Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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minor ex parte concava quam ex parte convexa; prævalebit im
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preſſio fortior, & motum Orbis vel accelerabit vel retardabit,
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prout in eandem regionem cum ipſius motu vel in contrariam di
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rigitur. </
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>Proinde ut Orbis unuſquiſQ.E.I. motu ſuo uniformiter
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perſeveret, debent impreſſiones ex parte utraque ſibi invicem æqua
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ri, & fieri in regiones contrarias. </
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<
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>Unde cum impreſſiones ſunt ut
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contiguæ ſuperficies & harum tranſlationes ab invicem, erunt tran
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ſlationes inverſe ut ſuperficies, hoc eſt, inverſe ut ſuperficierum di
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ſtantiæ ab axe. </
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<
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>Sunt autem differentiæ motuum angularium circa
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axem ut hæ tranſlationes applicatæ ad diſtantias, ſive ut tranſlati
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ones directe & diſtantiæ inverſe; hoc eſt (conjunctis rationibus)
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ut quadrata diſtantiarum inverſe. </
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>Quare ſi ad infinitæ rectæ
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SABCDEQ
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partes ſin
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gulas erigantur perpendicula
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Aa, Bb, Cc, Dd, Ee,
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&c. </
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ipſarum
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SA, SB, SC, SD,
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SE,
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&c. </
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proportionalia, & per ter
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minos perpendicularium du
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ci intelligatur linea curva
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Hyperbolica; erunt ſummæ
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differentiarum, hoc eſt, mo
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tus toti angulares, ut re
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ſpondentes ſummæ linearum
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Aa, Bb, Cc, Dd, Ee
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: id
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eſt, ſi ad conſtituendum Me
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dium uniformiter fluidum, Orbium numerus augeatur & latitudo
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minuatur in infinitum, ut areæ Hyperbolicæ his ſummis analogæ
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AaQ, BbQ, CcQ, DdQ, EeQ,
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&c. </
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>Et tempora motibus an
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gularibus reciproce proportionalia, erunt etiam his areis reciproce
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proportionalia. </
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>Eſt igitur tempus periodicum particulæ cujuſvis
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D
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reciproce ut area
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DdQ,
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hoc eſt, (per notas Curvarum qua
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draturas) directe ut diſtantia
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SD. Q.E.D.
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DE MOTU
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CORPORUM</
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Corol.
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1. Hinc motus angulares particularum fluidi ſunt reci
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proce ut ipſarum diſtantiæ ab axe cylindri, & velocitates abſo
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lutæ ſunt æquales. </
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Corol.
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2. Si fluidum in vaſe cylindrico longitudinis infinitæ con
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tineatur, & cylindrum alium interiorem contineat, revolvatur
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autem cylindrus uterque circa axem communem, ſintque revolu-</
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