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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 51v, page id 00068194:0102
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In sectione Conica
Si recta per ceninum chordam secet, quam ubet
chordam ei paralletam bisecabit
Bisece Be reltum per verfilem in R
XV y yg - 2YXFXX
BYqu = 21X f. B41 +1) ex (4L p= Bd, ex AR y
4 BYgo = BRqu.
B(), (X). XV, 19)
B(X) Y - 218 + Y73
p FF = 3] - Y FY- L1 + G)Y
Cy+ (X)Y = 1 (21 4 27Y) 4 (2rE +  G
IR = tu 2....
SP) = FGF) + WI) + FV
----
S (R) = ZFy + L (X)(1 = (Y + (X) V
Ergo LMV) = 2 FY + K Y WIR)
_sis = F) + XY X
per Ax). n8) en PX
= WV,
WR = 2 XY C et = cBF: BX WB): P) = r H : NY
CW = CB + BWa B1 BW = iBX + L BY CW = CB + = (X)+ = BY
11 . V..
V() - L GX) AE, DY.
Tangit YT. sectionem onicam et angulo TYP recto ducta
Y P occurrataxi in P dico essi XP = BR + BX Bt
Seu X ad BR ut CX ad CB seu XP CCX BR: BC
Si non tangit, ero curvam paeter Y in alio puncto secal ut E.
sungatur a. ex puncto E, in axem agaturrorpalis hF, n est in quam ex
Pagatur per noimalis YD juagotur TE. ob trinogula YDE sie 2t YXP
simuilia etit Ergo YDser XF: DE = YX : XP dunsus
FEqu = XYqu = FEFXY, FE - XY = 2XY + DE, DE
urius FEqu XIqul: F. D  PF. F.B - PX. XB = BR. 3C
IR. FB et BF = PX +XF FB = BXL XY
PF, FB = PK. BK + PX. FX + XF. BX ZXF. XP
Ergo BF. FB - PX. XB = FF PX. FX + XF. BX f XT. AF
qu
EqtaX
2XYYDE, DE. Erg DE: DX PX +BY TX F,.NY u
sit et hyp. DE. DX Et fit 2XVF DE, DE:, PX. A F _A + uF
Erg. DE: XF = (PX + BX +XF,:, 2X Y + DE) BR: BC
sed ex hyp. DE: XF seu XP: XY = (CK  : XY) BR: BC
et fit Px + BF jam PX + B XF 2BX + 2XF et fit
2BY+ 2F2XF ∞ PB + 2BX FXF, et
seu pX + BX + XF: 2X Y + DE = CX: XY
sed px - 2BC + BX ergo sit 2BC + 2DR + XF = CK: XY
ut Ergo fit 2BC + 2BX + XF _ Cx: 2XY + DE = CK : XY
sid 2BC + 2BX = 2 CX et fi 2CX + XF. 2XY+DE = CX: XY
Ero (t XF: DE = CX: XY = ( ea hyp) qu  = qu DE q differeusa quatratdum tE at. X 1s
XY : s XP = XY: CX. BR: BC
X Cxqu : XYqu. = BR .BC seu BC = XY
qu:
BX BR
3R BR + BL. 6
XP = 269.B X + B
eR gulBE BA (qu P2. B2)
Xqu. BR XY 1u erit
n 
XNou BC 2BC4 11 Ladiam
U
DEim (XY +FE) est etiam XY (+XFqu
(X qu BXBC+ DY, qu, Bx (2B C+BX = Bx ju  BA (EXB FB2Z. B
BFE BAqu +, BX. XF + XFqu B4 pa = 2BX. XB
ergo DE ad DY seuXF ut 2B+ +XF ad 2ZXY + DE
Sid ex constructione ob trianus angulum pYG rectum est Y
est Y D se XF ad DE ut YX DE ad DYs XF ut
ut 2 Y ad  p DEFEqu = XYqu = 2BA in (BX +XF)
+  eE et  _ (2XB + BK + VC) BR in BRIXF
=2CB_ F B)
BR. XF BAB.
BC
BL. BBC 2BX) BC + BX, BpL, nr ta N XF. BX M DL ApAC O~ 2 + B (2BR in DX) (= 
D XEBC n
fit 3C =BX = BR (2BC + BX)
l. BX= oc 2bR 1. . Di d Gu. BCigu aM
+ 2BR in XF
+BX BA C) (BY YF ∞B)  Nene M et + F. XF
et
 vede 
sit X= 2XYL De
ME 2BR+BB
xY  XF. BR
hine in Ellipsi faret satus rectum
majus dxc later recto una
maxus i ayc maje quod non licet
Bgu, : BRqu - BC qu
natur 2BKN Eut sse quantilaes afirmativa
 uia unu er Tilhus
 X
(2Y X) = 2+ dx
EY d XX -
2Xdx F dxdx
 2rap +  X ax = 2yd
dq-  + x
si fiat X p - Y + ZX
targense
natur 
esse tangens sed
irere curvae in
ilio puncto E, dmatur ad uncum normulis EF
et in hanc ax Y normalis ED quia
e