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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 3
# Folio 3r, page id 00068021:0005
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lno G
2b2. 1674.
on
net hodu catesqua invenis
se ratio nihili est, quia evenit in qualibet aequatione uti
methodo tangentium ommuni reducta ad unam incognitam
capitatem. Mroclaro admodum consilio cartesius adhibuit
liferam .V nam  cum opus habeat litera B, P manifestum est
ipsam esse duplicem, nam n figura superiore
rabetur BP, et (∞) P. quod si ergo ei dedisset nomen
v.g. P. tunc habuisset tres literas duplicis valoris
p. GX. Y, at um ut litera D, seu AP, est
semper eadem, ergo BP e  x. patet non nisi duas
esse literas duorum vatorum. Nam V. et s. non nisi
unum habent vatorem,Quando datur aequatio: v - 2∞x + X + - s,o quae est
genenalis. et adhuc alia, v - X 1 a. fit  X B v - a. ex et a
et = 2 YX B  - 2v + 2aD. et X  V= 2a D + a
quad
Unde ( - 2V + 2a0 + v - 2a v) F + et - s 1 0.
unari non posse, tare
enim non nisiun
si e incogluta aeparet
quod si elidere velis v. fiet K   a + X - v. p o. recto
Si puss BP, 8y H v X.
At haec si BP sit linea consans  cum
Quodsi ponamus B2, 87 y.
scilicet ei. At est parabola.
Hnc AL est linea recta; et fiet:  y. B v - X. Ergo X, vP - xy
8230 = 2VBY) F225
Unde _ = 2V X F
= 203 + 207y et X
Uene (B ∞) (= 28 v) (+ 2re VD)  B. V F  eY VD + rV C
+ BrV2
mntus qua nisi duarm incognitarum nem
Hinc ergo salis ee rideo hoc quidem casu elidendo X redir in eadem, quae
proverustent non adhibendo V = X.
i sit TEa Lar 1 v - X. fet S 2aX  V - 20∞ +X.
et X p quae aequatio jungatur prioreg generali: v 20x +X +s - sv
1 - y et X 52-25 y +y
fiet: rax + y - j adeoque
as
qa
X 1s
detadeoque hunc valorem utrae aequationem generalem inserendo, fi quia
=L VX 1
v
-Zv
4 aV das V ax V
+ ZVY
ta
1..
et ordinando : ( V 4 + 4 av y + 4a v
+ 4a.
= +asex
+
fiet.
V= X 1x +y-s
10. multipliando, per 4. 2. 0. methodo
- 4a252
+ 8av H.
= 4
Huddemana, sequetur
sive dividentus per 4 fiet: X + 2 a V H 0.
52
a
+8a ubi in locum ipsius V substituendo  Sra + x fiet:
+trax + X -s +2a20. Multiplicetur aequalio setermina adhuc
aliter per  - L (X - ) o(X + 1) 2. et fiet : 2y+ - 8 a v 
y4
- +a p2
F 4as2 v
+ gapv
1 ubris pro  na
ubi pro + 4as B ponatur 4as Yax + tasX
= 254
+ Sarsve
70 et fier
+ 4ars et pro 4aY, quia v2 2ax + 2X trax + X, erit 4 a v 
4
8a3X + 8aX Prax + 4a X, et substitutione facta, erit
aequatio: y  porro ex aeg. D, multiplicando per s, fier: a s+p s V + raBs 2+2450
 et pus
2a H. sive y4 pa y + rans
4 2a2)
inseratur is valor in aeg. 8 fiet: y 4 - py  - 2a0s
fierex aeq  2 sequens: Y - 4a 5 -ay. 70 + 4a05 v, (yt + 2ab3) +4 a vc 4a v4
(a + b
a = b
et pro s2 substituendo, y +EaV +2a ex aeque D
+rav 2aV
=gar
+ 4 a2s sive -yt +2a . +4a30N~
Quae aequatio est absunda, sequitur um
-2aV .4 4aV
V, vel pne - 20.) + 4 at et et b0
+20 24
ul sue  portie las egudte se elitiratua quantatiti car ul qud q aespr