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Philosophical transactions, Vol. L. Part II. For the year 1758.: Giving some account of the present undertakings, studies, and labours, of the ingenious, in many considerable parts of the world.Various

History

Philosophical transactions, Vol. L. Part II. For the year 1758.: Giving some account of the present undertakings, studies, and labours, of the ingenious, in many considerable parts of the world.

Name: Philosophical transactions, Vol. L. Part II. For the year 1758.: Giving some account of the present undertakings, studies, and labours, of the ingenious, in many considerable parts of the world.
Author: Various

Various

Science -- Periodicals

Exhibeat jam sphærois prædicta planetam quemvis figurâ hac donatum,
et corpus S satellitem circa planetam tanquàm primarium gyrantem.
Quantitas materiæ globo sphæroidis interiori incumbentis æqualis est
4_bbc_D ⁄ 3_a_ sive 4_bc_D ⁄ 3 proximè, et si materia illa locaretur
in centro sphæroidis C, attraheret satellitem S secundum SC vi 4_bc_D
⁄ 3_l_², quæ reducta ad directionem SD fit 4_bck_D ⁄ 3_l_³, et ad
directionem DC fit 4_bch_D ⁄ 3_l_³. Cum igitur vis 4_bc_D ⁄ 3_l_² non
turbat motum satellitis, utpote quæ tendat ad centrum motûs et quadrato
distantiæ ab eodem centro sit reciprocè proportionalis, vires illæ
4_bck_D ⁄ 3_l_³, 4_bch_D ⁄ 3_l_³, in quas resolvitur, etiam motum non
turbabunt. Itaque ex vi D × _c_ × (4_kb_ ⁄ 3_l_³ - 4_kb_³ ⁄ 5_l_⁵ +
2_khhb_³ ⁄ _l_⁷) auferatur vis 4_bck_D ⁄ 3_l_³, et ex vi D × _c_ ×
(4_hb_ ⁄ 3_l_³ + 2_hb_³ ⁄ 5_l_⁵ - 2_hkkb_³ ⁄ _l_⁷) auferatur 4_bch_D
⁄ 3_l_³, et remanebunt vires D × _c_ × - (4_kb_³ ⁄ 5_l_⁵ + 2_khhb_³ ⁄
_l_⁷), D × _c_ × (2_hb_³ ⁄ 5_l_⁵ - 2_hkkb_³ ⁄ _l_⁷), motuum satellitis
S perturbatrices. Designetur vis D × _c_ × (2_hb_³ ⁄ 5_l_⁵ - 2_hhkb_³ ⁄
_l_⁷) per rectam S_r_ (_Fig. 2._) ac resolvatur in vim S_q_ tendentem
ad centrum planetæ primarii C et ob triangula similia S_rq_, SDC,
æqualem D × _c_ × (2_b_³ ⁄ 5_l_⁴ - 2_kkb_³ ⁄ _l_⁶), existentibus ut
priùs, SD = _k_, DC = _h_, SC = _l_; et in vim _rq_ rectæ SD parallelam
et æqualem D × _c_ × (2_kb_³ ⁄ 5_l_⁵ - 2_k_³_b_³ ⁄ _l_⁷); atque hæc vis
posterior subducta ex vi D × _c_ × - (4_kb_³ ⁄ 5_l_⁵ + 2_khhb_³⁄_l_⁷)
relinquet D × _c_ × 4_kb_³ ⁄ 5_l_⁵ pro vi perturbatrice in directione
SD. Unde cum massa tota planetæ sit 2_ab_D ⁄ 3, gravitas satellitis
tota in planetam erit 2_ab_D ⁄ 3_l_² proximé, vel etiam 2_bb_D ⁄ 3_l_²,
et hæc gravitas est ad vim D × _c_ × 4_kb_³ ⁄ 5_l_⁵ ut 1 ad 6_kbc_ ⁄
5_l_³.

Deinde vis illius D × _c_ × 4_kb_³ ⁄ 5_l_⁵ secundum SD pars ea quæ agit
in directione SC est D × _c_ × 4_kkb_³ ⁄ 5_l_⁶, quæ addita vi Sq dat D
× _c_ × (2_b_³ ⁄ 5_l_⁴ - 6_kkb_³ ⁄ 5_l_⁶) vim perturbatricem tendentem
ad centrum planetæ primarii, atque hæc vis est ad satellitis gravitatem
2_bb_D ⁄ 3_l_² in primarium ut 3_bc_ ⁄ 5_l_² - 9_kkbc_ ⁄ 5_l_⁴ ad 1.
_Q. E. I._


COROLL.

Public-domain text, read in full here on John Shaqi.

Opening the text

History

Philosophical transactions, Vol. L. Part II. For the year 1758.: Giving some account of the present undertakings, studies, and labours, of the ingenious, in many considerable parts of the world.

Various

Science -- Periodicals

Exhibeat jam sphærois prædicta planetam quemvis figurâ hac donatum,
et corpus S satellitem circa planetam tanquàm primarium gyrantem.
Quantitas materiæ globo sphæroidis interiori incumbentis æqualis est
4_bbc_D ⁄ 3_a_ sive 4_bc_D ⁄ 3 proximè, et si materia illa locaretur
in centro sphæroidis C, attraheret satellitem S secundum SC vi 4_bc_D
⁄ 3_l_², quæ reducta ad directionem SD fit 4_bck_D ⁄ 3_l_³, et ad
directionem DC fit 4_bch_D ⁄ 3_l_³. Cum igitur vis 4_bc_D ⁄ 3_l_² non
turbat motum satellitis, utpote quæ tendat ad centrum motûs et quadrato
distantiæ ab eodem centro sit reciprocè proportionalis, vires illæ
4_bck_D ⁄ 3_l_³, 4_bch_D ⁄ 3_l_³, in quas resolvitur, etiam motum non
turbabunt. Itaque ex vi D × _c_ × (4_kb_ ⁄ 3_l_³ - 4_kb_³ ⁄ 5_l_⁵ +
2_khhb_³ ⁄ _l_⁷) auferatur vis 4_bck_D ⁄ 3_l_³, et ex vi D × _c_ ×
(4_hb_ ⁄ 3_l_³ + 2_hb_³ ⁄ 5_l_⁵ - 2_hkkb_³ ⁄ _l_⁷) auferatur 4_bch_D
⁄ 3_l_³, et remanebunt vires D × _c_ × - (4_kb_³ ⁄ 5_l_⁵ + 2_khhb_³ ⁄
_l_⁷), D × _c_ × (2_hb_³ ⁄ 5_l_⁵ - 2_hkkb_³ ⁄ _l_⁷), motuum satellitis
S perturbatrices. Designetur vis D × _c_ × (2_hb_³ ⁄ 5_l_⁵ - 2_hhkb_³ ⁄
_l_⁷) per rectam S_r_ (_Fig. 2._) ac resolvatur in vim S_q_ tendentem
ad centrum planetæ primarii C et ob triangula similia S_rq_, SDC,
æqualem D × _c_ × (2_b_³ ⁄ 5_l_⁴ - 2_kkb_³ ⁄ _l_⁶), existentibus ut
priùs, SD = _k_, DC = _h_, SC = _l_; et in vim _rq_ rectæ SD parallelam
et æqualem D × _c_ × (2_kb_³ ⁄ 5_l_⁵ - 2_k_³_b_³ ⁄ _l_⁷); atque hæc vis
posterior subducta ex vi D × _c_ × - (4_kb_³ ⁄ 5_l_⁵ + 2_khhb_³⁄_l_⁷)
relinquet D × _c_ × 4_kb_³ ⁄ 5_l_⁵ pro vi perturbatrice in directione
SD. Unde cum massa tota planetæ sit 2_ab_D ⁄ 3, gravitas satellitis
tota in planetam erit 2_ab_D ⁄ 3_l_² proximé, vel etiam 2_bb_D ⁄ 3_l_²,
et hæc gravitas est ad vim D × _c_ × 4_kb_³ ⁄ 5_l_⁵ ut 1 ad 6_kbc_ ⁄
5_l_³.

Deinde vis illius D × _c_ × 4_kb_³ ⁄ 5_l_⁵ secundum SD pars ea quæ agit
in directione SC est D × _c_ × 4_kkb_³ ⁄ 5_l_⁶, quæ addita vi Sq dat D
× _c_ × (2_b_³ ⁄ 5_l_⁴ - 6_kkb_³ ⁄ 5_l_⁶) vim perturbatricem tendentem
ad centrum planetæ primarii, atque hæc vis est ad satellitis gravitatem
2_bb_D ⁄ 3_l_² in primarium ut 3_bc_ ⁄ 5_l_² - 9_kkbc_ ⁄ 5_l_⁴ ad 1.
_Q. E. I._


COROLL.

Public-domain text, read in full here on John Shaqi.

Philosophical transactions, Vol. L. Part II. For the year 1758.: Giving some account of the present undertakings, studies, and labours, of the ingenious, in many considerable parts of the world.

Philosophical transactions, Vol. L. Part II. For the year 1758.: Giving some account of the present undertakings, studies, and labours, of the ingenious, in many considerable parts of the world.

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