# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00067993:0521
# Permalink to this reading: https://leibnizlegible.com/page/00067993:0521?run=44
# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 260r, page id 00067993:0521
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 259v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067993&page=521
# Source image: https://digitale-sammlungen.gwlb.de/content/00067993/jpgs/default/00000521.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 44, 2026-08-27T14:25:39Z — 110 lines, status machine
# Lines: 110 recognised, mean confidence 0.79
# 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.

secns auy dy l’ est
et tuosus accus dupliest quadratum eadi a quadrato seranti adentumd
dcans arcus dupli est a
ab +2 a b + a
B et linvestiges
Targeotomums daplis
sinum rectum arcum
dupli habebis
A
a - +ba b2
Nota si tangentem
seu
berrab
at+
ab+ at ab + a
a-2baF abtra- 2ba a fra a 
b2+a
(a6 2 ab pa - a + 9ba. 4b a ab s  + 4a-
La- +ba er ab a
ab1+ 24b + a a 642b- at qab abta
Senitus
a 2a b + b+
a= 4a b + 46+.
de ab sabi ra  = a   2 aeb + a - a+ 2a b b- 9ab- 2ab
a 2a67 (it a b
rangentem arcus lnic patet pangentem semiaum non inepte assumi pro basi, cum dipso posito commensum
sin vero in vestiges
dupli habebis
Aada
ut a Pellio ostensum bili pleraque
a- Es
alia commensurabitia sint Quemadmodum et area futeri arcus integri, quod
ara fiet ab area fuleri.
Unde sin Rectianu ractlnde brenoris calculi causa, si mndo suius derus carcus totius dividata per b et multiplcetur
est. 2a
ad Tangus esde arus 2ab per a. fit filcum. Ergs. si adjeriis ad
seu 1
eeL
serenula faciis ab
+b
2b
at3
b etq halebitm sactor.
3bi est
aio au a a eba a5b
+ er
a b - b + h1 - b et fulerum
Semurcorunt lum sub sum recto et langite
semiarcus est b’a
aes spppputa
= a
emirectangulum sub sum recto ed verso CP langenle semnitars et
-
b + a
6ta 2 quod si diuides facit:
harhas . et
a a2 pa
Ergo habenus valorem sectoris ita expressum: a
Ila poro
b3a
ba bEa b + b b2 esc.
b + a
+62
6+4
ab -  + a C2 a q et
ba= ba + Va- b a ett seu a l etc.
Jam sector est Fulerum + segm.
+ siniecau seije p
a + b
+ a
+ b3 - bu e seu posito a -1 fiet b - b + b - b + b 2l
dae nia
si a semorectanus uto per geartes subtrahas, erit
263 465, 66 8b) et vel omisso a, eut: 3b - + b + 6 B - 8 b3 e
3a 54
2
70
9a
24 4a 64
a22
a 64460
8a6
a- 24b7 b
e(A
qu 2a5  b+ ab 246 + ab 7a b ara b b
qaeb4
a 44646a b + 4a - 12 a b 19bd
128ab
a-4a Cb 10a b- 12a b + 55 b8
Eaque progressio faile contimari potest si tantum innerator sne a, intelligatur quadiatii productumque ejus
mulliplicari per 2a. Nmetor. Nominator vero quad retur, hac sola adhibila mutatione ut
notae ultimae, in qua b ad potestatem numeratoris ascendit nunerus praefigatur qui sit differentia
intermaxima ipsius b. polestattuo in numeralore X nomimatore quadrandae fractionis
ut in sequente fiet nota Bi6 in munerulore mulliplicetur per 128 - 55 = 73. Et
toin
128
n2bd fiet. B.  inouritatore adhoc sequenti 326r5 B.
31728
32675
Appro pinguationes Gregorii quarum mechodum suppressit
videntur fieri per differentias
B est
It seretum
-b
ab + b a a +b, ab - ab
Hii quadrur ado serminui procodentus
seu sinus Rectus est ad
suum Tangentem, ut
Tangens semiarius ad a ab
adium.