Full text: Gravesande, Willem Jacob: Physices elementa mathematica, experimentis confirmata, sive introductio ad philosophiam Newtonianam

PHYSICES ELEMENTA cum angulo IAb coincidit & angulo AEC æqualis eſt ; quare ſimilia ſunt triangula LbH, AEC, & #
# Lb, LH: : AC, AE aut CD.

183.1.

31 El. 117.
21. El. 111.
29 El 1.

Etiam propter triangula ſimilia AgG, AEC, AG eſt ad Ag, aut LI,
ad Li, ut AC ad AE, aut CD.

Hiſce poſitis concipiamus duo corpora Ellipſin hanc percurrentia, eodem
tempore, quorum unum retineatur vi, quæ ad centrum Ellipſeos C dirigitur,
alterum vi ad focorum alterum F tendente.

Dum corpora ambo arcum exiguum percurrunt AL, primum vi centrali
movetur per IL, ſecundum vi centrali percurrit iL, tempora autem quibus
corpora has lineolas percurrunt, ſuntinter ſe ut areæ LAC, LAF , ponimus enim integram Ellipſin æqualibus temporibus a ſingulis corporibus percurri; ideoque in utroque caſu idem tempus periodicum per integram aream repræ-
ſentari. Areæ vero illæ ſunt inter ſe ut harum dupla AC x LH, AF x
Lb; hæc autem producta quia LH, Lb: : CD, AC, ſunt ut AC x CD ad
AF x AC, id eſt ut CD, ad AF.

183.1.

354. 396.

Spatia IL, iL, viribus centralibus percurſa, quæ ut vidimus ſunt ad AC ad
CD, ſunt etiam in ratione compoſita virium, & quadratorum temporum , aut li- nearum CD, AF.

183.1.

402.

Vis per AC huic lineæ proportionalis eſt, ut demonſtravimus , & hac ipſâ lineâ deſignari poteſt; vim per AF dicimus V: ergo
AC, CD : : AC x CD q , V x AF q
Unde deducimus V = {CD c /AF q }; patet igitur propter conſtantem CD c , mutato
puncto A, vim V mutari in ratione inverſa quadrati diſtantiæ AF. Q. D. E.

183.1.

410.
412.

Circa motum in Ellipſi ulterius notavimus , quod nunc demonſtrabimus, ſi vis decreſcat in ratione inverſa quadrati diſtantiæ, circulum cujus diameter
axi majori Ellipſeos æqualis eſt, eo tempore a corpore percurri in quo hoc
Ellpiſim ipſam deſcribere poſſet.

183.1.

382.

Sit ſemi Ellipſis BAD; axis major BD; ſemi axis minor CA; F focus
centrum virium. Centro F, & radio FA circulus deſcribatur AP, de-
monſtrandum tempus periodicum in circulo æquale eſſe tempori periodico
in Ellipſi; radius enim FA æqualis eſt ſemi axi majori Ellipſeos, ut ex
hujus deſcriptione ſequitur .

183.1.

TAB. XV.
fig. 8.
379.

Dentur duo corpora in A, quorum unum in circulo, alterum in Ellipſi
moveatur, ſintque AL, AM arcus minimi codem tempore deſcripti; ſpa-
tia vicentrali percurſaerunt æqualia; quia ambo corpora ad eandem diſtanti-
am AF a centro dantur: ſpatia autem hæc ſunt iL, NM, poſitis Ai ad
Ellipſin & IN ad circulum, tangentibus, ut & NM, & iL, ad AF pa-
rallelis. Sint etiam IL ad AC, OM ad NA, GL ad AI parallelæ, & du-
cantur LC, LF, MF.

In circulo OM q æquale eſt 2 MN x AF; nam AF & OF pro æqua- libus habentur & AO, MN ſunt æquales.

183.1.

32. El. 111.
3. 4 El. VI.

In Ellipſi AC q , BC q aut AF q : : 2 IL x AC, GL q = { 2 IL x AF q /AC} ſunt
enim æquales AG, IL, & AC, GC tantum quantitate infinite exigua
differunt.

183.1.

La Hire
ſect. com.
lib. 3.
prop 3.

Triangula IiL, ACF, ſunt ſimilia quia latera ſunt reſpectivè parallela; ideò

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