# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/50577/text
# Catalogue record: 50577 — [E. Schenck] für [Leibniz]: [Abschrift einer Erörterung des P. Tacquet über ein mathemat. Axiom]
# Incipit: Duae rectae lineae nequeunt habere segmentum commune:
# Date: 1713-02-08
# Sender: Schenck, E. — Addressee: Leibniz
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=50577&katnr=46267
# The Leibniz-Archiv's transcriptions of the letters of 1713 (pre-edition): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-transkriptionen-1713
# Work: https://leibnizlegible.com/work/DE-611-HS-866840
# Title: LBr. 808 · Schenck, E.
# Folios: Bl. 18–19 (from the shelfmark LBr 808 Bl. 18-19): 4 pages, canvases 35–38, page ids DE-611-HS-866840:0035 to DE-611-HS-866840:0038
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-866840&page=35
# Lines: 82 recognised on 3 of 4 pages, mean confidence 0.85
# 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 18r — DE-611-HS-866840:0035
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 19v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-866840/jpgs/default/00000035.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 31 lines, status machine
e
So decoma-
Dua rectae linea negueunt habere segmen-
tum commune: et omnes rectae punctu-
aliter se interscian
e
29
Rectae Ad orcurrut recta ZD, ea si produeatur non
c
perget per Dio, sed in F, si ut rectam Xs non nis
punctualiter intersccet. Atioma ex notione ipsa
recta lincae evidentis simum est.
tam subtilites philosophantur, ut credant rectas
linear aliquao sii parte comriceri posse lubet in eo
rum gratiam hoc astiome amplius declarare.
1
G
habeant si fieri potest, duae reitae AX. AZ. partem
comunem, AD. Centre A desiribatur circulus, seians
rectai in B, et C. tum accipratur arcus 8
.
arcui BC, intelligatur duita esse recta S.A
e
Recta egitur CA et SA eundem prorsus situm ha-
A
. Sed recta 6o cum recta-
BA habere divitur comune segmentum DA, ergo
etiam recta Fo habet cum Bob comune segmentum
Do
segmentum habent.
 

## Folio 18v — DE-611-HS-866840:0036
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 19r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-866840/jpgs/default/00000036.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 28 lines, status machine
dumatur rursum Arcus FG aqualis prioribus BX
c
et Cs, et intelligatur duita recta esse GA. Rursum
liguet rectas BA, GA, cundem habere segmendum situm
42
respectu rectae sit. Sed jam ostensum eot, rectam BA
habere cum recta Fo comune segmentum D A. Ergo
c
etiam recta GA, cum FA, comune habet segmentum
cum DAt.
dam ergo rectae quatuor CA BA
Aus
GA SSd comune
et segmentum habent. Eodem prorsus modo ostendam
si per totam circuli circumferent iam sumantur
arcui prioribui aquales, omnes simul circum qua
rectat lineas dactas ad At unum idemus, habituras S
G.
comune segmentum Dod. Hoc tum imane absar
dum segnitur ext eo, quod oronerentur bina recta
CA, Bit, habere segmentum comune. Ompossibilo
eot igitur, ut sua rectae segmentum comune
habeant.
dn hoc axiomate vii tota nititur illuio celebrati in
Scholii argumenti, quo demonstratur, magnitu dinem
poni non posse: et est epromodi. Constent
si fieri
potest, magnitudines ea punctio. Circa idem

## Folio 19r — DE-611-HS-866840:0037
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 18v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-866840/jpgs/default/00000037.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 23 lines, status machine
es
centram descriptae intelligantur quotcumue, sircum.
ferentia circulares, et ponatur extimu seu
masima componi es centuco mille punitis, a
guibui singulii ad centrum commune duitae
itelligantur recta linca.
C astiomate jam explivato certum eot rectas
illai nunguam comriceri, nini on contro solo
quare Jam omnes medrao peripherias pertran
seunt in is aque multa designant punita
ac erant n exstima. Omnes rgitur cir
cumferentia concentric aeque multis punctis
conotant, ai proinde omnes inter se aequales
erant. Atque ita erroumferentia, hai in carta
descripta agualis probabitur circumferentia
firmamenti.
Adlico prope innumirn demon-
strationibue hic error obraitur. Sed unam
se
illam hoc loio attuli prae caeteri, quod passim
sit decantata, et ex presenti assiomate
pendeat.
immediats

## Folio 19v — DE-611-HS-866840:0038
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 18r); this page is its left half.
# No recognised text on this page (recognized).