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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 317v, page id 00068196:0630
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 habebitur aequata 4 quae de2 formula aequationis 14 quae
debet coincidere datae forta a ib, ubi a, et b sunt fa formula
datae ex y et x ravaliter integreque formatae
(17
Remlicebat statum ab initro sic facere: dx: dus = a: b
do v: v + dz. X:  + dc co: cd  Ct O posto v, 3, cd, dari per X et y
jam de= =V dx + dv du et du= Z dx + dZ du et deo dco ax + X dus
fiet de v + dq ZV a + dcocov Z:, dv. VZ c+ dVdo
Eet -dy: dx) = -b: a. latus autem suistrum aequavis. E vel  exhibeamur
aectus ipso ponendo formationes per Xiis esse rationalis e integras, et numeros
4, 5, 6, 78 significare contidem foatee formulas rationales integras. Monamus
p 10X + 26y + 1 et Z= 30X +40y+ 91 et cd = 5oX +60y + 51 erit d v =  10
et Xv = 2 et dZ = 30 et dZ = 31 et a c0 =50 et d0 = 6 et V =  70+ 71
et  = 50  81 et R- 40Z + 91 et 23 = 1002+ xF 10) et co =10 11
et 108 = 12O4 + 121, et fit ex 84. 6: 10. 70. I0XF goy1BI +71. 100. 3OXH0y1 31 4 01
120. 50X + 60y +5) + 121 + 30. (80. 10X+ 20yKII +81 90. 20X+40
16. 50X +60y151 F
450. 80. TOx +20y+1I. +8]. 100. 30X + 40y + 31. = 10) : 20, 70.10X et 8100. et 20
+10. 80. 10X.: 9030X.. 170,50X = 60. 8010X, 100. 30X. 11050X.. = - b: a
unde perinde est ac si parbamus 10 E 150X16B 170~9 11OXG +151X (1 161 y
+17+ yX + 152X + 162y + 153 et,, 430, in 190X + Ly CM, +50 in 230124
indivis. per 20, in 130X)  eu  + 40 in 90X + eu, +60, in 230X +  et,
vel Tubi -b: a alcendat
dB. . Ryeux. py ea
E
 in immentore et numeratore eunt prii numentor stae ipsi ae quandae aequetur
edus non sulori, Tabemusue literas conpartioes intrliendas decem
iseum fiat s in numeratorem compatatio, non
pec
 que fia
biunl litere
e
a
, b bia
sit inferior, poterit multiplicando Pattollilad p. dele in habeautersit
liferae conpantitiae. Nota: NZodet e   190 et 100, iem 10 et red finsti
noniunsuntur sufficit hotum nagna sed et 1 st abjici possint, et pro tis poni mutas
terns iier padfecturae sindt 15
xperopretium etit prosequi quont  s hac
 smplici positione, multiplicare fecta adendorm mogrdilliaat
proxinni est ut V, Zvela ex  et y ormentur Hormula integra rationat adrasica
sed ipsae 3 56,78 significent autum somalicas formaoes ubi musidebine
e quousus racinave proficiptua nostieno videbim quid fiat si utem modis 
stimand si quadratic soel estiam ost sint altiores aequales aut
in aequailes Et haec vietur compendiosissima ratio tractandi hanet
minam inde  siiliter plegeuad differentiales formutas
irratomales.
uquollies s cb 
dod  imaloeissimis manesa quosties quol tatemu literas ut v, Z co, toties 
EKhabemut E larbitrarias proficiente
ec literarum. jan in quovis quadu o sunt
. Et ad Tradum ascendimeus aequale numtro
ant termin
n+I nt 2,: 2 posito n numero
gradus seu ex pomento, et arbihariae sun  sunt 5n.   quibus D
tns
 alius gradus ipferior pe
epantio itaque numeu terurigore 
SM +
verum bis instituenda est
debet este n+ l. net de un
+1. pF2: 2 dee essae  nf1. diFE  posito n. p = gradii
a daule exaltioe sed pet sme exsitratione dato gradu a, et gradu b, 
n,vel salle
 et ex hiis ndiginio (4, siet ntqt 1. nq non major n, et dato 9. qutur na