = g9+hh. 
AllXx = f4 + g + h = 2H99 - 2shh- 2gghk
allyus = sa + g ati 4- 2 H_R + 2f sit - 2 tih 99
4UZ2 = f+ G2 + hd  affgu  2ffhih + 2g9tit
AllXX + AUyus = 2f + 29  = 4gghh = MM
fiet fa +9 + h - rghh = uUl mni seu gth- 2gghh  illum 
flrg- 2f89  EUpp - ho
Ex 1 et 3 fit AAgu = Cyghih = pllpp. furum fhi ssht = Ellnn-
seu sit  gg - h
99, tah, 5 -h  Il, p + m p. mtt, fag, 5- g, = Il, p F m, n- m
Cpm=f  df - dh
ff, 9+h, g-h= U, p. + n p- m
sit l,p - m des bf - bh l, n = m = cf - cg l, p - n = d9 - dh
et ex aeggue. 12, 3, fiet lesfat  lbpt m lyg. f. +h. = Ub, p + m H
Ihhf +g UC, n+m IF, oth = Ud, p+n
itaqusope a49. 4, 5, 6, 7, 8, 9, se loc non juvat
aub
Radicem extrahere
subtractio melius peculiari plagula
Generalis duadica
Non potest generaliter, scribis tas
ex fomunta dyadica
nec sed  Nac potis etiam generalita
sed 1(b (+a et isu A d Ia
sit ergo
11 + q quod et identicum est
Aaus hine
h = a + b- 2ab a takl- 2aK L= a nte
ab ex R, nisi conset
h esse 1, neq esse
Kh, nisi os ele et
nec ex vel esse
ergo vel ex Y vel
vel ex itkIh
H
isique ho hab
M b dabit: 2b
q
b
+ sil
-b
EK
ab +bh 
quaentum quantitus, quae sit b si b esto, et sit 0 sibus
aqua
x quaerantur X et y bi t but 102
Ergo y= mhtnah+
A Y (Et X = a si h sit 0
101 
A y-o EtX = 1 si hsit 1 et a sit 5 Y00O amplius variuni
yX
a
si hsit o siet X = la + p = 0 quod de-
similiter yla + mhenahtp bet esse = a Ergo fiet p = 0 et l = 1
et sed qulop e
minon
E1
lis
sit Eod si h sit 1 et a sit 0 fit X = m h Ca) 
Ergo LX + m + n+ p = 1
 sonto, se seo  f 1 orgo m + d -0
erjog= inhenunt1 si
11 12
ut oportet +  y - 1 EtX = 0 si h sit 1 et a sit 1
tah-2ah 2- 2t 2ah t a th rat) - rta. h
=fi + h
sublamono duadica generalis
deu a = h - 2H - L2b
non absolute fieri pt
res non procediret. si  pari ratrone non potest generalitar fier
Ergo tandem
a
-1
a 4  ha b, 1 - 2b
isnga= R + L Fb. - 2bA
scribi petibi bsta sed ilta namsibet a essent c
fien C) b+a
sublatis columnis,
nam si
si
ab  FL ergo )b Lakl
1000 ergo a n h tk
lie d
Subtractro Jgadica e etad
et X = a + mh+ nati,
quod debet esse  Ergo fit
et X= e nato quad debet essed
Et X = Rat FInat sit jam h, 
pa t sit y =  td mt et a, 1. fiet x = +n1. Eg 12C
ax seu n= -M. tandem
ii a o rit bal, n a
n=1
copi 1.L 1.  p
cup atI. _ p   dta Ergp H
o et (Erra = Eah
ab
xut
ed e fgh