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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 179v, page id 00068195:0358
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 178r); this page is its left half.
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 Caxis A Ex Y agatum nomalis in rectam
AB, quae sit YX, et in rectam BC quae sit YZcomplatur rectan
gulum Y ZBY. Habemus trimnenlim sunt secae ntque se YX et BV in W.
sint AX  YX, BZ, _ 1Z  EBA, AC, CB AF Et
Set 32
pL
Triangula sunt similia ABC, BXW, YVW
BX,
 DC BW + WV = V XIV+ WNY = y
BW
L(D)+ Aq = v
nx) +  Z - y
fit y = n + unque seu y- vn + Z -
m.
Cecom -Zu - gn hn
un
Em
= vp 4 Z
H= 1M
seu g  nB, + MZ et l - X = mV nZ  seu X = l + nq- mo
x
m
sit AY curva conica, cujus vertex A talus ricam semctats redum lates
sit AY curva conica cujus vertex A, semilatus rectum Y, semitiams versum 9, fit 22X +  xp = yy
B .52
Ex puncto C dato ducenda est perpendicularis CY ad conicam perpendicularis C3
es agatur normalis EF et EY produratur dubidem
eidem occurrat in p.. Diserentiando Erax + 2xxd Lydus seu dy: ex = Y = LX,: y - IX
rit pX Y G: GE firt r + Y X,; X+f, s re t Z = r + ZX, :y = X+f, :, e-y
sit ex Ex E in
fiit re +r ex = ry = Exy = xy+ fy
su (147) Xy Xfriq f Z ex = r e
compendo d +r = h ftr = 9. et fint hxy +gy + xex - re-
+ErX = 2r + 2rnzu- Ermr
6=q + 2 ex- +EF + UnZ +2rlu fr unez frmmvo 
= 
n
ADX BX - l - X
L
Im
duner
LMV
- re = - rell
+Gea = + X el 4 eh F etmv
+ gy = H
+ gluz + glno
t 4nque + h lbib
=HnZZ = mmo +2mn
+h mnZ
mn +ek mn
sexta per arbitrariam 
et fia et primum in summa destruatur q sfmnioz seu fiat +  + 1 + pl
aequationes 5 et 6 addantur in unum, multiplicata prius
hxy =
21
a
seu B = + ar = aq: h. seu p= fr a, ( fr-9,:, +rrq. si p posset esse a = R et p- +r. g
2
debet jam esse
xun =nn +h P mn = ir mm-mm- h P mn,
Pema -0
q0
+X (mm. un) e (mm- nu)
1+X) (mm - nn)  +2 hP mn =0 seu
n
r.mn
 (mm-nn)lemn
q4r -0, quod non licet nisi in casu circuli, vel ert m
vel erit mm-unrmn seu nm Fnn -2mn = 2nn
a
et firt a
= n 12. seu m = (1 = Y2) n
et p = + r -9
ergo vel erit
et fieri poterit h=a a = h = 44 fr + q
seu m -n
nm + un = (3 + 212) un = I l = n YC3+ 2t2)
sit jam circulus descriatas radio At, centro R, radio AK
curvam AY scans in puncto Y ax R agatur in ipsam BZ normalis XK R
 dato circulo, enunt et AA RK datae
sed video si non datur relatio inter AX et XY, ad conitam et
ad rectam; etiam non posse dari inter
et
L Y
ila trastra
ali pristeur
suns
qud utitte inii
ut si eaut earem
mnota AC sit Y B K sit K
 radius 
BF sit 1. R sit K BI sit i RI sit K. dfferentia
stitui mp
u stit
di
inter ii +KK et rr vocetur  +t, et erit aequatio
aqu
ry +XX -2iX = 2Ky = = H: et + erit + cum Y est major qua B
sed _ + est =, cum RB est minor quam Y, sed si sit neque major
neque minor, sed aequalis, seu cum B cndit in circunfentiam cidculi
0