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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 227v, page id 00068194:0454
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replicandum r est exempto quodom, qual quomodo inquirendum
sit in curvam, posito parallitas unius divectionis ad paralletas alterius directionus
sioc faccre angulum obliquam. Insoce figuram 6 et pone pilam M tormento
emissa directine AB, quae ad AE lineam dicctionis gravium
angulum faciat obliquam BAE, obtusum vel aculum prout
pila sursum, quod hic supponemus devisumve emittitur; BC parullat
ipsi AE. manifestam est ipsa DC esse appliratas litantuli, et ipsas
BC applicatas parabole ad id est curvo, Ac fore paxabola, si iisdem
ordinatarum Bc eadem progressione servata angulus foret rectus.
Nurc auter cum est obliquus inquitam, figuram, A B posita X erit
BC X posito ra esse latus parabola rectum. Ex puncto curvae
C)) ducatur (CD (FB ordinata ad axem ABF) perpendicularis, et
alia (C  (BD, obliqua seu ipso AE parallela, ac proinde paralleli
perpendiculams ad horisontem 1 erit, EBp Anguli datus  AFH (C B ((B))
ponatur latis, ut recta BC posita 1. recta CF sit . erit ergo CFB 
et FB⊓ X Y1 -E sive XX
Causa ponamus.
c
v 
 pro1=2) compendii
C. inde FB1 X. et AF, XX
nempe X  in figura praesent, quando pila sursum projecta est; at contra
X + X cum devisum. Uhile ergo sigium actibignum hoc loco retinere. Jam
EC  ponatur AFHZ. fiet: ZFCXx + x. ideoque sumendo Z pro cognitu,
et caeleras explicando ad psum per ipsum, ivestigandus est valor ipsius X, per ipsam y
, fiet aequatio 4 2 cZ. +c
P C4 2CX + X et extrahendo radiaem.
 ∞ + 2cZ Y  c H X. sive X ⊓ 4 sc + 2c2  7c
1I S c4 2Z 42c Sc + 222 + c2
transponendo
et
V (B CF.
Quae aequatio it reducatur, erit C 4 f.Z - by, B  c SC4 2cZ. et
Quardrando t 4 20Z = 2cby), +c2q
destmendo uliotique t 4 2CZ, fiet: - 257 + = to
ev
aequatio est ad Hyperboiem circa Myraptats inti oesmr pinr drorsibilis aliquo sallem
ed erarem inss Mic,
uiom se litera C
Casu examinandum.
hac aequatione fieri aequalio a parabolam 
nend MC  8. Treberet ex
Est autem e. infinita, ideo
quodsi angulus AFC rectus, erit C infinita, adeoque ex aequatione proposita.
fiet:
27 - 2by.1) 0. quae est  chandetenitbolam
eleganti calculi veri indicio.
Tantum quaerenda ratio est, quae hie canalytice o exhibentur, ela quadam
et
Sinthesi demonstrandi per ductum, linearum.
Te videndum est praeterea an aliquo
alius casu aequatio ad parabolum haberi possit. Nam tunc sarie cum AB ipsi C B
vel AE parallela est, c fit infinite parva, et angulus  destructis ommbus
corminis ii quibus est C, fit, +t o. Quod indicio est ordinatas quoque infunte
parvas, adeoque lineam motus, AC, coincidere cum rectu AB. quod itidem constat.
Uenum lantim examinandum est, an reductine quadam Zy destini posit. Idque verum est
et inveniemus curvam esse parabolam. num pot y4 faciamus y +pCo,
fier y F y H c  d Z. et g  co + ad  Z + d Z et infecda pro
vel  inferendo eorum valores, fiet 3 H C0 _=C
rende - 25co  2c
Eut, (+ equ
destructi destruindis estabit. 
2C90) (v
Lb
2
cor - 25042
=co (72C c03) ( c27d, et
siovergo  projectio sit horizntalis, sive  inlinata, motus projectorum sempererit
in parabola
F. aequatio ad parabolau