Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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puncta
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b, c
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perpetuo tangunt; deque puncto
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V
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ad lineam
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AC
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eri
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gatur perpendiculum
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Vad
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abſcindens areas curvilineas
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VDba,
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VDcd,
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& erigantur etiam ordinatæ
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Ez, Ex:
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quoniam rectan
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gulum
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DbXIN
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ſeu
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DbzE
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æquale eſt dimidio rectanguli
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AX
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KN,
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ſeu triangulo
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ICK
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; & rectangulum
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DcXIN
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ſeu
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DcxE
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æquale eſt dimidio rectanguli
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YXXXC,
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ſeu triangulo
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XCY;
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hoc eſt, quoniam arearum
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VDba, VIC
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æquales ſemper
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ſunt naſcentes particulæ
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DbzE, ICK,
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& arearum
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VDcd,
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VCX
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æquales ſemper ſunt naſcentes particulæ
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DcxE, XCY,
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erit area genita
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VDba
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æqualis areæ genitæ
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VIC,
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adeoque tem
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pori proportionalis, & area genita
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VDcd
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æqualis Sectori ge
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nito
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VCX.
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Dato igitur tempore quovis ex quo corpus diſceſ
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ſit de loco
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V,
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dabitur area ipſi proportionalis
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VDba,
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& inde
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dabitur corporis altitudo
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CD
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vel
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CI
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; & area
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VDcd,
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eique
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æqualis Sector
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VCX
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una cum ejus angulo
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VCI.
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Datis autem
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angulo
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VCI
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& altitudine
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CI
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datur locus
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I,
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in quo corpus com
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pleto illo tempore reperietur.
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Q.E.I.
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DE MOTU
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CORPORUM</
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Corol.
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1. Hinc maximæ minimæque corporum altitudines, id eſt
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Apſides Trajectoriarum expedite inveniri poſſunt. </
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<
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Apſides puncta illa in quibus recta
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IC
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per centrum ducta incidit
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perpendiculariter in Trajectoriam
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VIK:
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id quod ſit ubi rectæ
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IK
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&
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NK
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æquantur, adeoque ubi area
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ABFD
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æqualis eſt ZZ. </
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Corol.
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2. Sed & angulus
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KIN,
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in quo Trajectoria alibi ſecat
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lineam illam
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IC,
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ex data corporis altitudine
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IC
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expedite inveNI
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tur; nimirum capiendo ſinum ejus ad radium ut
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KN
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ad
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IK,
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id
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eſt, ut Z ad latus quadratum areæ
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ABFD.
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Corol.
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3. Si centro
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C
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& vertice principali
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V
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deſcribatur Sectio quæ
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libet Conica
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VRS,
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& a quovis ejus puncto
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R
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agatur Tangens
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RT
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occurrens axi infinite producto
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CV
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in puncto
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T;
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dein juncta
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CR
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ducatur recta
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CP,
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quæ æqualis ſit abſciſſæ
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CT,
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angulumque
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VCP
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Sectori
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VCR
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proportionalem conſtituat; tendat autem ad centrum
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C
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<
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Vis centripeta Cubo diſtantiæ loeorum a centro reciproce propor
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tionalis, & exeat corpus de loco
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V
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juſta cum Velocitate ſecundum
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lineam rectæ
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CV
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perpendicularem: progredietur corpus illud in
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Trajectoria quam punctum
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P
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perpetuo tangit; adeoque ſi Conica
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ſectio
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CVRS
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Hyperbola ſit, deſcendet idem ad centrum: Sin
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ea Ellipſis ſit, aſcendet illud perpetuo & abibit in infinitum. </
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<
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>Et con
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tra, ſi corpus quacunque cum Velocitate exeat de loco
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V,
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& perin
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de ut incæperit vel obliQ.E.D.ſcendere ad centrum, vel ab eo ob-</
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