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# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 7
# Folio 20v, page id 00068160:0040
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seu43) dr. 3
et y=
seu
2
y: do
dg= ed
19q -  etv 
+ 1
Ergo si
-hCY
posito e = S9q-hh, et A
O aequales erunt, in composita ratione
directa ipsorum du. et ipsorum
+h) - h CV (quae sunt
62 ∞2
tu
cproca. Unde sequitur summas ipscram y
areis sapplicatorum esse ut loguarichnos, positis v ut numeris. 
s
=X 1 3. fiet C = 4 et fiet: SGEL 25 - 2 X = y2
In numeris sit q= 5 et h=
23
sit X=5 fict y = 4  jam habeb habemus duas aequationes pro ipsis averdue
BR. sit dy = H9 denique
20
du = d dvX: y84 itaque dv sumta pro arbitrio
e
g 
Ady + va Vdv = C, fiet C =) ∞ +32 = 4C. et habebimus Et siet
25. 42.  400 F 9 = itaque eegq = 400 20 =400, et h =81, et
s ev - 36 et fiet 25.4.  = 40 + 481 - 36 = 415. 4. 98
1. 30
quod est falsum. calculm ergo resumamus ut semper habeamus probationem
in manu:
h
2549 -
259t 2X
= 169
et 167 = 2599 - 9l 4e+ 1v
(3)
jam 20dx = 20 dv.
2592
4e = 259 - s2.
(4) Rursus 
sit
e
25924C + 1Y dv =
esse aequale constanti 89C. itaqe tollamus D dus ex aeq. 7. per aeg. 6.
et fiet 1v ydyI9h 4C+ 1v. 20dv  1by 20dv, G=8a 4y
e
Et pro gest in aeg. 8 subestituendo valorem exaequ 1. fiet
35b 256 2
1q et
259
5q2
se
Cqte+ LV. 2OaY + 25
65 dh ) 4C oh
e
∞1)O
1V 
osi ACIV 9E
e
v +
st
de
, 259 95 2592 (3
2592
oli- 9h ) Re1d
+254
25907
25qV
89 4y: 20 dv. et aequatonem pyrgando
42
qu
a superfluis fit 2526259) - gh 259 + 881h - b onti4e1b =
s
2
acuv
10)
= 6904y: 20 dv. seu 1bC259 +81h4 9h 4e 1 V = 8904y12999: 20dr
O A eV, 9h
254
est
2
24+ erem si 16V 481h 254 sit = b
1N  259 - et
esqu
fiet  25q
48f. 100 b. fietq
b
2. a
481. 100 b 9h qu V- 
 o be A
36
400t
4y9dys
328
1- 8E- 9
antu
fet 481.75 bb - ob, 259 4 e1V 69( que0d ponntur constatu eb
fiet et+  b- t ponamus ostena 259 eetet daniq
+e +  ctites 81: 10 F, et 
cssrc
a  Ergo si 1b e +  8th: 25q ponatus stb
445
gr aX=4yguy
est
e
592 4C + IV 20 dv: 4y. jam debent  1V9 dy +4V20 dv
Ergo du 9d8 = ek2
328
8
52
u
25 Q +1s)
et
3
aC
28
et a seu Y 18H= reCog 162
(11) 299nge 495
sit, be2 18Ih: 4u9 =9tC. q.. b gh 4e: 2592. Ergo B48l b = 2168259 4 81h: 9h 4C
q
Et summ. omninu
et ordinalearum illipseds, tanslatarum ad abscissas alias, temporiser mers proportionales
erit  proportionalis ipsis bv - L∞
80
45
16. 91