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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 288r, page id 00068201:0575
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Aeq. 1 X (+ 7) a
Duae sunt datae aequationes:
lil
9 Xy 4 ad
Aeg. 2. (+ 4)1
Et altera ad sectionem soncum univessalum  ZaX F aX
X
+ (+F) a y + da ,0
+F)
vil LX) + ad X1 CY ida B0
npio.
Quaenitur modus efficiendi duas aequationes alteram ad circulum, alteram ad sectionem
1F
conicam Universalem carandem incognitarum, angutqs ejusdem
sinus rectus
Esto arcus ereule ABC. diameter Ad denta CD sinus versus
abscissa AD) Angule quolibet DAE ducatur recta AE
et CD producatur in E et CE appelletur Y. et DE =X.
fiet 2a =2ax = X F Y - Y X. sietque:
2aX - X 5 y +
Vo
X
=2t X)
Eisto sectio coniea ABC, cujus diameter Ad. vertea A.
ordinata sed non pegiendicularis CD. perpendicularis
ad curo ECP. punctum datum ex quo perpendicularis E.
et Ad rX
distantia eis apediametro paralleta ordinatae
EF tangens LC. quaenitur AD. Triangula FEp
et DCP similia sunt. Datur antem FE, d. et AF,, f
vocabinus  APHX, et DC, y. et D p p.. Sed possimus
Est autem
f (+
2aX =
Ix (+ +
P.
X H y. item est:
Sed cum tres sunt
incognitae adim alia opus est aequatione quae valorem exprimat ipsius p.
constat esse quod in eo constabit, cosi
ipsam CEC cogitemus esse omnium  possibilium minimam.
um dau angulur.  EF P. dat ratio E. videorem difficilions
fore, si angulus non sit rtus
pro aX substinatur ejus valor ex aeg. 2. ubi X Y  ax
punct residuum ducatur in latus rectum
+d
4.
F
=da
da
292
et habebimus
2a
292
+cV + da sonatur jam Z e Y + =X
XG. Sed ansilus quem Z et y comprohendent non erit amplius rectus
Rectangulum DEA (. rectangulo EFg. in circulo. At in Etres
Monsvlison
2-
 est, ut axis seu latus rectum, adrectum BC
rectomd
hansvesu ad transuersum. quae
cum in cucplo aequalia sint, ideo
et Triangula ista aequalia sunt.
In Hyperbola ut BC ad latus rectam
ita AE D (vel DEA) rectans. ad
dq 2t Et DE
Z
DEA a
id positos
EFg. Idem in parabola
lateris tectis ad peransesum ratio
arsu
exg
Z bq linea
b Z
fiet aequalio d DEA 4, y. -y
EFZ FI 2Z V + BN, et quia
v st Z b
. fet aequalio, quae est
quae e 27 L5 A∞y V +v. 4v+
mo vad Hipet. Parib Ellis
quaque investigarem
lucatur tangens
calculi
in Aeg. 1.
fiet pro a
tolli poter
fiet
vel CC
4
Ergo Z
7 +1
Ergo in pabola
DeA0
Etq
ponatur.
a Rei
et q