Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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eſt ſagittæ dupli arcus
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QP,
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in cujus medio eſt
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P,
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& duplum trian
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guli
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SQP
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ſive
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SPXQT,
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tempori quo arcus iſte duplus deſcribitur
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proportionale eſt, ideoque pro temporis exponente ſcribi poteſt. </
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DE MOTU
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CORPORUM</
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Corol.
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2. Eodem argumento vis centripeta eſt reciprocè ut ſolidum
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(
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SYqXQPq/QR
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), ſi modo
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SY
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perpendiculum ſit a centro virium in Or
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bis tangentem
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PR
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demiſſum. </
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<
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>Nam rectangula
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SYXQP
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&
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SPXQT
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æquantur. </
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Corol.
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3. Si Orbis vel circulus eſt, vel angulum contactus cum cir
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culo quam minimum continet, eandem habens curvaturam eundem
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que radium curvaturæ ad punctum contactus
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P
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; & ſi
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PV
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chorda
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ſit circuli hujus a corpore per centrum virium acta: erit vis centri
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peta reciproce ut ſolidum
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SYqXPV.
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Nam
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PV
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eſt (
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QPq/QR
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). </
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Corol.
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4. Iiſdem poſitis, eſt vis centripeta ut velocitas bis directe,
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& chorda illa inverſe. </
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>Nam velocitas eſt reciproce ut perpendicu
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lum
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SY
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per Corol. </
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<
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>I Prop. </
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>I. </
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Corol.
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5. Hinc ſi detur figura quævis curvilinea
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APQ,
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& in ea
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detur etiam punctum
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S
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ad quod vis centripeta perpetuo dirigitur,
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inveniri poteſt lex vis centripetæ, qua corpus quodvis
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P
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a curſu
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rectilineo perpetuò retractum in figuræ illius perimetro detinebitur
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eamque revolvendo deſcribet. </
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<
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>Nimirum computandum eſt vel ſo
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lidum (
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SPqXQTq/QR
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) vel ſolidum
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SYqXPV
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huic vi reciproce pro
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portionale. </
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<
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>Ejus rei dabimus exempla in Problematis ſequentibus. </
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PROPOSITIO VII. PROBLEMA II.
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Gyretur corpus in circumferentia Circuli, requiritur Lex vis centri
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petæ tendentis ad punctum quodcunQ.E.D.tum.
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<
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>Eſto Circuli circumferentia
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VQPA,
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punctum datum ad
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quod vis ceu ad
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centrũ
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<
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ſuũ
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ten
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dit
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S,
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corpus in circumferentia
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latum
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P,
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locus proximus in quem
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movebitur
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Q,
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& circuli tangens
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ad locum priorem
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PRZ.
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Per
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punctum
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S
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ducatur chorda
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PV,
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& acta circuli diametro
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VA
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jun
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gatur
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AP,
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& ad
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SP
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demittatur
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perpendiculum
<
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QT,
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quod productum occurrat tangenti
<
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PR
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in
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Z,
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