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# Piece: https://leibnizlegible.com/api/records/53356/text
# Catalogue record: 53356 — [Math. Untersuchung]
# Incipit: Recta est linea AB qva brevior alia ejusdem speciei inter duo puncta A
# Date: 1713
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=53356&katnr=23822
# Work: https://leibnizlegible.com/work/DE-611-HS-867168
# Title: L Br. 827 · Schöttel, Th.
# Folios: Bl. 58 (from the shelfmark LBr 827 Bl. 58): 2 pages, canvases 115–116, page ids DE-611-HS-867168:0115 to DE-611-HS-867168:0116
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-867168&page=115
# Lines: 91 recognised on 2 of 2 pages, mean confidence 0.86
# 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 58r — DE-611-HS-867168:0115
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-867168/jpgs/default/00000115.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 79, 2026-09-07T03:33:42Z — 44 lines, status machine
de lineis ad easdem partes cavis
f
Recta est linea, qua brevior
alia ejusdem speciei inter duo
puncta A et B dari nequit.
Haec proprietas est, reciproca. Nam sit alia linea
dico interendem puncta
quaecunque ABC; adria lia
posse AdB, a
ipSG.
ACB, dica aliam dari
pa BE, parti prioris ABC similem
um ejusdem specet.
condenam ipsi fis eli et ipsa ADB minorem
abitu
sre. 
OH Exempli causa sit ACB arcus circulii t xi Ad)
inor priore, alterius
alis arcus, circuli minor AdB. Is erit similis
inter puncta A et B. Poterit dari AdB arcus
B
mn linea minar pieti priore minor linea AdB
quae sit crcus alterius circali, et sit similis part
psi
 EB, parti ipsius ACB. Nam ipsi
AdB, fiat similis et similiter posita FG, ita ut
radias ipsius FG, sit aequalis radio ipsius ACB,
erit FC conq hrcus FG minoc ercu aequulis arcuit
congruus arcui EB. Idem poteit in parabila
fieri, vel alia linea ejusdem speciei cum prise
seu simili ex. er. si in Ellipsis A cujus pars
poti
est arcus AdB sit similis Ellipsicujus arcus
parsestarcus, ACB, similes autem Ellipses
sunt inquibus eadi in est ratio distantae folorum
a vistau ha  e ad diametrum per
beos seu axem directum:  porro semper minor
inter eadem puncta similis pricti habet mino
em curvedinem. it metandem quod memo
habire est A quaevis linea simiium
uisdem speciei minorum , nec 2 Duo puncta
interpositione evanescit in rectam.
De lineis similibus inter duo puncta quam habentibus
quod recta sit earum limes

## Folio 58v — DE-611-HS-867168:0116
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-867168/jpgs/default/00000116.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 79, 2026-09-07T03:33:42Z — 47 lines, status machine
ila ut recta dici possit ultima circulon
ultima parabiterum, ultima Ellipsium et
ejusdem speciei pabests distantia puncta
rum deferminantiam abeante in infintum
itaque modo loquendi toleranter vero, dici
int est rectam esse
ultimum circulorm
ultimam parabolarum
ultimam Hllipsium
erc. salva specre enroritem m
in curvedin
sdecrescentium.
acusatias Coquendi
s
limes exclu
sivus seu artimus qui non
ici  si quiescentit
punctis A et B moveatur linea inter posu
in se redibit, et absolvet solidum fornatile
tanto minus, quanto minor est aota
A linea, u ail
ad
easdem partes
et
sut enim intra Ie endo
Ca Va Hausolidumdinda
an non sidem locum hadea
eu
sit ad eusdem partes cava, saltem enim vitetur
minor linta sinter dur puncta minor esse
quae int ex similibus ea, quae minorem habet curve
dinem C illud fieu potr sed hoc ejami
pandum. Illud certum est lineam non , ad
api
t
quidem linea
ns
videmum Nam sopidum minore generataim fad et hina essi linea non
a
si duat lineas simies, non ad easdem partet
cavas inter cur quarum arcue inter eadem puncta
intercept girentur.  c duas reperiri quam
n
 neaA
vestigia sibe occurrant, qua seu quarm arus superti
cies gyrando descintae sibi occurrant, et se seeut, imo
tangant