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

Repræſentetur hæc eâdem vis per FI; in F ad orbitæ pla-
num detur perpendicularis FR & concipiatur parallelogram-
mum FRI i, cujus latus F i in plano orbitæ detur, & cujus
diagonalis ſit FI; vis turbans per F I reſolvitur in duas, per
FR & F i, quas hæ lineæ repræſentant , & quarum hæc in plano orbitæ agit: ita ut ad hanc debeamus referre, quæ ſpec-
tant vim turbantem, de qua in n. 1299. egimus; lineæ enim F i
& FI vix differunt, & planum parallelogrammi FRI i ad pla-
num orbitæ Lunaris eſt perpendiculare.

676.1.

1332.
TAB. XXV .
fig. 4.
192.

Determinanda eſt linea FR, quæ repræſentat vim, quæ ad
planum orbitæ perpendiculariter agit, & Lunam ex hoc plano
removet; relatio autem lineæ FR aut I i ad radium ET, eſt
ratio vis turbantis, de qua hìc agitur, ad augmentum gravita-
tis in Quadraturis .

676.1.

1333.
1286.

In caſu hujus figuræ in quâ linea Nodorum N n in Quadra-
turis verſatur, detegitur FR; quia IT (quæ eſt NT fig. I.) datur , & quia IT ad I i aut FR, ut radius ad ſinum in- clinationis crbitæ.

676.1.

1334.
1305.

Sed in omni caſu determinanda eſt vis, quæ Lunam ex pla-
no pellit; ponamus ideò lineam Nodorum tranſlatam ad ſitum
M m, quo, cæteris manentibus, mutatur I i. Ad m M con-
tinuatam, ſi neceſſe fuerit, dentur perpendiculares i X & IX, quæ angulum efficiunt æqualem inclinationi plani orbitæ.

676.1.

1335.

Ratio inter ET & I i, id eſt ratio inter augmentum gravi-
tatis in Quadraturis & vim, quam quærimus, quæ Lunam ex
orbitâ removet, eſt compoſita exrationibus lineæ ET ad TI,
lineæ TI ad IX, & tandem lineæ IX ad I i. Prima eſt ra-
tio inter radium & ter ſinum diſtantiæ Lunæ à Quadraturâ ; ſecunda eſt ratio radii ad ſinum anguli ITX, id eſt diſtantiæ
Nodi à Syzygiâ; tertia tandem eſt ratio radii ad ſinum incli-
nationis orbitæ: & ratio ex his compoſita, eſt ratio cubi radii
ad ter productum ſinu m diſtantiarum Lunæ à Quadratur â, & Nodi à Syzygiâ, ut & inclinationis plani. Ad hanc vim etiam
reſerendus n. 1308.

676.1.

1336.
1305.

Vis hæc in Quadraturis nulla eſt, quia punctum I cum
puncto T, centro Telluris, coincidit, & evaneſcit linea I i, li-
neis FI & F i concurrentibus, in plano orbitæ; quod etiam ex

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