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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 89r, page id 00068198:0177
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8
in Ellipsi sit semilatus transversum CA, q et semilatus
rectum S.R (posito esse focum sit Y+ itique posito puncto
quocunque P, Sit AB, X
gy = 2YX - Z XX
s
BP, y, fiet
Hinc habebitur (V, nam X fil q, et prodibit
eV = 2Yq = rq = rq sit XC A, a CV
semiax Is conjugatus CV, sut a, fietqus aa = rq
SV = CA, nam FV + S VS = 2 AC
A5. q.
AB,X BP, 7 S Si S+ sit 1, fet   N =
= 1g9- aa vet Yqu- qu A5 = 9+ 14q - qu
Si AS sit X, SR erit Y. Nam Si SK, s  3Y9 Er 1gq- qu - F 49 - 1 q uqu. qu
fit X A5. Nam
pro tangente Lydu = Erdx - frxdx fit dy: dx = Y - ZX,: y
= Y 49 + YqV = XY
DS, sit normalis ad curvam in  p. jam AB: BP = dy: dx. Ergo
BB = gu: dp = 2 )X = Y XX, :, - = X - xCir q
22X - XX 3:, 1 - n AB - BO - x = 2X - xx - x + E 3 : 1 
 = Y = =X
seu AB - Aqui, q X AB: BB = AT: BP - b: y unde
d
t = EYX YKX: 4qXx: F = y qX(:q. X) : (29X - xx (: q. X) seu
B
seu
4, et 2rggX - YgXX, :, 499 - 4xq + X 
siu A4 CA rA. C et ordinando XX CHArq) 4 -(2r94 + 49HF) X + 499 lt =
+ = 4y_: fg - X)
aequ. 61BB: BN ex ratendum ditest
-(4991 + 4 aaq
+t+aa
19++ aaaque t D + a 44
t
+
C
2t (++ +aa)
arqaagtat
H+aa
gthaah
991F 4ggitaa
X
et fit x a 29tt + gaa = x =
9+t
agqe
aa + H
=AB 29 - X = 2qua + 29+ t = 2gH =
seu X = aa LH
ad+H
aat k, - 2aat
ad
WHtraa
29aa = B
aa+H
aa + H
sa + H) 49+ d b- 4qVta a Fet 4aaqt d + (4, 9 (49t, dx
et y = 29-X, F: q fiit yt
dx =
(2) aa+ tF
4aagt dt Et y ax = 8a gtt dF
(et au + H
29a4 - 4=
Blaa + tF
hianculum sB CBP = Z yda CB. CB= HB -q = aatt
seu dx. 
T2Iaa+FF
294a - qaa - +t,: aa + tt = qua q1eq aa- +C, : pa+ t1 quod
dacendo in hyfit seu aati aatH fit  aagt, aa- At = cBp. ejus
aattt
(a + H) aaqut 2tdt - naquet (ua 1) 2+ut
+ aa + tF, aaqatsaa - 11) - aa +H aaquet itat- aagt Caa 1F at2+at
 aa +FF
elementum seu differentia
se  uaqu ( - 14) - 2 a a (aa +H) - 4 at gH. + (4nqt; Daat H
14) aa + t+
= gagt (aa- tf) 2 (aa + FF) 2t dt,
ser et, a g + aagt - 6a q tt,:, 13I aa + t = d. CBP cui adde ydx
aq + aagH -Caegtt + 8aqtt,: (3 adt tF = elen. sest A3PA
et fit qaa, a + + + 2 aa H,: B3l, aa +H seu elem sect
aaque dt P9. seu BP. at
fil dt,
seu deniue Elementum secboris AspA: aat Huic addatur se
es seu quana vocetur 9 fiat XLDdy. Est eulem
~B at. prorsus ut desiderabatur
unt 2t, haadt,: (2)atEt) - ga - H, raaat;
 saa + tt
s clega  lim mus lanctae. Hia potend t haberi ser led dodio postoa est
sen .
elementum
triansali
+L gdys= (aa + t() anq. + Caa H) aag, at, (2) apet
et recta CY, A
parallela
A I: BAH
aq. CA: H B