# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1066518432:0258
# Permalink to this reading: https://leibnizlegible.com/page/1066518432:0258?run=74
# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 230, page id 1066518432:0258
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1066518432&page=258
# Source image: https://digitale-sammlungen.gwlb.de/content/1066518432/jpgs/default/00000258.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
# Lines: 37 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.

230 DF VERIBOS EF NIOTTBOS COREORDM. LIB. II.
P. O. DC; ergo DO = P. O. DC, rel etiam P. O =DC2. Rs er
80DC media geomerica inter parametros parabola et paraboloi-
dis.
TI. In paraboloide est O. LR =DL, vel P. Q. LR, id est
(num. F. hujuS) DC=. LR =P. DI, vel quia parabola efcit P. DL.
aequale LT2, =L.TZ. DL; hinc DC: L R=DC: LP, atque ad
CODL: TR = DC: VT, hinC DL. LT =DC. LR, e per conse.
QuenS ZDL. LY seu parabOlA DZYL =EDC. LR (secundum hypo-
chelin) =R. LR. Similiter reperietur parabola, seu area parabolica,
DOVO =R. OS; ergo quadrilinCUM LTVO =R. YS. Sic etiam
quadrilincum IZOC =R. OC; unde quia (conAtr.) Y5 =OC, ad-
eoque quadrilincum LTVO aequale quadrilinco lL6C, (8. 413.)
eadem agux copia per sectiones IC _ FF Auet, atque adeo super-
ficies agux IFIFE manens erir. Quod erat demonstrandum.
S C H O L F O H.
415. ODe praelentis, ejusque qua cam praecedie, ex datis inclina-
tione canalis seu angulo C AD, sectione qualibet RF ejusque di
Stantia AF. a superticie aqua in castello AD, vel ab orisine cana
lis, innotescent proportio relocitatum P de F, dt reliqua sectio-
neS omnes. Nam ex dato angulo DAC e distantia AF, innocescet
ipla Or, X ex hac e angulo ABC, complemento ansuli C AD, eli-
cietur OD; unde, cum sectio E. F eique aequalis OL. data sC ex hy-
Pothesi, ca ex OD Tuberacta relinquet LD cognitam. Jam descripta
circa axem DO et vertice D parabola DCV, ordinatae L. I ec OV
exponent proportionem celeritatum aquae in L ec l. Sed, quia mul.
ti tunc casus, quibus distantia L. A actuali dimentione haberi nequits
Exepissime hic modus determinandi praememoratas celeritates in pra-
xi minime succedit, ex mechanice eas relocitates inrestisare con-
renit.
F1S. 97.
PROEOSIIIO ALI. PROBLEMA.
4.T6. Invenire per observationes artificio mechanico proportionem ven
locitatum in P. e F cujusque sectionis Ruminis canalisve P. F.
Hlabeatur tilum CP cum pondere P, aqua aliquantum specifice
crariore, alteroejus capiti annexo, demissoque pondere P’usque ad
fundum canalis CD, id pondus ab aqua per punctum E. sectionis