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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 31r, page id 00068196:0061
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Minimam ducere ad ex puncto
dato ad sectionem Conicam
communis
it sectionis conica aequatio quead etas fi potes arcu
e yy = 2aX + (a: b) yy, posito ex A vertice AXcesse X, et Xtss
et ordinatam normalem ZY esse y. d per verticem A ducatur axis.
inclo curvae
secundarius A, et in eum agatur normalis Y ex fiet A AL: L8=
tL: LX et AB+ LX = X fit A) = X - LX = LL: LX, et fiet
X. LX - LX = LG. Y L LX LY gy Y1 y. unde
X. LX - YL + gy = LG. Yt fit LX = L8, L - yy+ZL,: CX
) AG: L: AL = YX: XL, YL seu y
GL + YL - Y e XL: y = gL: AQ HL: y = 8L. AL
AL = X - XL = QL y. YL XL = (GLy: XL) + X = y8L: AG. seu
AL + FXL = X
X . AG. YL = yYL L + yA. ) seu L = X AP. YL: y (MLF AG) GY. VC
+ (DVa
XX + y y AC
AG. AL = AD: L = y: X - G+ GL
Y s +L = Y -GL - gu Expriore sit . Ae
Ex priore aq. pro est fit AY - 8Ly = A A(B + GL, et aequando
AQX + QL y - 2A8. Q LXy = A(P- ACL
ex priore essust  (L: A8 = 1(9Y - 92 - y 7) yy L. 18 - 8Y  91 8. 97 est yy
primum trans trans ordinatam pro coordinatis ad axem primarium substituamus
coordinatas ad axem secundanum pereundem verticem transcuntem sit. in
Vertex A s abscissa ex axe AX, ordinata ad AxemXY.. Axis semodarus
rvae
exis secundarius A, ad eum ordinata Y8. ob datum angulum ad A
unctum
datar AB: _L. F vocentur A X, X. XY, y. AG, F. C
rm  lum ad A, dabitur AB: LAL = a  b b: c: Reb
qui sl datum
dAL
AL = 8d: b R YI = yd :b LX yc : b aYL = yd: b
Honc quia GL+ YL - W, fiet 3 +dy = b W seu y - bu -c8,. d
et quia AL+ LX = x fint de +cy = bX seu ddg + beto- cc g = bd X
seu bb + set - bdX son X = W + b, :d
y = b0  (seu B ) fiet y = bW (seu YAI) - e C  seu MX)
X= CW (seu (N)  bg (seu AL)
qui valor substituendus est in aequatione data ead Conicam
2CX +  yx = yy. fint 2ab
2bh + 26Z
lb. Ce - (eb  si  eili
rou. + bb 9 2 be 9W 18
- bb W0lv  Cc be 8W
+2CV
abe sqa ) gro  tii i  ytbr . ) u
19 
bb+ cc = dd. ob triangula
eXt: Y L= +( 
similia AGL et YXL fit P: GL - 9c. b Cer CY AL- g d. b
ec Le
eYZ, v. fiet 8Y = AG+ Z, seu eua
et A4 = GH+ HZ seu 8 = Z+ h, erit
2CW =
2b9 =
2c9
19 q d
haec aequatio identificetur sequenti generali 5)
ab + mZ + nv + p ZB + r 77 + 5 v0
foret prolixior justo, ideo
faciemus v- id-g et
o sed quia is calculus
in hac pltima aequatione ftus Comissa penultima quasi nunquam caliulata esset
mk
metnu
ip asho  abto
  4b
e a late
W - v+ g
et de
sit eg= q af
ee = bb +cc
 in