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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 9
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Methodi tangentium cirversae exempta-
potest vel ideo quod nihil conferunt methodi hactenus vulgatae. Nimirum quaeritur
curva C(C) in qua intervalla ordinatarum BC, et perpendicularium
ad Curvam, DC, in axe ABB) sumta, sint ipsis ordinatis BC
reciproce proportionalia. Sit alia recta A D ad ipsam AB, arem
cormalis, in quam ducantur ordinatae CD ita ut ipsae AD ubscissae
ex axe A sint ipsis BC ordnatis ad axem AB aequales
erunt et CD go ordnatae ad axem AB, aequales ipsis AB
abscissis exaxe AB(B). Appellemus APH BC r y. et ABBDCBX.
constaet ex alibire a me demonstratis ex om ipsam BD vocemus Co
Constat ex alibia me demenstratis, esse omn ad p . Ergo
c  e et ipsam B(B) vocemus Z. Constat
ex alibi a me demonstratis: esse Scz 1 V. sive
esse coZ 1. .  At ex quadratura
Trianguli pates esse d A V. Ergo CoZ Ad
jam ex hypothesi est cp. ita enim erunt ipsae co ipsis y
reciproce proportionales. Ergo fier: 
jam
t
ZH 7. Ego sZ X. Ergo XH S L
bZ B y. adeoque
1
V3
3ba
ex quad ratora Parabolae; ergo X  y. quae est aequatio explicans
3ba
relatioem inter ordinatas et abscissas X, curvae quositae C(C)
naytica
inventam ergo habemus curvan,s quae est Geometca et uno verbo
Parabola Cubica, cujus vertex A. et poncndo
Videbimus ergo an verum sit hoc Theorema sane memorabile;
CCC)
suntinterceta in tervalla perpendicularium
n ad curvam et ordinatarum ad axem in axe sunta, AB P sumta
en ipsis iptis ordinatis BC. reciproce proportionalia. Hoc calculus
tangentium facile ostendet; aequatio Parabolae cubicae: XC
ponendo C latere recto, sive pro c ponendo 3ba, E sive c7 13ba
y
fier: 3Xba B y. Ergo  ex methodo tangentium slusii erit
⊓ XV ponendo BTH +. intervallo inter tangentem et
8ba
Ordmatam in axe:  jam BPe co est p 
Eir Eo. A  = B
ba d
. sunt ergo ipsae co ipsis y.
reciproce proportionales quod desiderabatur
Analys seos hujus artificium in eo fuit, quod ex ordinata abscissam
fecimus. n cujus stratagematis antea non venerat in menteru
Non est difficilior paulo vitetur quaestio, si quaerantur curva in qua ipsae B
intermulea ordinatarum et perpendicularium sine ipsis AB
abscissis reciproce proportionales. Nempe cop
et ent:
jam sed 1 V. ergo yB Y2sco = Jum FCo non potest inveniri
nisi ope curvae logarithmicae. Ergo et figura quae satis faciat
est logarithmdum si in pabtrplicata ratione logieri Chnorum ab
in qua ordinatae sunt in subduplicata ratione logarithmorum
ab abscissis; quae figura  est ex numero transcendentium
At revera difficilior est quaestio, cum quaeritur ut ipsae. AP sint ipsis BC ordinatis
abscissis reciprore recipioce proportionalis. Nempe X + co  a
et cozm d. et SZ B X sive ZH Z sive fier:
ed
 co X ( y. et co   VX, et fier: X +-
ponendo ipsas X arthmeticas, erit X constans, . et fiei:  + Y 2
x
d
a
et SXB.  59 - Y. et X + Y B S a. sine quanitu figura sive d X + s Ba
in quamudatum oiduntitim esta ape, et assisamr ep veie sive Jam
1 Novembr. 1673.
Ssumma
ddifferentia
Hreltisa