Page:Philosophical Transactions - Volume 003.djvu/75

This page has been proofread, but needs to be validated.

(698)

velocitati mobilis in recta $AB$ , ipsi $AD$ æquali, & ides eodem tempore perficitur utraque recta $AD$ , $AB$ ; & proinde eodem tempore perficiuntur accessiones ad planaresistentia $AE$ , $AH$ ; ideoque velocitates accessionum ad planaresistentiasunt in directa ratione $AE$ ad $AH$ , atque ideo percussio in puncto $D$ . est ad percussionem in puncto $C$ . in eadem ratione $AE$ ad $AH$ ; nempe ut Sinus anguli incidentiæ $ADE$ . ad sinum anguli incidentiæ $ACE$ , vel $AFE$ . Quoniam antem recta $AC.AF$ , æqualiter inclinant ad planum $CF$ , mobilia in rectis $AC$ , $AF$ , accedunt ad planum $CF$ , in eadem proportione qua moventur in rectis $AC$ , $AF$ ; & ideo percussio in C est ad percussionem in $F$ in ratione velocitatis motus in $AC$ seu in $AD$ ad velocitaten motus in $AF$ ; At demonstratum est ante, percussionem in puncto $D$ ad percussionem in puncto $C$ , esse in ratione sinus anguli $ADE$ ad sinum anguli $AFE$ . & nunc demonstratum est, percussionem in puncto $C$ esse ad percussionem in puncto $F$ , ut velocitas motus in $AD$ ad velocitatem motus in $AF$ . Igitur ex 5. defin. 6. Elementorum, percussio in $D$ , est ad percussionene in $F$ , in ratione composita ex ratione sinus anguli incidentiæ $ADE$ , ad sinum anguli incidentiæ $AFE$ , & ex ratione velocitatis in $AD$ ad velocitatem in $AF$ ; quod demonstrare oportuit. Neminem moveat, quod hæc demonstratio adstricta fit motibus æqualibus in lineis rectis & planis resistentibus; est enim vera in omni casu: nam, cumpercussiones fiant in puncto, in hoc coincidunt rectum, curvum, æquale, & inæquale; si autem in punctis percussiones non fiant. de illis non potest dari consideratio geometricia, sed judicandus est conclusionis defectus secundum defectum materiæ à conditionibus requisitis, sicut semper fieri debet, dum demonstrationes geometricæ corpori physico applicantur.

In Angeli his reply to Manfreddi, he maketh mention of an Experiment, which (as was related to him by a Swedish Gentleman) had been made with all due circumspection by Cartesius to prove the Motion of the Earth, The experiment was; He caused to be erected a Canon perpendicular to the Horizon; which being 24 times discharged in that posture, the Ball did fall 22 times towards the West, and only twice toward the East.

An