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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 14
# Folio 1v, page id 00068059:0002
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b+
esset
Si latus ectum fist semper idem Y, et ipsa
AB, sit a, et AX BX, a X-a,  et linea
et fint X- a = X. 2 +C: 
formantes deberent esse parabolae, leret YX a = yy. unde
fe pro puncto concursus fieret a=C unde res, non procedit.
Sed possumus et latis rectum variare, ita ut easumam constan
eu secundum variationem puncti B seu rectae AB non quidem ut
sit in data ratione ad et
sedut relationem ad eam habeat
cui accedat constans c. sit ergo r = h a + c posito h esse
numerum, et quia rX a=gu in parabola communi, fiet
hatc X eerae-haa -ca = yy
eum
quae si differentietur
secundum a, pro puncto concursus parabolarum formantrum
0 seu Ba = AX Bc. 1
invendendo, tiet: XH2haa esta
per si
hx: 2+C.rErgo ex 2 per be7
us
et Y
ferum recta
1) C. sit per E.
fiet tandem ex g7 adeoque linea formata est ipsamel
et fiet
ha hxitc
  C
ahy4 seu hx+ = rypTh,
 paente alia quaedam parabola, cujus vertex sit A
et
latus rectum sit ipsa constans c. Nec refert qualis numerus
sit 4. Quod est tucoreum notabile. Quodsi jam differenticmi
aequationem 3 seeundum X et y habebitur parabolae jormantis
angentium propritas, quae eint hatcax 2ddu
s
dx = ydus Et pror substituendo vatorem inventum
ex ag.7 fet _ hxdx 2ydg. quam variare licet
et
1C13
verbi qratia ex aeq. B est y = Cx: y et
(12
Et
que aequations esst, nam ds
hunc valorem subftuuendo in aeq. 10fiet, GXdx = 2CXdy: v
sed ad hibeamus parabolam
Vrr. X- a = y. Ergo ex c et 2 fit
3
(2
il dx = 2c dy:y
hhaa + 2hac +CC X - a = y3, quae si differenti, etur
(3
a
ubilam seu reaeegu
secundum a, fiet X- a 2hh  + 2AC= th aa + 2ha CB CC
se
3. Unde collendo a
lx aeg 3 per aeg. 4 ier aequ. inter Xc, et dividendo
Den 2 et 4 et r. fil X- a. ha + 2HC
sutrobique per hatc fiet C, 2h x - a= ha +c. seu fiet
2hX = 3ha + C seu a = 2hX - C, : 3h et X -q 3hX = 2hX + Cg. 3h
( seu X - a = hX + C, : 3h et rseu hatc) = 2hX - 2C,: 3. Ergo
Ex
C1)
leq. 2 per aeq. 7 et e fiet hh xx -ce AhXm a C. 27 siti = y
+et AB essea
et latus rectum
Y
ta+
= 2hha + 2hc