# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/14498/text
# Catalogue record: 14498 — [Über den Raum]
# Incipit: Non bene explicatum est qvid sit claudere spatium.
# Date: 1695
# Akademie-Ausgabe: AA VII (assigned, not yet published)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=14498&katnr=40866
# Work: https://leibnizlegible.com/work/00067971
# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 12
# Folios: Bl. 15 (from the shelfmark LH 35, 1, 12 Bl. 15): 2 pages, canvases 29–30, page ids 00067971:0029 to 00067971:0030
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067971&page=29
# Lines: 74 recognised on 2 of 2 pages, mean confidence 0.95
# 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 15r — 00067971:0029
# Source image: https://digitale-sammlungen.gwlb.de/content/00067971/jpgs/default/00000029.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 39, 2026-08-27T09:55:26Z — 46 lines, status machine
Non bene explicatum est quid sit claudere
spatium. in syperficie, quidem res difficultate
n
puncum describens
capet, omnes enim linea in se redetpts in superficie
quam clacudinlinea
onita ab ea partem abscindit( sed in solido
a superficie
res non est tam facilis Equidem quaedam solida
generentur motu lineae in se redenatis, ea etiam
in sua vestigia redeuntis, superficiamque
adeo sux describentis in se redeuntem, vesudi quae
abscimuntur
potatione describuntur, veluti cylutri sphaerica
phaeriformia, cylindrica, et cylindriformica, conica
et conocidea. Sed multa sunt solida, quae tatia
tali modo produci non possunt, etiam rectilinea.
 verbigr. octaedrum Nempecoriquae non
maetereo haec operatio non satis explicat,
re natimem habent sam Basin sane, posito Lolitum
habere Basin superficiem pro Basi potest sumi punctum
hoc solido extra Basin, et ibi affixumfilum circum
onei per extremam ambitum baseos. Ita abscindet
falum filum motum in sua vestigia redeunte abscindet
in
smce dagreum, hateni
solidum. Video tamen finummodum aliqo
en posse
proiis quae Basin non habent, secentur nempe in duas
ita duo solida habemus Basin habentia, in utroque procedatur
modo dicto separatium abscissae emut a o
et inta dupsbases inter cipt superticiei
Cytutum. Sed sigefila nolimus rnserit
sed haec operatio non explicat notionem
ea talis
est ut punctum ea ex puncto sumto in spatio
eligr
clauso non possit duci si spatium sit clausum potent
non poterit ex puncto, intra
in superficie eadem
ex punctu erunt pan
ad punctum extra ipsum, quod non transeat perambitu
ipsum posito duci pum linea
landentem. Et in solido abtolute clauso  absoude
dici potest expuncto intrapsum non posse duci lineam ad
punctum extra ipsum quod non ambitur occurram

## Folio 15v — 00067971:0030
# Source image: https://digitale-sammlungen.gwlb.de/content/00067971/jpgs/default/00000030.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 39, 2026-08-27T09:55:26Z — 28 lines, status machine
Ecce et aliam notionem. si spatium fit
lansum, (sive superficiei sive solidi) sit clausum
non potest recta elaudi in solido omnis linea
in parte ambitus ducta, ubi ad partis illius
terminum pervenit, continuari potest in alia
ambitus parte; alioqui ambitus non eut plenas
integer terminatio hiabit. Ex. gr. Esto
pypamis ABCD in parte ambitus, nempe
triangulo ABC ducatur linea AE. Quod
si jam hiaret ambitus, seu ab esset basis
A BCd, non posset continuar linea AE
in alia ambitus parte, sed hic sisteretur
sed posito spatius. lapdi ope qua ri trian-
cotina ab
in ambitu
guli BCd potent E continuari extra
pyramitem uerb: qr ad ex per lineam EF
operae pretum foret ostendere, quomodo
una harum notionum ex alia nascatur
si
Ad conciliandas notiones ostendendum esset
ex puncto a plami ACd, quod sit G ducatur ad H
punctum plani ABC, recta G, et in ea
sumatur punctum K, id punctum K c
cadere intra spatium clausum, rectanique
ex eod eo eductam si producatur
necessario incidere in aliquod ambitus
punctam velut L