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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 17
# Folio 7v, page id 00067979:0014
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linea restat ex perrunda Methodus, prindivisibilium, seu Fermatiana
ca culum egrego contrahit. Pone scibret circulum secare sectionem Conicam, in punctis
Ergo erit sits
aa
en
sed e i ea coinicidere, seu X (X) esse infinitae parvitatis. 
Dui
A5 esse 1 GY + DG, et GZ , jam GY_ seu F4
ave (a co co a)f + (acacO) X F GY. et 
PGH +DF-
+DF -
-DF +
+ DF +
γ, sive (aa04) d +(00a) y. compendiiantem
quae
V(Y)
AFL AX
I AF+ AX
+AF - AX.
inscribendo causa pro (acocoaf ponemus simpliciter f
pro (aaca) a, ponemus simpliciter d, quia non aliter occurrum
ry
a
1
d et f. at plo et pro (a60) X poremt pifa co
ponemus V. quia eaedem literae non aliter in calculi
occurrunt.
Erit ergo GL, P+ X. et DG
d + Y.
fX + X + d + 2dy + s, et pro y substituto ejus nalire e aX + a X fiet
(B) af X + X + d+  ( (3) id Traxtax + 2aX + a N, et contrahendo βp aX AbJ) los, fiet:
 (1 S + d2) + bX (ponendo bp B2f + 2a) + d X (ponendo DB+ + a) + (3) id raxta
atidem Si) h + bx + be +d X + 2d CX + 83 e + ( sid Srax trae +a X fa ex + a et xdeletis
communibus fier: +(V) id Srax + aX  bC + d Cx + . . . . . . . . . . . . . . . . . . . . . . . . Aquadrandontrotio
abjectisque
fet: 4d
gd aX + 4d a X ( b C + 45be X + 45
om
+9d a ex + +da e, et Q rursus deletis communibus, abjectisque ea fiet: (2DC + 4
ab 2bg + 168 be
e multiplicatis,
1N  da C 4 0d’a CX, et quadrando utrobique fiet:
ex, Gd....
X + 16524 4d rax + a X (abjectis silicet omnibus in radice contentis per
divisis omnibus per e,
4at2e
vel X
ax
4 1 e  16d a  2(+ AD) 1+ 2X +
aut a
ordinataque aequatione habebimus:
dbu X3 +oqfisob Xa 2
184 2 84 an.
AsX + ubgsa
+214
M
xd a
da..
L 495
= d’a
n
252
v
X f d a39
8
in circulo
unde nisi erroo in calculo insit erit XF, 2g. quod
X
Est autem d in parabola pa, in circula p0.
utique absurdum, necesse est ergo in calculo ermtum esse. Unde in circulo ( XX + XaX +d a 4 0
fieretue:F X  _ + LaX + N Y, - 2aq + a, sive fiere X +   S - a -a
sive X + 2aX + a 570, sie X ⊓ -a quod est absurdum, calet ergo enor in calculo
Egitur pro constructione Ellipseos redeamus ad calculum a nobis ab iitio indentum exploratae
veritasis resumtaque analogia, et ponendi:
F(+F) 4(+F) f B_ h,, et d p, (1 +d tet 1+27 
et stabit analogia gnero ds: d +2ddy +8. v2.
a
a + 5XV
1
a. Ergo si d ro. problema erit planum, item si h0.
poncudo aq + y Z Reret
q + qua
7, et sotoe pot. st problema mollo et dua habebimus aequationes: dz - 5y Z A y.
Le potius a9 + y 5, 4 Z quae est ad circulum; aquatio
:7a modo silice signe in caelers pore nata
3 s9
autem ila est ad circulum aq + y
untemu ut res postulat. Caeterua ex his atet in paribola problerun esse planum; mo genercliter
ponendo aZ 1 pro aq + dea tiet: altra aequatio: d + S V
a
1 3 14. Hui patet oame
constun problema ope axirculi et cugusdam Hyperbore lari rectum Z transver sumque aequalia habentis
a
Y 19
ayr
pone. V
vagt
7 3
a + y_a eit 47
127 12d Sagt st + Saitus et act
aequatio ( ordinata eri. +a V frodV + daY
1 +
ye
atC
A Va, ma aequatio k alta.
et ga erit = A2.
et.
sue Y e   + 22
inzaque Atque ita
+ 15d9a) +d a 4 10
nunc quidem modum ostendemus, quo constuctio 
set. ii Ellip si quoque 3 Hypebula sic satis dorevis
ceddi possit Tantum ergo ponemus gp r. et  0 idque univers aliter adeoque in ipsa quoque parabola observari potest
dimo male, .d non pucedit, nisi in parabola. Ex aequalione
Ebrr  2s 
quod si jam (extra pacabolam.) ponatur 1. 6br + EOY, huc 8p(.6b7F 2( +Zg. entu
+ 2t bg - 1 4
selur
qu
e.5
valor 
inde
Atabela 9 ex supposita b. sed  non podenda bps r2B. possumgetiam faceae D V4+0. ptque ita sumere 9 talem hut fiat  j0
quid mea sententia ontarum coutumt est, quia universalis d sit ostrnctio, excepta partctu
satet autem
AF+ AX