Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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dum Trajectoria deſcribebatur, demitte normalem
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OH
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Circulo oc
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currentem in
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K
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&
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L.
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Et ubi crura illa altera
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CK, BK
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concur
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runt ad punctum illud
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K
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quod Regulæ propius eſt, crura prima
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CP, BP
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parallela erunt axi majori, & perpendicularia minori;
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& contrarium eveniet ſi crura eadem concurrunt ad punctum remo
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tius
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L.
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Unde ſi detur Trajectoriæ centrum, dabuntur axes. </
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autem datis, umbilici ſunt in promptu. </
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DE MOTU
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CORPORUM</
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<
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>Axium vero quadrata ſunt ad invicem ut
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KH
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ad
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LH,
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& inde
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facile eſt Trajectoriam
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ſpecie datam per data
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quatuor puncta deſcri
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bere. </
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<
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>Nam ſi duo ex
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punctis datis conſtitu
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antur poli
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C, B,
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tertium
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dabit angulos mobiles
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PCK, PBK
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; his au
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tem datis deſcribi poteſt
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Circulus
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IBKGC.
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Tum ob datam ſpecie
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Trajectoriam, dabitur
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ratio
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OH
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ad
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OK,
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ad
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eoQ.E.I.ſa
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OH.
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Cen
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tro
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O
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& intervallo
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OH
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deſcribe alium circulum,
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& recta quæ tangit hunc circulum, & tranſit per concurſum crurum
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CK, BK,
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ubi crura prima
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CP, BP
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concurrunt ad quartum da
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tum punctum erit Regula illa
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MN
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cujus ope Trajectoria deſcri
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betur. </
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<
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>Unde etiam viciſſim Trapezium ſpecie datum (ſi caſus qui
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dam impoſſibiles excipiantur) in data quavis Sectione Conica in
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ſcribi poteſt. </
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<
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>Sunt & alia Lemmata quorum ope Trajectoriæ ſpecie datæ,
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datis punctis & tangentibus, deſcribi poſſunt. </
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<
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>Ejus generis
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eſt quod, ſi recta linea per punctum quodvis poſitione datum
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ducatur, quæ datam Coniſectionem in punctis duobus interſe
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cet, & interſectionum intervallum biſecetur, punctum biſectionis
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tanget aliam Coniſectionem ejuſdem ſpeciei cum priore, atque
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axes habentem prioris axibus parallelos. </
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<
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utilia. </
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