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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 146r, page id 00068200:0293
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curva Hyurbitae per progressionem infinitam
4 Meii 677
De curva Hyperbolae aequilaterae. Ejus ordinata ad asymploton sit.
e
abscissa X. efrolentia a. erit yp  et du p a dx
an
aa 8 dy 1 at dx
seu 
s
452
dx + a
Vat+ X
dx
a
y2
.. Elementi ecurvae quadratum, dx +d dy
L
evidentur pleroque series oblatae reduci posse ad
finitas figuras si modo incognitae simul in aequationem
ingrediantur Adhibenda hic series Neuloniana generalis pro
omnibus radicibus, ibique explicandae lterae variis modis sed Xtvariae in se
invicem ducendae quantitates, et deinde extrahendae vidices. Non opus
Cogitandum quomodo commode tactari possint totae series reperta progressio
nis ratione, ut aliu sit in qua eadem prodeat aequationis ratio, prorsu
ut in locis curraturus.
1
X
1
A
posito g. co. . x a. ba esse constantes et Z+1 esse quantitatem
co
areas
ex series prodibit
scinita
integram affirmativam, erit curva geometrice quadrabilis, ut in novissima
sua Epistota anno savit Nentonue. Quid si 7 et co essent quantitates
indefinitae a in quibus scilicet involveretur X. et anon Z+
fieres
rco-co finita anbutas quantitas constans integra affirmativa, an B dinc curva
S+Y
20
a
nAbX
eris quadrabilis.  ita est nam termini f posito Z
fier contnuo inter extr series cujus termini erunt 
Y- 1 
s 1a
A B
Y- L
s- 2
e C
Y - 3
S.
17
s-
C
.
e
cs
de. ducta in  2a
posito Q.
sbi patet Uno exteminis evanescente, sequentes
bX
eas
cot a + bx
C
P) Y.
8+
omnes exprescere quia unus quisque ducitur in sequentes omnes, itaque ets
ulcuno involverentur indeterminata tamen si modo r sit constans et extamim
possit tepminabitur serres, unde mirabilis ratio quadrandi curvas ranscendentes
vicissim quaerenda methodus oblinendi semperteries terminabiles ets
termini ingredientes sint transcendente hoc enim ad larum rerum perfectionem
restare videtror
y.