Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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Reg.
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8. Inventis longitudinibus
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AH, HX
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; ſi jam deſideretur </
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poſitio rectæ
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AH,
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ſecundum quam Projectile, data illa cum veloci
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tate emiſſum, incidit in punctum quodvis
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K:
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ad puncta
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A
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&
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K
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erigantur rectæ
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AC, KF
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horizonti perpendiculares, quarum
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AC
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deorſum tendat, & æquetur ipſi
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AI
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ſeu 1/2
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HX.
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Aſymptotis
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AK,
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KF
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deſcribatur Hyperbola, cujus conjugata tranſeat per punctum
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C,
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centroque
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A
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& intervallo
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AH
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deſcribatur Circulus ſecans Hy
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perbolam illam in puncto
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H;
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& Projectile ſecundum rectam
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AH
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emiſſum incidet in punctum
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K. Q.E.I.
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Nam punctum
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H,
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ob
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datam longitudinem
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AH,
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locatur alicubi in Circulo deſcripto. </
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gatur
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CH
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occurrens ipſis
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AK
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&
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KF,
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illi in
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E,
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huic in
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F;
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& ob
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parallelas
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CH, MX
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& æquales
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AC, AI,
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erit
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AE
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æqualis
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AM,
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& propterea etiam æqualis
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KN.
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Sed
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CE
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eſt ad
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AE
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ut
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FH
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ad
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KN,
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& propterea
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CE
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&
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FH
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æquantur. </
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<
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H
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in Hyperbolam Aſymptotis
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AK, KF
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deſcriptam, cujus conju
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gata tranſit per punctum
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C,
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atque adeo reperitur in communi in
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terſectione Hyperbolæ hujus & Circuli deſcripti.
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Q.E.D.
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No
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tandum eſt autem quod hæc operatio perinde ſe habet, ſive recta
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AKN
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horizonti parallela ſit, ſive ad horizontem in angulo quo
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vis inclinata: quodque ex duabus interſectionibus
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H, H
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duo pro
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deunt anguli
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NAH, NAH
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; & quod in Praxi mechanica ſufficit </
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