# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1066518432:0407
# Permalink to this reading: https://leibnizlegible.com/page/1066518432:0407?run=74
# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 379, page id 1066518432:0407
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1066518432&page=407
# Source image: https://digitale-sammlungen.gwlb.de/content/1066518432/jpgs/default/00000407.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
# Lines: 44 recognised, mean confidence 0.92
# 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: the recognised lines in reading order, one per line.

A P P F N D
E X
ictud, in omni actione corporea tantum virium corpori acenti decedere,
quantum corpus actionem suscipiens lueratum sit.
TI. Propositio IV. Lib. L. 5. 44. Facilem suppeditat modum de-
monstrandi centrum graritaris dari in unoquoque COrpOTO, et hOC
centrum unicum esle, si grarium directiones parallelae fuerint. Nlam,
si fuerint corpuscula quotcunque quam minima A, B, C3 D, et C. Fi8. 150
quomodocunque polita, et tanquam elementa corporis etiam cujus-
libet spectata, a quibus demissae sint ad planum Pe positione datura
perpendiculares Aa, BB, CC, Dd, eC. e plano Pc aliud paral-
lelum ducatur OFI, cujus distantia Fe a plano PC ca (IE, ut Factum
ex De in aggregatum corporum A + B F C + D + ec. aequet Tum
mam Factorum A. Aa + B. Bb + C. CC + D. Dd = BC. COrporum A,
B, C, D, 8c. in luas respectiras a plano Dc distantias Aa, Bb,
C0, 8c. ec in Pc Tumatur Pe, talis uc (A + B + C + D + ∞C). PC
sIC = A. Pa + B. Pb F C. PC + D. Pd + eEC. ductaque per e recta et
Occurret CTI in puncto F, quod est commune centrum graritatis
corpusculorum A, B, C, D, exc. vel corporis totalis, quod exhisce
corpusculis componitur. HIoc punctum F. ideo dicitur corporis to-
talis centrum graritatis, quia ejus partes seu corpuscula A, B, CX
una parte lincae, vel plani GTI, aequalium sunt momentorum cum
corpusculis C, D, ecc. ex altera parte ejusdem plani vel linex CII,
et quia hoc idem accidie respectu cujuslibet alius lincxe LMI, GuX
Per hoc idem punctum P duci potest. Nam ducta per P linca Pn
Darallela LM, ex productis Aa, Bb, CC, Dd, XC. e FC, in a.
B, n, d, 8C. de c. reperietur (A L B + C + D + 8 C). PC = A. A∞ + B.
BB + C. Cn + D. Dd + C. dc (A + B + C + D + XC). PC = A. Pa +
B. PB L C. Pn = D. Pd. + ec. Quandoquidem omnia triangula Pau,
PBB, PCn; _C. Timilia Cunt. Jam ex hisce duabus aequalitatibus ul-
tro sequitur, omnia mOmenta COrpOrUM A, B, C, D, _C. relpC.
etu utriusque plani Pn e PV ejus normalis simul aequalia ese relpe-
ctire factis ex agoregato corporum in distantias centri F ab utrO-
que plano vel linea Pn, PV, quod cum ita sit, necestum etiam cst
ut corpuscula, quae sunt ad unam partem rectae L MI aequalium sint
momentorum cum pondusculis, quae lunt in altera parte ejusdem L. M.
Cum itaque omnes lincae, quae per punctum F. duci poltunt, AnEaXCS
aequilibrii pondusculorum A, B, C, D, ec. liquet corporis CX
hisce corpusculis tanquam luis elementis conslati centrum giaritatis
unicum eNse in F. Ouod erat demonstrandum.
Hlanc eandem propositionem Wallisius ex aliis principiis eriam eli-
cuic.
BbD
TII. Cir.