Huygens, Christiaan - Christiani Hugenii opera varia; Bd. 1: Opera mechanica

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9660CHRISTIANI HUGENII

11De de-
SOENSU
GRAVIUM.

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
22TAB. V.
Fig. 3. 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.

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
33Prop. I.
huj. eadem proportione qua tempora deſcenſus ; ſitque

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Scan	Original
61	34
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Scan	Original
61	34
62	35
63	36
64	37
65	38
66	39
67	40
68	41
69	42
70	43
71	44
72	45
73	46
74
75
76
77	47
78	48
79
80
81
82	49
83	50
84	51
85	52
86
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89	53
90	54