Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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DE MOTU
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CORPORUM</
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PROPOSITIO XXXVI. PROBLEMA XXV.
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Corporis de loco dato
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A
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cadentis determinare Tem
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pora deſcenſus.
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<
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>Super diametro
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AS
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(diſtantia corporis a cen
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tro ſub initio) deſcribe Semicirculum
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ADS,
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ut &
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huic æqualem Semicirculum
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OKH
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circa centrum
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S.
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De corporis loco quovis
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C
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erige ordinatim ap
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plicatam
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CD.
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Junge
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SD,
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& areæ
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ASD
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æqua
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lem conſtitue ſectorem
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OSK.
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Patet per Prop.
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XXXV, quod corpus cadendo deſcribet ſpatium
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AC
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eodem Tempore quo corpus aliud uniformiter cir
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ca centrum
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S
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gyrando, deſcribere poteſt arcum
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OK.
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E. F.
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PROPOSITIO XXXVII. PROBLEMA XXVI.
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Corporis de loco dato ſurſum vel deorſum projecti definire Tempora
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aſcenſus vel deſcenſus.
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<
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>Exeat corpus de loco dato
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G
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ſecundum
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lineam
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ASG
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cum velocitate quacunque. </
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In duplicata ratione hujus velocitatis ad
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uniformem in Circulo velocitatem, qua cor
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pus ad intervallum datum
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SG
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circa centrum
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S
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revolvi poſſet, cape
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GA
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ad 1/2
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AS.
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Si ratio illa eſt numeri binarii ad unita
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tem, punctum
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A
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infinite diſtat, quo ca
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ſu Parabola vertice
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S,
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axe
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SC,
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latere quo
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vis recto deſcribenda eſt. </
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>Patet hoc per
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Prop. </
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>XXXIV. </
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>Sin ratio illa minor vel ma
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jor eſt quam 2 ad 1, priore caſu Circulus,
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poſteriore Hyperbola rectangula ſuper di
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ametro
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SA
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deſcribi debet. </
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<
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Prop. </
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<
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>XXXIII. </
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<
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>Tum centro
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S,
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intervallo
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æquante dimidium lateris recti, deſcribatur
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Circulus
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HKk,
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& ad corporis aſcenden
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tis vel deſcendentis loca duo quævis
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G, C,
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erigantur perpendicula
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GI, CD
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occurren
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tia Conicæ Sectioni vel Circulo in
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I
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ac
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D.
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