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# Piece: https://leibnizlegible.com/api/records/58124/text
# Catalogue record: 58124 — [In subsectione polygonorum]
# Incipit: Radius, seu latur hexagoni 1.r.
# Date: 1673
# Akademie-Ausgabe: AA VII,1 N. 003
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=58124&katnr=Cc2+522%2FA
# AA VII,1: its series at leibnizedition.de: https://www.leibnizedition.de/de/reihen/reihe-vii/
# Work: https://leibnizlegible.com/work/00067993
# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folios: Bl. 305r (from the shelfmark LH 35, 2, 1 Bl. 305r°): 1 page, canvas 611, page ids 00067993:0611 to 00067993:0611
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067993&page=611
# Lines: 102 recognised on 1 of 1 pages, mean confidence 0.72
# 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 305r — 00067993:0611
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 306v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00067993/jpgs/default/00000611.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 102 lines, status machine
Radius. Seu Lacus Hexagu
sinus Hexagoni L Cd. a.
I. sinus e a
H. radii HaC.
ai
1
Fulcrum ad = YJ. radi.
1
2B. Rad.  Rg. C. L. rad- LI. sin, 2 rac.
2..-
In subsectionibus Polygonorum, haec est regula progressionis. Sumatur duplum Qua
drati Radio duplicetur, quadratum radii a producto subtrahatur Rectangulum
quod semilibram projicit, spatium dimitium percurrat, supposita saluet homogenertat ) factum ex ductu fuleri seu q sadicis ex quadrato Radii demto quadtato sinus Polugoni
produdi Residui radio L.
praecedentis  in Radium duplicatum
Hinc patet latus sequens esse semper majus dimidio
4
ne
C
ne
Si cgjungantur huc duo: scientia grogressionum, et motus seu ea quae alibius dixiderave tentandi
seu per motum extibem cundi per
t geometria
es catus postisiles donec eveniat datus, ar inquam, agenio pusu
r.
542.
sa
Hae 
1 a 23 = Ida
13+ a 1
4ua 11212 a
19 - a2 (Ag 243
143
115
13 + a = q 23 - 1 22a
utus
ca + 4
e
e
24
E racii= . sinus = H. fuleri. ad
-
24
9c 1=a
sinus sagittaCulium Radius. Flacru
seu = Y,4
Radius, = r, quad.
seu 1. = A43
P. sing.
Rq12- a
1. sagittae db. +  sings c d = (. lateris
,  sagiltae db. _1, Radius ,, - 1, 4. rad G. tinus
+ta
+Y, g. rad. - g. sin
+ Y, q. rad. = q. sin
H. rad  4. rad. + q. sin.
2.
= v4.
rad.
L. Rad, Er, 4. rad. - 9. sin
+ Rao
HRad Futrad =  rad quad. s.n.,
eRqD Aad D rad-  sin.,
Rad. Rq. C rad- B. sin, 
2
24. rad + q. sin. -
Rad 2, RgC D rad = G. Sin.
110 1-91
2 - A1 12
9 4
Cui addatur sinus habebis p
D rad- sin teu
E Rad + A sin = 2W RadSim
Diameter multiplicetur per sagittam
a ai prequene
 lateris sequentis ~1
2Rad A Rad. = Rq I rad 1t, q. Sin.
tam.
Sagite
(4) LRad had = RqCH. rac L 1 t. 3, NB.
eq. r - a C2s
H. Lat. odec 
Lalusd.idtedgria
Lsagrat
polygoni sequentis correctionem eide sei
praecedentis
1. lAqque 12 ( 2., L R9 Aa, p A. - 
n 
it l
radro sutit
seguens semperend: R4+ X f B4. -4d
eteri  n  a,   
pondum est h.l o. 4- E A. n. 1 A2. 2 . Ag
inveniemus: Radus supponatur 1. Latus prrecedem q
dmplicatum subtrahatur a . productm
1a. subtra hatur a 2. Cx din b9. ex lalus quafitu ted opus
crre
Hq. 44. - 4 a
e
Radiopositor 1. et a. sina lateris prucedentis Latus
Er per subsictipes dato labre praecedente sequensta
rator