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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 23
# Folio 5r, page id 00068041:0009
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de
dy
ego.
XFa
Ergo dx X + dxa
aegu ydyue
seu 2 xX + ax
aequ 2 77
seu gyaego +2ax
texnatum
togarichmoa
quia saZ
est log2
A Byee
AB aequ. b. BC aqu 
AB aequ X A. B aq B b.
BC aequ y.
in gerere
1B. CaequfX. 1Ci B. 1B. P.: . f XC,
Ergo 1B1 P aequ H. X2.1
fiet 1B1P aego X
2C-1
Ergosfiet X
-
fXC
2e-
seu b.
sit faequ. e.
26 =1 esse aq. 0. se e aequ seu curvam esse parabolar
si deberet esse X aequ X fieret X2C-2
C - 1
a aequ 1
ergo e aequ. 1. seu curva quaesita erit recta.
si deberet esse X
eC -1
 aequ X+a,
ces non poterit e
esse constans Est autem f X aequ y. et uosus
est X. aequ X +a. Ergo X. aequ XX + aX.
2
Est autem X aequ 3 et X aequ 7Z. Ergo 77 aequax tax
Ergo f aequ. 3. Ergo X
Unde aequatio
2yy
XKtax
seu
20
XXXAax
log. X
2y y aeg.
nta
aequ
Xx+ax 
aeq. log. xtax  de
Ax X
 log. X2X + a x
XX + ax
Elogx log. X
aequ log. XY = aX. e Aydy XXtax Y lugu
429
log. X  = ta
loq XX + aX
e
aequatio differentialis
log. X
Iupax
XX + ax Unde habebitur
sed jam aliunde habetur alia
aequatio differentialis ex natura problematis, unde
sequeretur c aequati absoluta verum o hos
nimin efficeret, tentandum tamen, ut res accurate pervesti
getur. Imo fortasse non salis, quia ita devenitur nunc ad
differentias differentiam. pon ponamus unitatem
erit  eo casu loganithmus XX + ax
aequ
log. X
Silam, poncolg semper logarichum unitatis esse 0. logaribhmus X
sit  ergo necessario log. XX + ax erit 2C
memgre
quando xx xy. Xx +ax. sed inteocasum non este dabiles nsipla
 aeg. 0