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# Title: Leibniz-Handschriften zur Mathematik LH 35, 11, 18C
# Folio 49r, page id 00068193:0099
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t.
eet
tas
ta
duc.
ab-
sis
la
b-
a
L-
aM
ba
(3R
Ex
1
epr
Seit. 1. Cap. 3. De Duitibus
Nam ex quovis puncto rectae DE ducantur plana intor se paral
ela FG secantia lineam AB in punctis X, patet normatis ad eam
FG infinita in AB poni puncta Si comparabilia ipti C, secundum
sit
C
seriem punctorum G rettae DE. Sed Superficies HL M ett rursus
una dimensione altior linea AB: nam per quaevis rectre DE
puncta ut G transeant, plana GX secantia superficiono in li-
nea PQ utia comparabili cum linea AB. Et eodem modo so-
Lidum RSJV est una dimensione altius supenficice ALM,
quia quodvis ea dictis planes solidum secat m superficie ut
.
LZ quae ipt supenficier AL M est comparabilis.
(a
Deop. 11.
Itaqe id quod secundum ordinem punctorum retae al-
fet comparabilia continet infinities, vel infinitenes infini-
1ta .
es, el infinitis vicibus infinitetres infinities, et ita porro
altrus ipto est dimentione una, duabus, tribus eto.
Prop. 12.
Si unum maliud ducatur absolute numerus dimensu-
num ductus inde facti, est summa numerorum indicantium
drmensiones eorum, quae mvicem ducuntur; et, si series or
dinatim ducatur in seruem, numerus dimensionum ductus; ett
summa numerorum indicantium dimentiones terminorum se
riet utriusque, unitate aucta.
Ut si sit recta ducenda m planum; elementa quae inre-
eta sunt infinities, ea m plano sunt infiniteres infinitus;
ergo m ductut sunt infinitis vicitus infinitenes infinitus.
et cum dimentio rectae sit 1, et dimentio plani sit 2, utique
dimentio duitus (solidi) erit 2, plus 2, seu 3. Quod si
series rectarum ducatur maliam seriem rectarum ordina
tim, scu itogonium m uogomum; elementa quae in recta
sunt