Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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inde eſt, cape
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Rr
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æqualem (
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GTIE
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/N); & Projectile tempore
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DRTG
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perveniet ad punctum
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r,
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deſcribens curvam lineam
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DraF,
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quam
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punctum
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r
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ſemper tangit, perveniens autem ad maximam altitudi
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nem
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a
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in perpendiculo
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AB,
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& poſtea ſemper appropinquans ad A
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ſymptoton
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PLC.
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Eſtque velocitas ejus in puncto quovis
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r
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ut Cur
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væ Tangens
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rL.
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E. I.
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DE MOTU
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CORPORUN</
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<
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>Eſt enim N ad
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QB
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ut
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DC
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ad
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CP
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ſeu
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DR
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ad
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RV,
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adeoque
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RV
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æqualis (
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DRXQB
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/N), &
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Rr
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(id eſt
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RV-Vr
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ſeu (
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DRXQB-tGT
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/N))
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æqualis (
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DRXAB-RDGT
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/N). Exponatur jam tempus per are
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am
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RDGT,
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& (per Legum
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Corol. </
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<
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>2.) diſtinguatur motus
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corporis in duos, unum aſcen
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ſus, alterum ad latus. </
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<
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>Et cum
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reſiſtentia ſit ut motus, diſtin
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guetur etiam hæc in partes duas
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partibus motus proportionales
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& contrarias: ideoque longitu
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do, a motu ad latus deſcripta, e
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rit (per Prop. </
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<
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>11. hujus) ut linea
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DR,
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altitudo vero (per Prop. </
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111. hujus) ut area
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DRXAB
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-RDGT,
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hoc eſt, ut linea
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Rr.
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Ipſo autem motus initio area
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RDGT
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æqualis eſt rectangulo
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DRXAQ,
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ideoque linea illa
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Rr
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<
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(ſeu (
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DRXAB-DRXAQ
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/N))
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tunc eſt ad
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DR
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ut
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AB-AQ
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ſeu
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QB
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ad N, id eſt, ut
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CP
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ad
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DC
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; atque adeo ut motus
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in altitudinem ad motum in
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longitudinem ſub initio. </
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<
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>Cum
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igitur
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Rr
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ſemper ſit ut altitu
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do, ac
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DR
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ſemper ut longi
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tudo, atque
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Rr
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ad
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DR
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ſub
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initio ut altitudo ad longitudinem: neceſſe eſt ut
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ſemper ſit ad
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DR
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ut altitudo ad longitudinem, & propterea ut corpus movea
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tur in linea
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DraF,
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quam punctum
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r
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perpetuo tangit.
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Q.E.D.
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