Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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inde pondus aquæ totius in vaſe eſt ad ponderis partem quæ in
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defluxum aquæ impenditur, ut
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IH+IO
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ad 2
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IH,
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atque adeo ut
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ſumma circulorum
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EF
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&
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AB
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ad duplum circulum
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EF.
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DE MOTU
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CORPORUM</
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Corol.
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4. Et hinc pondus aquæ totius in vaſe
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ABDC,
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eſt ad
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ponderis partem alteram quam fundum vaſis ſuſtinet, ut ſumma
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circulorum
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AB
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&
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EF,
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ad differentiam eorundem circulorum.
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Corol.
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5. Et ponderis pars quam fundum vaſis ſuſtinet, eſt ad
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ponderis partem alteram quæ in defluxum aquæ impenditur, ut
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differentia circulorum
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AB
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&
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EF,
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ad duplum circulum minorem
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EF,
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ſive ut area fundi ad duplum foramen.
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Corol.
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6. Ponderis autem pars qua ſola fundum urgetur, eſt ad
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pondus aquæ totius quæ fundo perpendiculariter incumbit, ut cir
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culus
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AB
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ad ſummam circulorum
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AB
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&
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EF,
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ſive ut circulus
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AB
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ad exceſſum dupli circuli
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AB
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ſupra fundum. </
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<
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>Nam ponderis
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pars qua ſola fundum urgetur, eſt ad pondus aquæ totius in vaſe,
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ut differentia circulorum
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AB
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&
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EF,
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ad ſummam eorundem cir
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culorum, per Cor.4; & pondus aquæ totius in vaſe eſt ad pondus
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aquæ totius quæ fundo perpendiculariter incumbit, ut circulus
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AB
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ad differentiam circulorum
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AB
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&
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EF.
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Itaque ex æquo
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perturbate, ponderis pars qua ſola fundum urgetur, eſt ad pondus
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aquæ totius quæ fundo perpendiculariter incumbit, ut circulus
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AB
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ad ſummam circulorum
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AB
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&
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EF
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vel exceſſum dupli cir
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culi
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AB
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ſupra fundum.
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Corol.
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7. Si in medio foraminis
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EF
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locetur Circellus
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PQ
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centro
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G
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deſcri
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ptus & horizonti parallelus: pondus
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aquæ quam circellus ille ſuſtinet, majus
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eſt pondere tertiæ partis Cylindri a
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quæ cujus baſis eſt circellus ille & al
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titudo eſt
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GH.
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Sit enim
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ABNFEM
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cataracta vel columna aquæ cadentis
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axem habens
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GH
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ut ſupra, & conge
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lari intelligatur aqua omnis in vaſe, tam
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in circuitu cataractæ quam ſupra cir
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cellum, cujus fluiditas ad promptiſſimum
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& celerrimum aquæ deſcenſum non requiritur. </
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PHQ
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co
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lumna aquæ ſupra circellum congelata, verticem habens
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H
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& alti
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tudinem
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GH.
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Et quemadmodum aqua in circuitu cataractæ con
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gelata
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AMEC, BNFD
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convexa eſt in ſuperficie interna
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AME,
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BNF
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verſus cataractam cadentem, ſic etiam hæc columna
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PHQ
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