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

MATHEMATICA. LIB. I. CAP. XXI. eo ſi hæc dicatur 2R, erit IL = {AI q /2R} = {Bi q /2R}: ſed{aB q /2AF} ſe habet ad {Bi q /2R},
ut { M-N q /AF} ad{N q /R}; idcirco
IL, AB: : {N q /R} { M-N q /AF}

185.1.

31. El. 111.
8. El VI.
La Hire
ſect. con.
lib. 7. cot.
prop. 6.

Sed ut vidimus AB, I i: : M-N, M + N; ergo ex compoſitione rationis
IL, I i: : {N q x M-N /R}, { M-N q x M + N /AF} = { M q -N q x M-N /AF} : : {N q /R}, {M q -N q /AF}
Eodem tempore percurruntur IL & i I, prima vi qua corpus retinetur in
Ellipſi quieſcente, ſecunda difterentiâ vis hujus cum vi qua corpus in El-
lipſi mobili retinetur, ergo vis in Ellipſi ad differentiam hanc, ut {N q /R}
ad {M q -N q /AF} .

401.

Dicatur {N q /AF q } vis qua corpus in Ellipſi retinetur in puncto A, & fiat
{N q /R}, {M q -N q /AF} : : {N q /AF q }, ad differentiam virium {RMM-RNN/AF c }

Si agatur de diſtantia alia quæcunque quæ dicatur D, vis qua corpus reti-
netur in Ellipſi hac analogia detegitur , {I/AF q }, {I/D q } : : {N q /AF q } ad vim quæſitam {NN/DD}.

185.1.

381. 411.

Difterentia virium detegitur hac regulâ , {I/AF c }, {I/D c } : : {RMM-RNN/AF c } ad differentiam quæſitam
{RMM-RNN/D c }.

185.1.

410.

Idcirco vis integra qua corpus in Ellipſi mobili retinetur ſequitur propor-
tionem {NN/D q } + {RMM-RNN/D c }, quando corpus & Ellipſis ad eandem
partem tendunt. Si motus hi fuerint contrarii vis proportionalis eſt
{NN/D q }-{RMM - RNN/D c }.

185.1.

427.
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