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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 310v, page id 00068194:0620
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RY, vertice R, exs RW, aung ulo s silo Y sit rectus
sit extie conica (sit latus rectum r, transversum t
sid 2Y RW _ + Y. Qu RW = quWY, uti quae est.
aquatio ad parabalam cum t est insinita id Ellipsin cum t est
quantitas negativa, ad Hyperbolam cum est affirmativa
Ducatur recta quaecunque  per punctum , positione da
positione data, per punctum datum A, lecans axeri conitae in puncto dato B
inhac recta positione data suma in hanc rec ex R agatur
hormalis RG. datur ergo et punctum G. Ex puncto A ducatur
recta AY ad curvam Conicam, et X ad direchicem
ducatur normalis XY vocetur AB, a. AG, 9. WdG, C
AX, X. AY, v. XY, y jam D WY producatur dum
si opus donec ipsi directici occurrat in I. jam BR + RUI, :, Wo(tYI
= BG: GR. YI = Y, BR: BG. Etsit BR+ RW, GB:, WY. BG + yBR =B B. se
eu seu BR GK+RW. GR = WY. BG+YBB
nhilo = 10 f. 8G+q sR C BB R
Rursus BI: D BG: BR = BI: BW : BI
BG: BR = BR + RW, ii a + X + XH (XI =) y RG: BG
Et BG: BR = BRF RW, BG:, a BG+ XBG + yRG
sit aBG + XBG+ yRG = B qu BR + RWV. BR  - BB. BW
compudio a + R vocetur e fint AEBG +yRG = qu BR, : BR = RW, unt B1 = ZBG+y RG; BR
Rursus est priese aequatione AID = BR GA BG. RG DY L BCBRy BRgus  jus
quot duos ipsius Ali valores aequando, fiet BR. BG. WY + qu BR. y = qui bR. ER
=es 3G. GRE+ qub R. y ( qu. BR. GR. siet D 
sn BB. BG(. WdY = BG.GRi E = qu BG. y, Seu WY = GEGR - 9BG1: bR
Pro  substitui potest ve pro y substitui potest (Vo-XX) S
quod si valore ipserum W Y et. Rud substituamus in aequatione
ad conicam generali, bet supra posita, fiet
Exy BG AC  2E BG pubR. rysis guber =  ( E guli Ait n qu bcy)
-rcy. PGbt
(EE quBG+ gyquRG + Bigu BRL
ex + Et. BR (LBG FytG -qu BB)
seu ordinando
X. BE. BA
1ADA DZAE
+(r. 1) quesajyu fb it)  BG GR Ey +4-45Z
 qu. Gk) exucm eg nsithi bpel t  al. b95 p2 loqu + HqL,
= qu. BG,de
ca st aequatio generalis ad conicam, parcllelis normalibus 
comrdinatis ordinatis normalibus ad direntricem, posita abseissa X,
ordinala y; abscissa inde a puncto concursus et directricis
somta  E, angulo directricis ad exem determinato per
rationem rectarum BG ad RG, posito R esse verticem Conicae,
tit
dividatur haec aequ
+BR )Cub. BR - 0
sid per B qu. BR.
553. 979  t in uys a bi n u r 
et compendiose seu
B intersectionem oxis et directricis RG norimalem ex R ad directricem
et BAq et qu. BR esse qu BG + GR qu. GR sintosquals, aiiue
9y -  vo -xY
ut sam tllams conjngimus convergente
paralelae, sollere licebit y stubstiuto velore
vergens
(oVAXX)  onatu ut
lineisi jam velinue lobere y, pro eo ponendu V N, considerandum vit plorum Ex et gus coefficientis
Notandum hic, Y se habere ad BG, GR; ut y ad GR, BG+
ilanii ,agsen GR BG, seu nisi angulus dirictricis
latans sub 25) tolli pro XXFyy
e contra intentum. Sed si f-g, et
fo
FK, sit
locus
ocu et
ose
i Es
lnendur pud
BG=GR, evanescet, BG. GR vel qu BG in aequatione
enius f farit=gr
sint Yrt afam taa Ahis) ebpru + 2s (B + rpay + u8. 1 =0 a C E+ r. t Ety + pir 9 + (() (1 
ad exem sit semirectus non posse XX
substimenda V, sod ita assurgeretur ad X
comprndio faciumusevi H +X Torhus +v YK
Cetanont hoc mode Z alei obsevanatenem in
sit f rhfX et ArtXX + rEgq = 1rgq0 vv + artl v
s x quiblixx
1g eB d +ahqZ
cd t. C)Atgtan
uum vocubimos
direchicem
AP
q=(bb + pp)
erque lagae te
proet ponatir vata
Fa
etoabu
e intX= etvs
teu X- CP -t2sp
cgvas epfute
sit a 0 seu P = X, et coimidant
Bet A, et praeterca ut sit curva
sit hypertola cujus centrum si
nempe faliendo
Y non sit = , seu etsi Hyperbola
non sat aequilatera
itaque in sola Hyp. officert hac mahodo lica, ut hotendo s1
aequate proveniente habeatur solum , t  sine 
et ila aeguntro secundum v et X nito e et x
XX et X, et ita habetur aequatio intor cercergentem e
parellirum mon assurgen ad ruperbolam,s ubi pro vD
et xx ponondo quae eas possunt habetur aequatro
Idi gratus. Sed intarim alia ratione, essi non statim
simul totcuntur
juti si ses taster fols sunam,
hede da