# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00067993:0232
# Permalink to this reading: https://leibnizlegible.com/page/00067993:0232?run=39
# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 116v, page id 00067993:0232
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 117r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067993&page=232
# Source image: https://digitale-sammlungen.gwlb.de/content/00067993/jpgs/default/00000232.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 39, 2026-08-27T09:55:26Z — 124 lines, status machine
# Lines: 124 recognised, mean confidence 0.68
# 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.

raX. AF H a e ABBY. CD7. Sta - X.  FCF a- ∞.
e
AE
I
AF. et 45p AF, Cd. er AE, B
TL. CP iotu
CDCF
a hax-X
a hax +x
pro 2ax = x, substituendo ejus vatorem, explicata X per y. fiet 
a TaX X
ao 
seu a -x Xy Ca3 + ayt -2ag
ute
43 -ayHB
ponea um averoniau minariu
poremus;im ia aa a qu
a moia +y conam lart
2ay 2 et A= XF
aer esta
vergo pro D
arrux
=X
a 2aeyle  a-ay
acc
us
aty
ymer sD. Dae 12aydi vely 2ag. vel Y 424y
la
tia
6. fier
FVera ae i Ex pro uu i. mr
 Et pro y. B AB, ponende LB AG. expro B ponendo  fier ne  ine vit axdendiu agari
Ergo Z
e
aar est autem + aC1.
uuc
zat
phaer B
hasorae a
4 arbrae-d
en
atum
a
au in
t
loae
2a2yia Bp
aty angl onim ed e
at Z 2at qu.
L) atla 2,  4arq
eere
seu 
et 
laum
21) Vaqm
2XZ
ah2a2
nnatC, a Z 17 a+ 242
 - y + yY seu ygy 1 y3
31C5I qiquanitur
05
at aZ
sit radius unitas habeaturque tangens in fa anguli in fractione quantum opus est accurata, et
quod comandissimum decimali. ejusdem tangenitis quaevatur quadratum Hoc potito a fractione
s subtruratur Quinta pars quadrati tangentis. Residuum multipliaetur praedictum quadcatum tangentis.
factus a radio subtraratur; Residuum per langentem multiplicatum dubit arcum. Numerum quo si dividas
circum ferentium circuli secundam Ludolphi numeros expressa seu numerum 628318. Quotiens dabit rationem
erius ad liramfrention tam exacte, ut si mogens tengens sit minor
am
el
a p 100,000.
jangens .....
100000. auseratur
s
 2yt O aY rae 2+62
sed haestalias rdicaratius oti
 DF
2
a, ar, 4 X, F 243  a 1, a, Z 1 2a Z
iea
e
a 10070d0, 00qouo anferatur qolata purs quadenti tangents
residuum multiplicetur per ipsum tangentis quadratum, et dividetur per
106,0007, 00000 001000 00000 factus subtratatur ab
Si arc tangene si quaerimus magnam exactitudinem, 
exactitudinem excuyli causa, ut erroru sit dinoret serund. vel mediverem
varietas praxeos cujus fundamenta dedi, oritur vel () ab exactitudine quam quaerimus vel (1)
a datis quae habemus, vel a regulaa qua volumus uti. Nam vel ina  Quod altinet
nti
exactitudinem quam quaerimus, ea vel magna es vel modidens, vel exiguat Magna
ut si desideremus ut erpor du sit innum multo major secundo, ut si sit minor (quam 13
feri potest ut velimus errorem minorem secundo, vel certe non musto majorem, ut si non
sit minoq quam 1 secundi d ed et fieri tamen potest, uta _ contenti sinus si licet
enor sit circiter duodecim secundecuminaemque saepe si se quintae pareus minuti; imo
cartis
bebinc
et  si minutum dimidium non excedat. Denique nonuunquam contrnt crimus, modo duobus
rulsa unum minulum vel duo terave consistat error. Quod altiner
vel ex datis angulis et uno iatere Zeliqua
De priore gunc lantum dicom
qeou caluuto Frigonometrico, i ex datis lateribus anguliain vessius antur, vel mogl q
vel
as
arpyr
La
quo
Zn et  at
a
pur 
ary
ao
y ergo tae
ra
ergo e
a Biava a cum
si sit
dadedsive DY) atL a L. 24, 242, 4+ Z a Z
ad e
ara
 a , na
2
Y
ha