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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 299, page id 1041163592:0333
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I
DRINOIDIA MATHEMATICA.
5) 57
mittantur perpendiculares BE, DL, et vis qua particula Mediis LIvEu
decundum rectam FB oblique incidendo, Clobum seric in B, exie SECVAVOS.
ad rim qua parricula eadem Cylindrum ON6 Q axe AC l circa
Clobum delcripeum perpendicularicer Fcriret in b, uE L D ad
L. B vel B F ad BC. Rurlus efficacia hujus vis ad movendum
Globum secundum incidentia sux plasam FB vel AC, eAt ad cjus.
dem etlicaciam ad movendum Cilobum secundum plagam decermi-
nationis lux, id est, secundum plagam rectae BC. qua Cilobum di-
recte urget, uE B F, ad BC. EF conjunctis rationibus, etfrcacia
particulae, in Clobum secundum rectam sB oblique incidentis, 2d
morendum cundem secundum plasam incidentia liae, est ad efi-
caciam particulo ejusdem secundum eandem rectam in Cplindrum
perpendiculariter incidentis, ad iplum morendum in plagam can-
dem, uE B F quadratum ad BC quadracum. Ouare A ad Cplin-
dri balem circularem N AO crisatur perpendiculum bFI F, e sIL
bF aequalis radio AC, ee b TI aequalis F quad
CB: exie b FY ad bF
ut erectus particulae in Globum ad efoctum particulae in Crlin.
drum. Ft propterea solidum quod a rectis omnibus bF occu-
patur erit ad Colidum quod a rectis omnibus b F OCCUPATUE, ut
effectus parcicularum omnium in Globum ad effectum particu-
larum omnium in Cplindrum. Sed Colidum prius est Parabolois
vertice C) axc CA e latere recto CA descriptum, de Tolidum
Posterius eA Cylindrus Paraboloidi circum (criptus: et notum eA
quod Parabolois sc Cemistis Cplindri circumseripei. Ergo vis
tota Medii in Globum est duplo minor quam ejusdem vis FOta
in Cylindrum. Ec propcerea E particula Medii quielcerent, de
Cplindrus 2c Clobus aequali cum relocitate morerentur, Foret re-
sictentia Colobi duplo minor quam resistentia Cplindri. Q. F. D.
Scholium.
ad relictenciam comparari portune, eaeque in-
veniri quae ad mocus suos in Mediisresisten.
cibus continuandos apeiores Punt. VF Si balc
circulari C F BFF, quae centro O, radio OC
describitur, ex altitudine OD, construen-
dum sic Fructum Coni C BG F, quod omni-
um eadem basi ec alticudine constructorum ec lecundum plasam
utd
1
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F adem MCLHOUO LLGUEX alIX inter se quo-