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# Catalogue record: 41579 — Aus und zu Mariotte, Essay de logique [Paris 1678]: Demonstratio reperta (Demonstratio pure analytica | Quod in multiplicatione - in - faciat +)
# Incipit: Sit quantitas x-b multiplicanda in aliam x-c
# Date: 1678
# Akademie-Ausgabe: AA VI,4 N. 222
# Other printings: zit. Couturat, Opuscules, 1903, S.146.
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=41579&katnr=53792
# AA VI,4: its series at Leibniz-Forschungsstelle Münster (online after accepting its terms): https://www.uni-muenster.de/Leibniz/seite5.html
# Work: https://leibnizlegible.com/work/00069349
# Title: Leibniz-Handschriften zur Philosophie LH 4, 5, 10
# Folios: Bl. 51 (from the shelfmark LH 4, 5, 10 Bl. 51): 2 pages, canvases 101–102, page ids 00069349:0101 to 00069349:0102
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00069349&page=101
# Lines: 96 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.
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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 51r — 00069349:0101
# Source image: https://digitale-sammlungen.gwlb.de/content/00069349/jpgs/default/00000101.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
Demonstratio pure Analytica
Quod in multiplicatione in  faciat +
sit quantitas X. = b.
multiplicanda in aliam X - C
fi ajo multiplicationem fieri hoc modo:
Manifesta autem est parssum multiplicationis
3
X = b X = cX. quaeritur solum ade
X b
b
an admitti possit - b in -c dare + bc. quod sic ostendo
Lonatur X a esse aequale ipsi b. patet fore X = b
eaderu
fortuma
aequ. nihilo. ac pocide idem autem prodibit multiplicando
X - b per X- c. Sive X sit aequate ipsi b sive non, qu
tantum e inter quia inter un cum literis generatiter calculumus
valores quoslibet literarum comprehendimus, semper ergo
eodem mudo prodibit X. b+ A +bC, quia
etsi
primum ponatur X aequ. b. se rel qec. ergo
etiam erit X + C aequa b+C. Ergo X + XC aequ. b X + CX
multiplicatis scilicet omniper omnibus per X.. Et po XC poncudo bc
(quia X aequ. b) fiet X + bc equ. bX + CX
fiet: X = b X + bc aequ. 0.
= C X
X = b per X - c. prollibit
X - b X + O. aequ.0
c X
+X
si v
jam si multiplicetur
+ X = b
+ X L C
 Cx +C
= b X
Nam si id quod nihilo aequale est mulliplices in  id quod etinmm
ni hoc loco X Ca) multiplices per quidvis productum etiam
L).
nihilo aequale erit. Hinc conferendo has duas aequationes invicem
necessario fit bc aequ.. adeoque - b in -c dedit O seu, bc
quod autem processit posito x aequ. b. ut procedet etiam
+
bc
B.

## Folio 51v — 00069349:0102
# Source image: https://digitale-sammlungen.gwlb.de/content/00069349/jpgs/default/00000102.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 51 lines, status machine
in alia mulbiplicatione quacunque, ut facice
patet, nam pro si
per. X- C.
-b muti multiplicanda
utique poterimus facere a aequ 
e + X si sit daplo major quam X seposite  quia
A est major quam X. adeoque et major quam b posito X aequ. b)
et fier
e. + X - b multiplicenda per
et necessario fiet productum 
ex = eC + XV b X = CX + b
C ceX
X = C.
debe
nim fit enim utiue ex  - ec + X = b X - cA 4. O.
quod tantundem esse debet quod ex - ec (quia X - b aequ. 0.
ergo et C+ X - b in X - c idem quod C in X - C.) Ergo
+ = bX
es
C
X +
oste
D. aequ. 0. ergo ut supra D aequ. + bc
idem fieris
Item ex = Cc +
dBa ets. & faiset retenta nec perX
bbape etx
Nimirum ostendimus ex - ec + += bX 2 cX + bc essae  aequ. d - b in X = C
a - b in a aequex
aequ d. b in X -c. ut ostendimus.
e
et
 Id - b in C aequis
d - b in X aequ. eX +X = bX seb valorem ipsius d))
jam
dc
-
C
Est autem id est (quia daego e+ X) d- b in -c aequ.
-ec - XC. O. Ergo d b in XC aequ. ex-
Ergo summa collecta eX +. X - bX - eC = XC. O.
superiori:
aequale Cex = eC + X. - b X = CX + b c.
utriaque isdem fiet O aequ. + bc.
Ergo ablatis
Breviorem hanc
demonstrationem reddidissem si vacasset. facile etiam
patet idem fore et si adhibuissemus non X = c sed aliam
quamvis ut fio
f
=