Full text: Volumen primum. Opera mechanica (1)

De de-
SOENSU
GRAVIUM .

28. PROPOSITIO V.

SPatium peractum certo tempore, à gravi è quie-
te caſum inchoante, dimidium eſſe ejus ſpatii
quod pari tempore transiret motu æquabili, cum
celeritate quam acquiſivit ultimo caſus momento.

Sit tempus deſcenſus totius A H, quo tempore mobile
peregerit ſpatium quoddam cujus quantitas deſignetur plano P. ductaque H L perpendiculari ad A H, longitudinis cujus-
libet, referat illa celeritatem in fine caſus acquiſitam. Dein-
de completo rectangulo A H L M, intelligatur eo notari
quantitas ſpatii quod percurreretur tempore A H, cum ce-
leritate H L. Oſtendendum eſt igitur planum P dimidium
eſſe rectanguli M H, hoc eſt, ducta diagonali A L, æqua-
le triangulo A H L.

28.1.

TAB. V.
Fig. 3.

Si planum P non eſt æquale triangulo A H L, ergo aut
minus eo erit, aut majus. Sit primo, ſi fieri poteſt, pla-
num P minus triangulo A H L. dividatur autem A H in tot
partes æquales A C, C E, E G & c. ut, circumſcriptâ tri-
angulo A H L figurâ è rectangulis quorum altitudo ſingulis
diviſionum ipſius A H partibus æquetur, ut ſunt rectangula
B C, D E, F G, alterâque eidem triangulo inſcriptâ, ex
rectangulis ejusdem altitudinis, ut ſunt K E, O G & c. ut,
inquam, exceſſus illius figuræ ſupra hanc, minor ſit exceſ-
ſu trianguli A H L ſupra planum P. hoc enim fieri poſſe
perſpicuum eſt, cum totus exceſſus figuræ circumſcriptæ ſu-
per inſcriptam æquetur rectangulo infimo, baſin habenti H L. Erit itaque omnino exceſſus ipſius trianguli A H L ſupra
figuram inſcriptam minor quam ſupra planum P, ac proin-
de figura triangulo inſcripta major plano P. Porro autem,
quum recta A H tempus totius deſcenſus referat, ejus par-
tes æquales A C, C E, E G, æquales temporis illius par-
tes referent. Cumque celeritates mobilis cadentis creſcant
eadem proportione qua tempora deſcenſus ; ſitque celeritas

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer