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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 3
# Folio 6r, page id 00068021:0011
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Mellodos tangentium invorsa
 cira methoios Tangentium invgisas notandam est, quando ex data BC.
 quanitur BD. inquisitionem vel ideo salis difficilem esse, quia BDB  habetur
da il smpliciter ad quadutum, ascendens, nam B+y
1
q
X -- X. a
pr
atqui talis aequatio ordinata serandum aise, non potest ad duas sadlces
L3t
e
mulla
aequales determinatiquia omnis  aquatio pora equadratica
ad duos aequa les radices determinari potest; sed conbra ad duas qual
e
oppositas, seu mole naequales, forma  sive signo inaequales, jam
determinata est. Esto : Cun malo videndam est an
remedium quaeri possit
sulsti tuta alia nequ adi 24l vel explicando
quod experiemur vel alia inquirendi ratione substituta:
Nenige adn tntum denser haberii potest summaomnium
BG, vel summa omnium L; sed et summa omnium
EF AH. vel FM
Nimenum AE suuma omnium AE aequatur seginen do
AL CA duplicato. Sumum comnimm EFconcabo
AFL CA. dous licato. E Jami cncurum simpler
auctum segmentui simplici aequatur grianus ulo ABL.
e
Eogo summa omnim AH)seu AE + EH, (ponendo EH EF
auu vel summa omnium Ex MF seu EF + EM, 
ponendo EM  AE) aequitur Triangulo ABL. A+x
e
Appellando ergo AB, X,
BL, p.
2
BD7I. Erit AD, p.
. adeoque A~ AE XA
3
vel si mavis   et AE erit: -
sive AE p + illet yl 1SyX. porro EF 
sine A  EF
~ = AE
3i - yl + yx. fier: EF  ∞X
et EHs  NX, et AHO H AE+EH p 2Xl - 2yx + yX
e
21
sive AH+ 2yl ∞ = yX, Ponamus jam exempli causa AH
v
esse applicatam parabolae quae valeat L fier X
a
H
a
29l- yx
sive +2lX + yxa -2yla 10. et l p Pna
Est autem L
A 
3
A BC  Au bG
cujus quadratum: 4uta = 4 y3a7
2
Xa2
+ +X
N N
AVa-4uaX+ ax+ vxa
rear
L II
ea
el
rya 2 F2ya = 2X
na A Xa, fier: Gp 274 -2X
Xa
m
Y, addatur ei BL Y, fiet:
V ponendo p p GL. Sive
na