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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 17
# Folio 7r, page id 00067979:0013
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versus D axi
A, aci AE, par allela  64  a Y. jungatur recta 2 K, et ex puncto
K ad eam normalis erigatur K3, quae possit + ur + mr, denique centro 2, radio 2H
erigatur circulus, qui cur Parabolam socabit in punctis Y unde demissae in K in
definitam axi parallelam perpendiculares erunt V quaesitae, quae ordinatim ad angulos
rectos axi parabolae applicata, designabunt puncta, ad quae ex puncto D
ductae recta ipsi parabolae parpendiculares sunt
potest E
Nuta sura - n. haberi Germetiore non potest, ideo pro = n, poni debetex
Veniumm nunc ad constructionem ellipseos:
nam ya 42d12 a-9 l3 (+ 41+) - 24
cujus equalio est:
Melius est resonere malogiam, quae rat: et
 quaedam contrahendi caus. mutare, ponamus: HDeZ
et fae fer (( +( + 417) Ex calculo illic patet, si (+ 4)4 (+) f p0. tunc in omni sectione
conica problema Aeri planum, d constructionem brevissinami, quare datae sectioni destribetur
fautum similis; ita ut f hunc eveniat qualem defictenamus retenta G ad eam ducatur
minima quod utique trevissine fit, cum ex calculo proposito atqui mndma ad unam contunata
est etiam minima ad altiam et forte altram ne duci quidem necesse est, sed sufficit intelligi
videamm quid ad duas sectiones conicas similes sive parallelas requiratur
AX HX.
8Z12 XY eV. ZVn v. constad esse XP ⊓ a 4 a X, et 2P, b+ 6Z
Item y Fidrax + aX et V Y SibZ +
sie st+ L
et+2q
bive
s attpax rarx
b0bc
b + 2627 +678
271 +72 +
vel bt F 27b+ = by
271 + 7ut 
2
F +
eu
at
2xq + X2X
sinde le
273
a + aX
4 2
EoZ
2Z + _.  r+
1
a4 +2XaG + ax pommus p b sed nondum omnes paestemntis conditiones exhaece
exqu+Xq
 e
ua
sunus, supares enim ut 4 catra adsiciamus
datur niXZ est  ZBN C ZP
Z, et AX AB+ BX ZL
Ergo x  Ergo AZ B X - C + a = b + a X ponamus 1. + a 1γ. et 1.4 B Y  et - e+ a 5, h.
L+ 1 0
 Jam ut X quoque et y alter
aqu +2xaq + ax
2xq + x q
2x 4+ X9 4
fiet Z5 Y X + het ba. Ergo. 
cum deriremus:  ideoque
b+ + VX + hag ba + gX + 2)xha +nXba +ha + 2lba +b
bc2
d∞ 2b+
2212+
Vxaharba
002t. +
or b
Vue schat bactia ertibae abs
02+
incognito b, et F. patet
vel alterutram earum vel rationem earum, pro arbitrio assumi posse. Ponatur  ( b fiet
aqua
2Xqu+ 29
1Z+X 7. Eog et dividendo utrumue per a s bt fiet q2
b +2
2XG FX I 2Z4 FZ + evitque enitque et dabitur 0. eritu t B
expiiniamus x per sa + bp +nt et Z per m + ba exq per am + 2ma b + b a. Ergo quae
a
s
ponciltur t+ b 0 foret semper eadem
ratio seu Z HX X. quod nolabile Theorerua pone dati; id enim necesse, 4 ex ut lalculus mimo fiat brevis
feti 4
214
i n
++
9 seu be va 14x
+Z 1 1 nt
(1E2
a Y Y th. Z +HX
sive
ponma
qq
a + a X
b + )X+hatba
co
12
cum ergo una tantum aequalio
habeatur et duae dentur conice