Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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DE MOTU
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CORPORUM</
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PROPOSITIO XCVI. THEOREMA L.
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Iiſdem poſitis & quod motus ante incidentiam velocior ſit quam
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poſtea: dico quod corpus, inclinando lineam incidentiæ, refle
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ctetur tandem, & angulus reflexionis fiet æqualis angulo inci
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dentiæ.
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>Nam concipe corpus inter parallela plana
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Aa, Bb, Cc,
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&c. </
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>de
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ſcribere arcus Parabolicos, ut ſupra; ſintque arcus illi
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HP, PQ,
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QR,
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&c. </
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<
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>Et ſit ea lineæ incidentiæ
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GH
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obliquitas ad planum pri
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mum
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Aa,
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ut ſinus incidentiæ ſit ad radium circuli, cujus eſt ſinus,
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in ea ratione quam habet idem ſinus incidentiæ ad ſinum emer
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gentiæ ex plano
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Dd,
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in ſpatium
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DdeE:
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& ob ſinum emergen
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tiæ jam factum æqualem radio, angulus emergentiæ erit rectus, ad
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eoque linea emergentiæ coincidet cum plano
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Dd.
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Perveniat cor
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pus ad hoc planum in puncto
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R
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; & quoniam linea emergentiæ
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coincidit cum eodem
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plano, perſpicuum eſt
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quod corpus non po
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teſt ultra pergere ver
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ſus planum
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Ee.
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Sed
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nec poteſt idem perge
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re in linea emergentiæ
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Rd,
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propterea quod
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perpetuo attrahitur vel impellitur verſus Medium incidentiæ. </
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>Re
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vertetur itaQ.E.I.ter plana
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Cc, Dd,
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deſcribendo arcum Parabolæ
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QRq,
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cujus vertex principalis (juxta demonſtrata
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Galilæi
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) eſt in
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R
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; ſecabit planum
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Cc
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in eodem angulo in
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q,
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ac prius in
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Q
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; dein
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pergendo in arcubus parabolicis
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qp, ph,
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&c. </
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>arcubus prioribus
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QP, PH
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ſimilibus & æqualibus, ſecabit reliqua plana in iiſdem
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angulis in
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p, h,
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&c. </
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<
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>ac prius in
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P, H,
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&c. </
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<
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>emergetque tandem ea
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dem obliquitate in
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h,
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qua incidit in
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H.
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Concipe jam planorum
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Aa, Bb, Cc, Dd, Ee,
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&c. </
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<
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>intervalla in infinitum minui & nume
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rum augeri, eo ut actio attractionis vel impulſus ſecundum legem
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quamcunque aſſignatam continua reddatur; & angulus emergen
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tiæ ſemper angulo incidentiæ æqualis exiſtens, eidem etiamnum
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manebit æqualis.
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E. D.
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