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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 180r, page id 00068194:0359
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Grundis illa Quaestiro: ex datis Tangentibus invenire figulam sive ordinatas etiam replicari potest, ita ud
data aliqua aequatione, quaeratur figura cujus tangentium tangentes aequationem habeant datam
Regula  Tangentibus investigandis, breviter rememoranda est: isto cnvae ordinata tangens De mexplrcans
dinatarum
escista
Ante omnia aquatio  figuraita poliatur, ut non nisi duae restest
quantitales incognita AB= . et DA = x. d Aeguntio e Termini incognsti a fractionibus suadita
quaeritur AC, ex data BC.
ac surdis liberentur Aequatio jam hoceratione inventar ita  formetur, ut ab uno latere
omnes termini d pondntur ipsa Xis ab altero omnes ipsa  affecti
neque ynei
utroque affectus
picitur
ibem
est, utrobique ponaturi ita quasi alterubi non esset positus. Hoc facto in latere ipsius Y cuilitet
terminoi di suntt praesigaetur numeu tot unitatum, quot graduam est potestas quae terminum incognitum
ejus lateris afficit Penique in latere  ipsius X. autu interainus  mutetur in = AC.
aequatio ita reformata ipsius F AC. quantitatem dabit. Ipsa 8Y. per productam p.
dividatur erit 
posit = disfcontia ipsamua it, seu posito as y esse pserum b qua
chatrices. Exempli causa:
ap. pD s p
men no
2ax = X Egoro 
a -x ua
mordu D R
2ar - 2
a - x  a - X
ax-x vax
Drax. 
Sed Minis longa fueriut h ambagus cdatis differentis quarere summas se figuram, rectus
decta perpendiculari BE, nterum ipsis AE.
aiqua
quaeritur tergo problema: data AE invenire figunam
n cinfistamus in hunc finem methodo Cartesianae ubi Ellipsim proponit in exemplum et ex
AB indanit, nos tentab inus posten aegressum. Ita autem ille
Esto DA= Cy. AB = x DE = v,
EB= Ergo AC = v y, ideoque AE = v= 2vy4y2
Et quiu in Ellipsi did X = 1y -  y unte fit
et EB = 5u=o v- 2vyt + x
tollendo X fit: - F y +Y y +
2V
+ v s
 +1
n 
et nc
2= et ut is abomnialio liberetur
Jam posito EB esse pergendicularem seu minimam, erit AB seu _ Aquatio proposita duas habebit
radices aequales, ideoque ponendo y = e eandem habebt formam aequatio, quam ulla
quae fit ducendo in se y - e. Uende Y 4- 2ye +: Cumque haec aequatio sit
priori aequalis et eandem habeat formam aum priore, ex unus terminius sit idem, erunt reliqui
quoque aequales Ergo +42 2 y = 2gC. Ergo Ar - 21 == 2et + 
911
sive
sive
=. 2V =
=- - r
av = 2Vr + r - 2y
v = y = +. X - 7
Credo me per errorem invertisse, deb enim esse: r= y - Z y + Y vel  + y + Y
quaeritur quomodo invenri queat X.
 X + V = 20y F y, pro. I penatur ejus aequivalens
t
u
et 2Vy -
a
+ a
27
uet:y
Jam inerso modo cognita v, ignotaque
R e sumauda aequatio prior:
fiet 5 =
am
qu
p
Eyo fet.
5
ex
12 1
+ +2.
+
sive
d= X 
v