# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068194:0533
# Permalink to this reading: https://leibnizlegible.com/page/00068194:0533?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 267r, page id 00068194:0533
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 266v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068194&page=533
# Source image: https://digitale-sammlungen.gwlb.de/content/00068194/jpgs/default/00000533.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 126 lines, status machine
# Lines: 126 recognised, mean confidence 0.83
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

Ellipsis
2aX - a X = y, inde La p- fa Xp = +7, seu p= 3
hoc inquam duudatur y = rax - a , f seu  f
ordmatae Ellipsis, ejus eto at a x. 1x
E additoque 1.
2ax- a
rax- ax
2ar - a X
a + aX atx - 2a ta + 291X
aga
xl
Vrax-ax
a - a x. Eex dordatur 
a dx
VY har-a
addatur 4. Taa cx-
considremusEergo latus curvae Ellipluae.
sat + ax t atx + 2+X
2Fx - tx
a= ah+ Ysax vel a= ay -=FV sax,
vel at - 24y + a y = y aX,
a - 2a + a = X
+ ad
a- ZX
fiet
Tax
a y, dabit: a - y - a - y, Ergo 2- 
etc. Jam vax
ea + a, aequart:  a  a etc. Quo posito si vifferentia
iter 2a et a in illa Hispothesis summa erit horum  + et
afax a  sax Videndum an inde aliqua lux ad summam ejusmodi indagandam imo differenti
sax sta nihil aliud est quam spatium quoddam Hyspertholicum. Inprimis
et Xa-axy +ay axy considhatione dignum, quod eadem oritur figum quomrlocunque explicetur
 sive per + sive per unde etiam e differentia inter haec duo
etc altemantem, et simplicem a + a +  et. detere haberi
vax
Ergo
a = ay +  yrax + xy, vel a ay- xy = ytax.
vel a - 2ay - a Xy + a - 3ayX + Xs = YaX 0
vel a - 2ay + a  = 2aL 3ayX = xy
24y
Uinde ad extructionem radicis a latere X verim potest
+ a
Lax +X aX + sax + X sa X - 4
(aX)
+sax + aX + sax +  ex.
a sax + Xa, est ita ut jam haec summa, ubi numeratores tantum sunti
2) summa lamen horum omnium facilius ila miri potest:
compositi, priori licet implicatissimae ubi nominatores copositi erant aequetur
atax xa ita resolvi et in partes Xa-a unde priori a rursus atiquad
sax + X fiet a X + aX sat + rabu
à 
 adruntur addatur, et avaq - 3. unde QX -s-
Jam
a vax +xa,
a
e qu Eahoop. Eodem modo si pergatur ad
saex sunde vy, et a X- yi ebile) + a.
Unde itrum a, quod rursus per sequens
i inveniri posset Ais inveniendi feguram ex dato Tangentium propia
uus sive
a d est metur
XB
tate, ar xpos eadem opera credo et Geom Arithmetica summarum
ladicum
perficeretur; postumus enim semper opinor ope divisionum istarum exeogitare figuram
ex cujus quadratura pendeat seriesalicus Geometiaae finitae infinitaeve summa. Et quona
credo ostendi posse ommium figuram dari posse quadraturam opel logari thmorum jam
superest rem illam anaximano cendere, quomodo scilicet Tatae tibet seriei Aritimetiae adhiber
aequatiorum, per Tabulam Sinnum, sive Cyclicam, et
ottadu oanum sequtionum per topltolicaro 
implicalo ex ayperbi
Ergo
Unde fiet: sax-
vel etiam sax
at x
ax sax
e Hoc tans
vel etiam
Ergo reliqua-
a + sa
Arisi Xa = y. erit Xa.
A + Vax
Ergo ay = - X a +
i- ayt ay - - xa  13
rgo ray Daeytar
lim sigura
haec ergo fegmrelicet tam
Jam
ores dat
a + ra
a - 2x
hiffece
ab altre latre Tabulis
reprae sentabitur ex
no; logari qua s ipse
oefulissi pro ratica
ad quam op ipsramento
n
sia
meoa grandis culcul
libro apparat
su vs
dabralius
abent dita
a inus
eadem habeat rata
vi ad duato
nia condenda
dudni cabulo, intes
oudenda inversa: in qua
Obusa
nnlibed Numero
B regione
resondet
sino sum
latulalis qui et
respondet si sumalus
ogerithmo; idem tad
qae vi reppondet, 
quadralica ubica lete
Huie Tabulae fundamentum
sionum 
Logarithmo
vassitat
uti cme ed p