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# Piece: https://leibnizlegible.com/api/records/58101/text
# Catalogue record: 58101 — [De angulis atque triangulis]
# Incipit: Si motu lineae super centrum angulos
# Date: 1673
# Akademie-Ausgabe: AA VII,1 N. 007
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=58101&katnr=39657
# AA VII,1: its series at leibnizedition.de: https://www.leibnizedition.de/de/reihen/reihe-vii/
# Work: https://leibnizlegible.com/work/00068195
# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folios: Bl. 127–128 (from the shelfmark LH 35, 12, 2 Bl. 127-128): 4 pages, canvases 253–256, page ids 00068195:0253 to 00068195:0256
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068195&page=253
# Lines: 236 recognised on 4 of 4 pages, mean confidence 0.66
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# 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, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 127r — 00068195:0253
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000253.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 83 lines, status machine
65
2
si motu lineae super ceut
gulos explicis, et in finita
imagineris parallelas
in plano, et oes lineas
datas in infinitum pro
nlad
nfinca Ecorentitea datti
us
30
moter duam lincanir
ad se iclinantium
 a. b. c. c
disquiv eloces anguli sunt
in dasc velocitatu
at basis immu
bilis in mere intel
ini t ideo lata
non sequamt sib
et ingulos Lado
quod extra mensura
b
3
= =
seu centrum molus
admininanque divitas. 6 4
t = 
3
4b a = q  - 4
H.
i
mis
... (. d ∞.... D
DBs let.
n ne peut joindrea des figures regulieres
Josans caisser du vuide, si non
Er
d
Ili tres anguli sunt = a rectis
C
4
3. 2: 6. 4
2 - 4 3
ef
3f
2l
2
C
Adc
2 4b +2
= b c - d
c d a
3ba + abc -
2A. 4C et B3 hexagons. G e
Demonstrad propositionis
b
= c -
C Ergo a +b
3
brd =f
Ad- a eDB. = a Gd
aDe = g Ad
Ergo N a De + e Db.
et
a0b = gta + dGa.
Or adb + aDg = 180.
Ergo gsa+ dGa + abg = 180.
Galtruche crededit Angulos et bases crescere proportionaliter
Demonstranda est exacte haec propositio per analus sin, rectam in duas paralle.
las, seu aequidistantes cadentem facere angulos aequales.
dependet hoc ex eo, quod duorum arcuum equalium, latribus
aqualibus, chordae sunt aequales. Sed generalius, quia
omnia sunt paria. Hec propositio atilis ad alia multa demonstranda
es
utile enim saepe continuare lineam datam, item assumere eus
parallelam, ducere rectas inter quaelibet puncta data
descrbere circulos ex distantuis datis, ex punctis in lineas demittere
perpendic coones. vntus tit
sed non analube
LH 85, (12. 2
124
7:

## Folio 127v — 00068195:0254
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 128r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000254.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
HEEEM
s
q
49
C
3 + 4
3b
a12
pd. 9) ab 12
9 + 24 +16
12 2ab 1b2
 .. . 
BABC = ABEBC = AC DB = AD DB + CD D8. (ABrDC = AC)
Ergo BC =- AC DB t, BC2 = AC =  DB2,
1B
AB2
ACZ eDOZ AC= 9B2
adde: ABE
AB = AC DB et AB = ACZ DBZ
Bc
AC L DB= CBC2 + ACe DB2 AB
BC= AC DB C2
BCL
ABEBC2
aet
= 167 CB
EC
ABZ~ BCZ
BC2 ACE DB BC
ABE
AC DBBC=
AB BCZ
3CZ
Methodus Demonstrandi. 47. pmi 1t
facile in angulo semi recto, aut semisemrecto,
per Arithmeticam infinitorum, utendo ductibus
linearum in lineus soliquis, qquid impriu

## Folio 128r — 00068195:0255
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 127v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000255.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 10 lines, status machine
cet D
+
a +
l
+ b (4)
b
2b
1+ 2ab +
H
b = bbb

## Folio 128v — 00068195:0256
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000256.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 106 lines, status machine
C+X
:
e
in se
d.
- + la-
d
 Ni
0
 33
d G 
ees
dase
Le
ssl. ..
22. F 555 (. 1
80
c et
- 1e
+f0, cI+
2e
a re
ve 1
II + et i e ∞1o et - ilo
c
vix ti
a10
e (1)  n
ii anta
11+
11
id. 810
et
H4
∞I
len  
nso H a vto
2
e
l
e 4
∞
c
do
c 41
du
sta. d 53
e
s
8
in 2E a
∞d
d
et e
P
 is
ex 
e
2
1 a F1F ∞
∞ GS=
e e
+ + 285
s5 8 y
-
e
1  7
OF d   +
5E
.d X e. 2C
ee  eat
s
cy 3
tuctcs es
F 2 3 =
  A XF
  t  55 5l sug
ue e
E
E 25
21
c
8L
+vissi
t
e
∞10
11
∞10  
es
te
YL
23
3d5
8: 3 = u E
u Z +Y d
u
E
87. 3.
tic. e
220145 1e
C D. b = a G
ad
  de cate
=- 6+2
=c