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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 280r, page id 00068194:0559
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Schediasma de Focis Conicarum, Octobi. 1674
invenire locum, unde ductae ad data duo puncta rectae datam faciant summam,
aut dato differant intervallo  locus est Hyperbola
utrobique:
 b
2
aliti
to Ellipsis. Quod
data summa vel datum intervallum  b
Ex dato puncto loci quaesiti assumto C, demittaluu
perpendicularis in AB producam si opus est, CE,
appeleanda y, et AE vocetur X. erit
AC y + X porro EB AB+ a AE
vel AB + AE= AB AB - AE, vel 3, AE- B
ergo EB ( F) a (+ F) x. ciusque quadratum,
EB2
) a (+) raX + X Ergo CB 7) a +) axrX + y
Ac proinde jam AC + CB b ergo
=s +X +b  + Sa stparaarus et quadrando
32(( X - ab fyrx + b  a A) rax (X (1y) et ordinando:
 4) raX  2b S ex,  et quadrando, fiet:
seu AB
e. D
42 (4) 4 d’a X + aX H y + Xd qende apparet si a sit major quam b
l
 locum esse ad Hyperbolam; sin contra
ad Ellipsin; denique si a sit infinite parva
locum esse ad circulum, si a X, sit dupla ipsius X locum esse
circylarem seu
esse ad Hyperbolam catera rectum tanspersumque aequalia habentem.
stniil seu impasibilem
ti  si a aequetur ipsi b locum esse ad patabolam, denique c
b sit 0 locum fore ad line rectam, quae clarius apparent
aequatione hunc in modum ordinata etque explicata
-a
b
V B. velbus .d X + aX. d
1.
2ba2
Unde illio quoque intelligitur et locusq fiat ad porubolam lipieam b
Excmplicausa ponendo
itiu
6
dabit + X (+) aX + a 0 quae est ad panabolam. Explicato  signo
e infinitam
nnfi se papva
(+) quemadmodum necesse est, ut = ax  x fiar quantitas nihilo
major, quici a p S.X + ax Ergo + aX - X p a et a pX q8B
 Parabola Ad punctum autem esse patet, quia non nisi unica est in
in cognita, nempe X). ergo non nisi tot esse posun punctia C, quot aequatio
aX- a Y x, admittit radices, nempe ad summum dico. duce sunt vie
Ut autem ad Parabolam quoque et Lineum rectam perveniamus, una ex mutata
monnihil quaestione. sive formula problematis, altera ex explicatis psius aequa-
tionis incognitis. At cumatem Parabolam hoc habere cum Circulo commune,
ut flexus ejus non nisi ab uno  dependeat. itnde patet lapsum esse Cartesium
faltu