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# Catalogue record: 38295 — Propositiones duae de ordinatis ad arcus extensos applicatis
# Incipit: [Fig.] "Si curvae AC(C) in rectam AB(B) extensae applicentur normalite
# Date: 1676-04
# Akademie-Ausgabe: AA VII,5 N. 075
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=38295&katnr=Cc2+1466
# AA VII,5: the volume in the Repositorium des Leibniz-Archivs (CC BY-NC 4.0): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-bd-vii-5
# In the Akademie-Ausgabe: AA VII,5, p. 207 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/VII5B.pdf#page=207
# Work: https://leibnizlegible.com/work/00068196
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folios: Bl. 439v (from the shelfmark LH 35, 13, 1 Bl. 439v°): 1 page, canvas 874, page ids 00068196:0874 to 00068196:0874
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=874
# Lines: 37 recognised on 1 of 1 pages, mean confidence 0.90
# 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.
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# 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 439v — 00068196:0874
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000874.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
sry.
fig. 2
23V CC
E
AD AGC) AB A13)
DSi curuae in rectam extensa applicentur normaliter in punc
ejus ordinatae BC
(B) (C) in punctis crdinatae LM (L) (MM)
3) aequales ordinatis BC (B)(C). et curva nova A MeM
9) per earum puncta transeat; erit area ALM A ad
 Superficiem curvae AC. revolutione circa axem AB
y genitam, ut peripheria circuli est ad radium suum.
pro Cuva frg. 1. substituatur polygonum figurae,
cujus latera AD. (DD(D) (D) DB eu. punctum medium
cujusque lateris, C. (C). (C) idumque et centrum gravitatis est
rectae lateris psius, superficies polygoni rotatione circa
AB genita constat e supificiebus laterum rotationo genitis
genita, aequatur rectangulo ex ipsa D(D) in viam sui centri
gravitatis DC: seu in cir lineam quam revolution.
describit, id est in circumferentiam circuli cujus radius (B) (C)
hoc vero rectangulum est ad rectangulum factu FG)G) (F,
figurae certeae factum ex (B(C) seu F(G) in D(C) seu F(F) es
ut radius (BsC) ad suam circum ferentiam; ergo et superficies rotatione
ipsus D() circa AB descripta est ad rectangulum F (G)(C) (F) ut
peripheria ad radium. Idemque cum fiar et in caeteri tota
summa rectungulirum EGHH + F(G) (EY () + (F) (GD()F
erius ut peripheria ad radium. jam a si polygonum sit
infinitorum laterum coicidet cum curva AC(C). et  summa
recrangulorum seu fig 3 concidet itidem cum A (2) (M) M A.
idem ergo de suplificie rolatione curae genita, et area
rop. 2. curva ordinatarum ad arcus in rectam extensos applicatarum
etiam fieri potest applicatione arcuum ad ordinatas hasin
Nam fig. 1. AE aequamr BC ordinate, huic si applicetur EM aequalis
AL seu curvae AC. I habetur idem quod ante punctum M. et ita in caetei
n
.3
figurae ALM. demonstratum erit