Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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Circulum ſemel deſcribere, deinde regulam interminatam
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CH
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ita ap
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plicare ad punctum
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C,
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ut ejus pars
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FH,
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Circulo & rectæ
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FK
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interje
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cta, æqualis ſit ejus parti
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CE
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inter punctum
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C
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& rectam
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AK
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ſitæ. </
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LIBER
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SECUNDUS.</
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DE MOTU
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CORPORUM</
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>Quæ de Hyperbolis dicta ſunt fa
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cile applicantur ad Parabolas. </
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>Nam
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ſi
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XAGK
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Parabolam deſignet quam
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recta
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XV
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tangat in vertice
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X,
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ſintque
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ordinatim applicatæ
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IA, VG
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ut quæ
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libet abſciſſarum
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XI, XV
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dignitates
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XI
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n
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, XV
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n
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;
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agantur
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XT, GT, AH,
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quarum
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XT
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parallela ſit
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VG,
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&
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GT,
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AH
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Parabolam tangant in
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G
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&
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A:
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&
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corpus de loco quovis
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A,
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ſecundum
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rectam
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AH
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productam, juſta cum
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velocitate projectum, deſcribet hanc
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Parabolam, ſi modo denſitas Medii,
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in locis ſingulis
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G,
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ſit reciproce ut
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tangens
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GT.
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Velocitas autem in
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G
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ea erit quacum Projectile per
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geret, in ſpatio non reſiſtente, in Parabola Conica verticem
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G,
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dia
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metrum
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VG
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deorſum productam, & latus rectum (
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2GTq./nn-nXVG
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)
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habente. </
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>Et reſiſtentia in
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G
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erit ad vim gravitatis ut
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GT
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ad
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(2nn-2n/n-2) VG.
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Unde ſi
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NAK
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lineam horizontalem deſignet, &
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manente tum denſitate Medii in
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A,
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tum velocitate quacum corpus
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projicitur, mutetur utcunque angulus
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NAH;
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manebunt longitu
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dines
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AH, AI, HX,
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& inde datur Parabolæ vertex
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X,
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& poſitio
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rectæ
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XI,
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& ſumendo
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VG
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ad
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IA
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ut
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XV
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n
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ad
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XI
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n
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,
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dantur om
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nia Parabolæ puncta
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G,
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per quæ Projectile tranſibit. </
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