Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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tione qualibet, & exponatur ratio illa per longitudinem quamvis
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SM.
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Deinde per computationem, ex longitudine illa aſſumpta
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DP,
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inveniantur longitudines
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DF, Df,
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ac de ratione (
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Ef/DF
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) per
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calculum inventa, auferatur ratio eadem
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per experimentum inventa, & exponatur
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differentia per perpendiculum
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MN.
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Idem
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fac iterum ac tertio, aſſumendo ſemper
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novam reſiſtentiæ ad gravitatem rationem
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SM,
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& colligendo novam differentiam
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MN.
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Ducantur autem differentiæ affirmativæ ad unam partem
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rectæ
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SM,
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& negativæ ad alteram; & per puncta
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N, N, N
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agatur
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ourva regularis
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NNN
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ſecans rectam
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SMMM
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in
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X,
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& erit
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SX
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vera ratio reſiſtentiæ ad gravitatem, quam invenire oportuit. </
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hac ratione colligenda eſt longitudo
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DF
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per calculum; & longi
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tudo quæ ſit ad aſſumptam longitudinem
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DP,
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at longitudo
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DF
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per experimentum cognita ad longitudinem
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DF
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modo inventam,
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erit vera longitudo
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DP.
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Qua inventa, habetur tum Curva linea
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DraF
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quam corpus deſcribit, tum corporis velocitas & reſiſten
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tia in locis ſingulis. </
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LIBER
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SECUNDUS.</
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Scholium.
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<
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>Cæterum, reſiſtentiam corporum eſſe in ratione velocitatis, Hy
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potheſis eſt magis Mathematica quam Naturalis. </
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tio quamproxime ubi corpora in Mediis rigore aliquo præditis tar
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diſſime moventur. </
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>In Mediis antem quæ rigore omni vacant re
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ſiſtentiæ corporum ſunt in duplicata ratione velocitatum. </
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<
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actione corporis velocioris communicatur eidem Medii quantitati,
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tempore minore, motus major in ratione majoris velocitatis; ad
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eoque tempore æquali (ob majorem Medii quantitatem perturba
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tam) communicatur motus in duplicata ratione major; eſt que re
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ſiſtentia (per motus Legem II & III) ut motus communicatus. </
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Videamus igitur quades oriantur motus ex hac lege Reſiſtentiæ. </
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