# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1066518432:0077
# Permalink to this reading: https://leibnizlegible.com/page/1066518432:0077?run=74
# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 49, page id 1066518432:0077
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1066518432&page=77
# Source image: https://digitale-sammlungen.gwlb.de/content/1066518432/jpgs/default/00000077.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 38 lines, status machine
# Lines: 38 recognised, mean confidence 0.91
# 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.

DE VIRTEDS ETMOTTBOS CORPORVH. L. IB. L. 43
eROPOSITIO XIV. THEOREMA.
112. Recta AD curva P. R A perpendicularis, mediae directioni BD Fi8. 31.
potentiarum curva perpendiculariter applicatarum, occurret in punctoD
lineae mediarum directionum CVD.
Sit Ad CurrX Clementum, eE ab TanOOnS CVEVX in a, _ bD linca
bisccans anculum, abF crit media directio potentiarum arcui curre
FRa applicatarum: unde cum b ipsi B infinite ricinum sE, sequi-
tur unam bD alteram BD secare in puncto D currae quaesitx. Igi-
cur probandum tantum reltat, perpendicularem currae AD trantire
per punctum illud intersectionis D, duarum infinite ricinarum BD,
bD. Centro quolibet P in tangente BF aNumto, e radio EP de
scripto lemicirculo LCHI, agantur radii FCs tangenti AB, ec fip
tangenti ab paralleli, junctisque FC, Fg, agatur Cm radio FF
Parallela, recte Fe productx occurrens in h, et radio Fg prolon-
sato in m: denique ductxe sint semicirculi tangens OIE in puncto
C, _ F.M eidem tansenti parallela, quae proinde radio LC Dei-
Dendicularis exit. Jam quia FC tangenti AB Parallela cA, crit an-
suluS ABTI = FFO, _ duO FFC X FOF limul aquales angulo
ABE, seu duplo anguli DBF, quandoquidem BD angulum ABF
bifariam dividit, isitur FFO = DBK, unde rectae BD e OF. sunt
Parallela. Pari argumento probatur, parallelas esse bD et eF. Igi-
tur dueta mL. Parallela ipsi BE, vel sE, ABuTa ABBD _ FOML.
erunt similes, cum compostae sint ex triangulis similibus ABB, BDb,
ex FCm, Cm. Hlisce pesitis, parallelx FK ex Cim a media FB
provortionaliter diridentur, atque adeo Cm: Ch = FK: F. H (vel
propter parallelas MF ex CIE) = FO: MCr. Friangula vero similia
GEB, ∞ CIm (nam per conAr. PB e Im parallelx TunE) PEX-
DenE, Cm: Ch = CL: CF. TOIEUT FO: MG =CT: GF; atque adco
FF junsens puncta F, L. Parallela est rectae ME, ac proinde LFC
es rectus, cum P. MI perpendicularis sit ipsi FC. Vnde propter (i-
milicudinem AGuTAruM ABBD, e FCm L, erit AB: BD = FC: CL,
hinc, quia angulus LFCr rectus eAt, angulus D AB itidem rectus crit,
aeque adeo AD currX E. R A perpendicularis in A. Quod erat de
monstrandum.
R OL K k L a M.
et3. Aceosle etiam criansula ADB ex ML. C similia TunC, ex
quo