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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 253v, page id 00068196:0502
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 - 2X = 119X = 600 X + 6224 X +38502 -36520 =0
+ 2
 2 XC
.. X
A1 + 5632
264.
25 X
X. A + a d  mha = fbX + cX + d X + ex +f
mam. X
X +MX = n X + pX + 9
X +2MX + mmX = nn X + 2np X + 2ngX
a = - 2 b = 119
pp X + 2pgX + 99
c=600 d= -614 e -- 5818 f- 5ero
bja
An = o + L, aa
4= 3f
M 42a
5888
2p9 = C. Erg p = C odh p = e
2YF
21b.
60c
ere in verticem resret
qua incerioi)
inposit
a + 2)
3 + 35
Mela fortasse res pracedit pro iveniepia aequa stuauto
y.a. et yy+
lis larras quas constat jam sum quaesitae ibi ocunhere
ubi datum essangulus langenlis ad ordinata
bi in casu osco
cognium
inveniendam at. si sit
pVidetur tammusque aliquis esse aliquando el ad punctum
a +X
dx: a+ X = ay: a et dy: df -x: ysil (dy: dx: a: a +x seu -ay = ax + XX
ilidem quaeri potest, (ob osculum differenlialis nam et haec curvaequae est parabola
frculum priorem tangib
et quidem revera hoc mndo circulaementio omitti posset  ita enim idtiam effecimus, ut de construi
Eagres proderit si
possit parmbola quae necessario langit curvam aequationis 1. si modo quae diximus vera sunt
ru
eu indemente
AB, X. BC, y
QR,Y
est aranqay
ad hoc solum sufficiol sic ostendo. ita ermus fit ady = a dx + 2X dx seu. dy: dx = - a +2X: a, qui vali
ela ex aep. 6. aequitus
B ducto ex aeg. 1. dat aa= -aaC ax + DaX + 2XF. datis
aaaxtrax iadatuddd, et proinde et y, adeoque punctum curva, quaesi
ulum que e diu
e
indentis
moti
sut
rax = gy PB
rag - y raa
datur et
veie
+ x - q
etque
+ Lax +aa= aa aa seu x+ as
qui
a+X-
nec
ae l
vet
e satur
siptetur Bcunc ete
unctum A carvae transcludent
an proa
R:: pBse
uideo
sed jao praesum o
videruta ne
oplibe drecta assumibrli qut intera
nerantem, et hujus es tensione
a+ x- q
ar cujus diferentralus
Ax. = y: at X G Z a: y seu -yy = a + X- ga. Ergo a+ X- q - yy. a - a.
et ex set 1 fit 2pX = a + x- 94 seu a t gX = 4. seu X:
=a,: 3
valores X et y substituendo in aeq. 1. fit 29. a = 5rra. et RC =  A- Fraa = r +. B
seuRC=
2 g+ ta 2 +
2 a - Y se seu KC = (( 944
seu AC = L rC 894 + saa - 4 ga + 12 r9 - 127 a + grr
quaeramus idem Methodo duarum differentialium; 2aX = gy, et
et
9ast ; aa + 349. 189 a + Z aat Z era
 a r 6a
h. fit
et _-2 r=X Ax + 2y -9 dy=0 seu dy: dx = r- X: y- q= a: y Ergo Y y = xy =ya -ga
e 
20.
tist
et
non
fferentialis rdu + Xdy+ yex = adus  seu dys: ex dy: a =rX= a: y. fit: yy= da - ra -xa
derum videre cohijam vrdeot nec oscuta sufficent  se  e
ex lolli possunt ∞ et ys, et restabunt Ce
79 7 ej 0 prtiia esitio inter Y et q. Sec lipae eus habris, natiras orur ro quia abes
aneenta 
nicunalem,
cujus novae aequationo
loga
adam
ovam
 et etus loco ad hibenda est aq
id, tet ti o t u . Set Scar+ ad. di est ad generatria