Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  Corol.
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                  4. Globus in fluido compreſſo quieſcente ejuſdem ſecum
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                  denſitatis movendo, dimidiam motus ſui partem prius amittet
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                  quam longitudinem duarum ipſius diametrorum deſcripſerit, per
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                  idem Corol. 7.
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                  PROPOSITIO XXXIX. THEOREMA XXXI.
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                  LIBER
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                  SECUNDUS.</s>
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                  Globi, per Fluidum in canali Cylindrico clauſum & compreſſum uni­
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                  formiter progredientis, reſiſtentia eſt ad vim qua totus ejus motus,
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                  interea dum octo tertias partes diametri ſuæ deſcribit, vel ge­
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                  nerari poſſit vel tolli, in ratione quæ componitur ex ratione ori­
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                  ficii canalis ad exceſſum hujus orificii ſupra dimidium circuli
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                  maximi Globi, & ratione duplicata orificii canalis ad exceſſum
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                  hujus orificii ſupra circulum maximum Globi, & ratione den­
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                  ſitatis Fluidi ad denſitatem Globi quamproxime.
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                  <s>Patet per Corol. 2. Prop. XXXVII; procedit vero demonſtratio
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                  quemadmodum in Propoſitione præcedente.
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                  PROPOSITIO XL. PROBLEMA IX.
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                  Globi, in Medio fluidiſſimo compreſſo progredientis, invenire reſi­
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                  ſtentiam per Phænomena.
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                  <s>Sit A pondus Globi in vacuo, B pondus ejus in Medio reſi­
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                  ſtente, D diameter Globi, F ſpatium quod ſit ad 4/3 D ut denſitas
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                  Globi ad denſitatem Medii, id eſt, ut A ad A-B, G tempus quo
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                  Globus pondere B abſque reſiſtentia cadendo deſcribit ſpatium F,
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                  & H velocitas quam Globus hocce caſu ſuo acquirit. </s>
                  <s>Et erit H
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                  velocitas maxima quacum Globus, pondere ſuo B, in Medio reſi­
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                  ſtente poteſt deſcendere, per Corol. 2, Prop. XXXVIII; & reſi­
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                  ſtentia quam Globus ea cum velocitate deſcendens patitur, æqua­
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                  lis erit ejus ponderi B: reſiſtentia vero quam patitur in alia qua­
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                  cunque velocitate, erit ad pondus B in duplicata ratione velo­
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                  citatis hujus ad velocitatem illam maximam
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                  H,
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                  &c. G, per Corol. 1,
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                  Prop. XXXVIII. </s>
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