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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 82v, page id 00068194:0164
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aequatione
pr sectionis conicis transformanda in aliam
corrdinatarum rectangularum
24 2aX + a Xx = yy. fiet:
2aGe
Pra
raro La
sep Z= Tur
2 2t qu  
(1+ W
2Z + 21. Y Zu + vBi tr
1+ I: rY
seu 2a. sitrr Z. rv + a qZ - 2r ZV  vV = rY ZZ + 2rZV + vV
seu 2a Sierr Z. W  trriusqe + 2YZV + _, V
422 + 2ar5 + a irs
haec deinde aequatio amplius variari potest, auctis vel minutis
per constantes ipsis 7 et v. et hac est omnis variatio
possibilis salvo eoordinatarum angulo recto.
Ut ex angulo recto fiat obliquus sit ABX BC
B, AP  A PL c. et PL: LB:: ∞: 1
ergo _et X =   = H + co rec- 1
et y = Cd: e expumto dato E
minima ad sectionem conicam iL 2aX. + a XX = yG. Ergo
Xa dx + Fa Xdx = fyay. seu dy: dx: : a + a X : y.
Ergo fit BP= a + aX. sit BF = B b et EF = C
fiet L ideo ob LG: GE:: PB: BL fiet b: C -y :: a + a X : y
seu by = ea + ea: qX = ay + ∞ a: q X y quae est  ad paa
aequatio ad Hyperbolam, retentu jam aequatione praecedente qua emulavicuus
directricem  conicae, aliam pro axc substituendo salvo angulo recto coorti–
natarum fi matemus similiter aequationem istam, fiet:
o=eZ Ldgen +  rr
Auiurr
Arim
s
rrZV
seu o= = crrea su EC fgrantia Z + er + g arb: a V + rZ +, 1EV- rv
Hanc aequationem  prius multiplicatam per urbitrariam h addamus
aequationi , et videamus an componendo fiat aequatio ad circulum
et sufficit considerum terminos prodituros qe, vn, et ZV. et
quidem pro ZV habebiinus et debet autem evanescere Zn, et fier
coefficiens ipsius ZZ aequalis coefficienti ipsius DD, prorit collenda ZV
2r +2ar: q + h - h rr L 0. Ergo h h: F=
h: 2Y = 2 =c 1 + aq: rr - 1 rursus rr( a: 9) + hr = 1 (4 a: g - trr
prodibit aequatio
ergo fit r Mrr+ MY+ th  hh 4 seu Y = Atih a -r c ostin A
h= rY CEV 1- rr: 2Y. Ergo sit ( c- Er = - 1 +
nisi in Ellipsi ubi latus rectum
mnjs tan verso
in hoc genere fieri possit, quae amus ordinatas oblique
sa cm po
ut apparent quid
et in +Gg. C et ex proZ ponamus
mus co., atque inde qponendo
lemus p
quod
redilent
+ lon feear et poro V poret seu 2hr = 1 - 1Y Ego I = = 1 a: 
ponem it. E a iarr et (5 er 1gq ) eni
lyo
aonem 3+ Tentandum in ordinatis oblejuis. ia mius proceo
aibenta  vn
 ibed eeo