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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 299r, page id 00068194:0597
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pay.3.
Itaque altins assurgendam est faciamus q. _ A = ly tm Gs + Ny 4 P yt 4,i, 39 + qys 4 55
Ergo sulfiit g + mur s
aequam quadrato
+E1r. H5155. + 3
ceyy
+ n 4 2X1 (+ ZNY qy
y aequa 4 +fy+ 299yy
+ f.. + 25997 +g
3 + by3 + ccgy + dy + e.
9= e seu g9 = +cc sc f = = b 4b se = d3 2te + + bb = cc
fit set = d ib = 2 ce =  bb fit d = 2 b cc - 1 bo
qui imo video, ne hoc. ut tactem ex AX t cx + dd si quaddatis A. ex x - E et
ex X -G sit quadratus, non esse ops ut necesse ut quilibet horum sit quadratus,
sed ut habea du ut sint facti exiquadratis et fuctore communu. Sit
ergu quadratu ab 5y + 99 qu est ges+ 2599y + g ducendus in i yy + hy+ 
et fit poterit etiam res cedo obtiveri per multiplicationim authmeticam
Nam si sit S + byd + ccGy + 8y +e fint 1by = rcc yy + 38y+4-0
quae cum prioe habet, divisorem communem, inde bllendo y habebitur aequatio
nova sed hanc forte brevius obtine bimus conparatione quam s sublatione
fit ergo yt +9 yst +gyy 4
 =  V. Ct aa. HK
+sina quy e asgpbys F 9 tek
aa
a
Led saltem sieri potest, ut unus sit factus ex quadrato in simplicem, alter
vero sit simplex. Sieg ut si sit X - =
sed sufficit ut un sut facti ex quadratis et factore communi. Itaque sit
EX-5 = facto ex Hyy +gy +9. in h yy Her y + 1 yy + y+ 13
9y + y F554.
et (. x. (e) = fado ex Bgy+ hy th illigus t 
+55.
itaque factum ex sytgu in exgy etky +C, debet A comparari generali A +b)Engrdis
et fieth, sibi yt + astit y + fth yy
ffyy + 2599y+ g
i gi i KKy + +
.
+1 y + 2fid yy+ Hsey
fsi y (let2fggi y+ gliyy
+Rt yy + 2 fNy + ffH
+5fKK P + sgGKCK yy + g’ XX y
se l’efsemus X = l9 + monx rum s 5, cstip res reducacatur ad prioret mulliplicando ob term. nin et ult. fit,  Btdgu fggy +9C
1-8
het y + 2st 9y + d 7
fit feta
∞ ay +by régys +doyte
(ff = a: i 8= e: 13 Ex termosecundo fi
Ex terno. 2d0 fit 2599i (= b - ff KK) = b 2 - a KK,: i et 4ff9 i = aaei: t = b - 2R biX K + 915;;
seu 443 = b8; - 2ab iKtt a t
ex termino penultimo 2599t ] = d - g HX) = D   _KK ,. F et 4sD F = 4ue:1 = d P- 28 e lt e. R: H
sen que  = d2f- 28 e  +  . 1
Ex termino denique medio dervasa lege aequitatis, tit
2e13 + a13+ 1  ei: P +aL: 1 + b at. 21 + 81- et : 2t = c
seu 2e1 +3 + 2ait + bKKI F - aK  F + d 1’ F - eK 1 = 25;76.
lt
habemus ergo tres aequaliones linea subducta notatas, et tres etiam liferas,, i, t, +3, sed quae
reapse sunt habendae pro duabus adeoque evolutione sacta habebitur
Fortasse tamen ante evolutionem posset. conjungi duplices aequatio
nes lineatae, secundum, E; et secundum (7
Si veremur ne cursus evanescant desiderata? ob similem tractationem, secundum F et
Secundum (Z), video modum hanc similitudinem vel n rumpendi hoc aquilibrium, si s conside
remus ipsius Xd +. X +. X +. X esse tres radices, quae diversimodae X -8, X (E) et X- (E) quae diversimodo
s
ute tecu
Ergo X =G:
Zy9Fry+d
Al. yt + mm y + nyy + pry + q
+ 28r.. +285..
 P
Yds
aiqu
N y +by + ce9y+8gtC