# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1066518432:0227
# Permalink to this reading: https://leibnizlegible.com/page/1066518432:0227?run=74
# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 199, page id 1066518432:0227
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1066518432&page=227
# Source image: https://digitale-sammlungen.gwlb.de/content/1066518432/jpgs/default/00000227.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
# Lines: 42 recognised, mean confidence 0.86
# 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.

N
0
et
.
 .. .. .. . .. ..
DB VERFBUS ET MIOTEBUS CORPORUM. LLB. II. 199
PROPOSTTIOZZVI. PHEOREMA.
359. Ordinatae quaecunque aequales ab es od in scalis densitatum ex FIS. P.
elasticitatum aeris ultra communem scalarum axem AI productae, in
scala gravitatis variabilis e curva scalae elasticitatis aeris reciproca
perpetuo areas aequales AC Ca e OF eo abscindent.
Ordinatae aB et ad luis respectiris ab e od indetinite vicinae pro-
trahantur in n e f. Jam graritas aeris aT loco a incumbentis, aeri-
que in hoc loco densitatem ab vel od inducens (5. 358.) XquaEur
clasticitati aeris exposita per abscistam A0, e pondus aeris lOcoe
incumbentis aequatur clasticitati aeris in an quae repraelentatur abscil-
la A0; adeoque differentia ponderum aT et a l, id est, pondus
columnulae aerex aa aequabitur differentia clalciciFaEUI AWN EE AO
hoc cA 00. AEqui (5. 32.) Pondus columnula ea exponitur solido
ab. ac. ac; ereo hoc tolidum aequatur alii solido ex co in dacum pla-
num FO. OD, vel (5. 357.) ipa aequale planum eo. od, id cAt, ab.
ac. au = eo. od. 00; leu deletis (lecundum hypothesin) aequalibus ab
ec od, rec. lum ac. au =rec - l0 oc. 00, e cum descendendo vertus CB
ee FD hoc ubique creniat, ut sinsula elementa arearum ACca e
OEeo aequalia sinc, equabuntur etiam univerta, id est omnia ac.
au seu area ACca, quam illa exhauriunt, crunt aequalia omnibus
oe. vo, seuarex OF eo. Quod erac demonstrandum.
C OROL L A R LUN I.
360. Si nunc scala clasticitatum aeris AFDZD pOnatur esse Pa-
rabola indetiniti gradtus, cujus quae libet ordinata rOFD SIE ut ATOm
seu ut dignitas abscisa AFO ab exponente m denominata, erit
Propter rec.- lum DTOTE, aequale dato rectansulo DOE, atque adeo
Propter TE TO alteri rDLO reciproce proportionalem, TF IO reci
PTOCC UE AFOm. atque adeo curra F LF 2F hyperbola indetiniti gra-
dus m. Sit insuper curra C TC2C alia lyperbola indefiniti sradus
n, adeo ut quaelibet ejus ordinata LC IA sit reciproce ut ablcislx
dionitas n, id elt, reciproce ut OFA. Jam sixequales ordinatae TA LB
vel TOFD exponunt densitatem aëris in TA, (5. 359.) Quadrilinea
ATALCC _E OTOTEE aequalia erunt, atqui juxta methodum su-
Pra (5. 92.) expositam invenitur Ouadrilineum ATALCC = (O A.
AC =OTA. TATC): n - 2, ec quadrilincum hyper bolicum OF TF XO
A