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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 27
# Folio 7r, page id 00068045:0013
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et pulcherrime angens hujus curvae transcendentis
l
Est etiam
Tangu in tangente autem paratiolverdis quaerenda e et h
sunt constantes, fiet edus aequh. X - C h- dx. q udd
Subi pro e substituendo valorem habetur tangens curvae
transcendentis. Et ponendo dys dy: dx aequ siax: a
d
h - 1
fiet + ah X- e aequ e Vrax-xX,
vel bonamus
dy: dx .. a: ray - yy filt :: h. X- e
seu e
2: ray-yyS
et eaequa
t
a e trayyy
a
1E
12ay -yy
h-
(aequ X - C) aego e
E = 1
: C
 iih
fiet denige e aequ. - it
FC I
aeqo = (k-1BE
ex quo repertur valor ipsius h.
c
Hoc quidem protigiora
Sunc sunt justo, et puto rem dan posse compendiosus
atamen hinc saltem Methodum excolui causamus
didicicur nuper non suecessent, quia inter qui alia
quia conceperam cunicum punctum transire omnes
e
plu
parabolocides neglexeramue rectam C.
fliter et Torte simplicius ba aqu. -e X+ ee, fiet X-X + 2C aequ. 0. seu Cry L. X
seu fiet: bv aequ. LXX + ( XX seu. byE aequ 3 XX. Est autem tangere
e
paratolocidis: b k. yE
-
posito P esse foroutam uco ordinatam, curve quadrandae, nempe BP
jum
seu - = X: p4). bh. 1,E= 2. jam 6y aego 2XX fiet - =x: p aeq. hXx: y seu
y aequ. phx. rursus y aequ. XE:
X aequ 2b. phx. seu X
i
ala
sit
2b. Ergo denique fiet:
ek: h
 aequ 2b. h. P seu X, aequ 2b hp
s
 lag. 2b aequ log. 26: h aqu = log. h. seu l.g 2b aequ - h. logs. h
2h: h seu X4 g. (Xp, ex
aequ 1. Unde rattur, min s
seu 2: k  , log. X _q. 1og X + log. P. seu a aefo  2log X + 2log p: log X. son 12.  X.B
quadrandi figuram quamvis, potest enim s assumi pro quacunque et logu
unde habetur b. et fiet:
 posita p aequ. VraX - XX. siet: X
seu
seu 2.h log. Xqulog X += log 24- X iloghabita ergo hoc modo h,
itemque b _ (quia log. 2b a qu. - h. logh) fiet 2b y aequ XX quadratiix
2
aiatipu arietem baquti u uit bu 1. 
lipaga fret haey 2. A 2baque 11 2.  bug. 1. 2