Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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qua corpus in Ellipſi mobili
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upk
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iiſdem temporibus revolvi
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poſſit. </
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LIBER
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PRIMUS.</
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Corol.
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3. Ad eundem modum colligetur quod, ſi Orbis immo
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bilis
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VPK
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Ellipſis ſit centrum habens in virium centro
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C
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; ei
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que ſimilis, æqualis & concentrica ponatur Ellipſis mobilis
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upk;
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ſitque 2 R Ellipſeos hujus latus rectum principale, & 2T latus
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tranſverſum ſive axis major, atque angulus
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VCp
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ſemper ſit ad
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angulum
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VCP
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ut G ad F; vires quibus corpora in Ellipſi im
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mobili & mobili temporibus æqualibus revolvi poſſunt, erunt ut
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(FFA/T
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cub.
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) & (FFA/T
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cub.
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)+(RGG-RFF/A
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cub.
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) reſpective. </
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Corol.
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4. Et univerſaliter, ſi corporis altitudo maxima
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CV
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no
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minetur T, & radius curvaturæ quam Orbis
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VPK
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habet in
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V,
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id
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eſt radius Circuli æqualiter curvi, nominetur R, & vis centripeta
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qua corpus in Trajectoria quacunQ.E.I.mobili
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VPK
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revolvi po
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teſt, in loco
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V
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dicatur (VFF/TT), atque aliis in locis
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P
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indefinite dica
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tur X, altitudine
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CP
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nominata A, & capiatur G ad F in data
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ratione anguli
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VCp
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ad angulum
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VCP:
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erit vis centripeta qua
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corpus idem eoſdem motus in eadem Trajectoria
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upk
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circula
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riter mota temporibus iiſdem peragere poteſt, ut ſumma virium
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X+(VRGG-VRFF/A
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cub.
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). </
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Corol.
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5. Dato igitur motu corporis in Orbe quocunQ.E.I.mo
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bili, augeri vel minui poteſt ejus motus angularis circa centrum
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virium in ratione data, & inde inveniri novi Orbes immobiles in
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quibus corpora novis viribus centripetis gyrentur. </
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Corol.
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6. Igitur ſi ad rectam
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CV
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po
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ſitione datam erigatur perpendiculum
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VP
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longitudinis indeterminatæ, jun
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gaturque
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CP,
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& ipſi æqualis agatur
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Cp,
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conſtituens angulum
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VCp,
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qui ſit
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ad angulum
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VCP
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in data ratione;
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vis qua corpus gyrari poteſt in Curva
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illa
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Vpk
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quam punctum
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p
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perpetuo
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tangit, erit reciproce ut cubus altitu
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dinis
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Cp.
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Nam corpus
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P,
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per vim inertiæ, nulla alia vi urgente,
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uniformiter progredi poteſt in recta
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VP.
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Addatur vis in centrum
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C,
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cubo altitudinis
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CP
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vel
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Cp
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reciproce proportionalis, & (per
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jam demonſtrata) detorQ.E.I.ur motus ille rectilineus in lineam </
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