Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Et, cum tempora periodica ſint in ratione compoſita ex
                    <lb/>
                  ratione radiorum directe & ratione velocitatum inverſe, vires cen­
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                  tripetæ ſunt reciproce ut quadrata temporum periodieorum appli­
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                  cata ad circulorum radios; hoc eſt, in ratione compoſita ex ratione
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                  radiorum directe & ratione duplicata temporum periodieorum in­
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                  verſe. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Unde, ſi tempora periodica æquentur & propterea ve­
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                  locitates ſint ut radii; erunt etiam vires centripetæ ut radii: &
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                  contra. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cor.
                    <emph.end type="italics"/>
                  4. Si & tempora periodica & velocitates ſint in ratione ſub­
                    <lb/>
                  duplicata radiorum; æquales erunt vires centripetæ inter ſe: &
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                  contra. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  5. Si tempora periodica ſint ut radii & propterea veloci­
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                  tates æquales; vires centriperæ erunt reciproce ut radii: & contra. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  6. Si tempora periodica ſint in ratione ſeſquiplicata radio­
                    <lb/>
                  rum & propterea velocitates reciproce in radiorum ratione ſubdu­
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                  plicata; vires centripetæ erunt reciproce ut quadrata radiorum:
                    <lb/>
                  & contra. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  7. Et univerſaliter, ſi tempus periodicum ſit ut Radii
                    <emph type="italics"/>
                  R
                    <emph.end type="italics"/>
                    <lb/>
                  poteſtas quælibet
                    <emph type="italics"/>
                  R
                    <emph type="sup"/>
                  n
                    <emph.end type="sup"/>
                  ,
                    <emph.end type="italics"/>
                  & propterea velocitas reciproce ut Radii
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                  poteſtas
                    <emph type="italics"/>
                  R
                    <emph type="sup"/>
                  n-1
                    <emph.end type="sup"/>
                    <emph.end type="italics"/>
                  ; erit vis centripeta reciproce ut Radii poteſtas
                    <emph type="italics"/>
                  R
                    <emph type="sup"/>
                  2n-1
                    <emph.end type="sup"/>
                  :
                    <emph.end type="italics"/>
                    <lb/>
                  & contra. </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  8. Eadem omnia de temporibus, velocitatibus, & viribus, qui­
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                  bus corpora ſimiles figurarum quarumcunque ſimilium, centraque
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                  in figuris illis ſimiliter poſita habentium, partes deſcribunt, conſe­
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                  quuntur ex Demonſtratione præcedentium ad hoſce caſus applicata. </s>
                  <s>
                    <lb/>
                  Applicatur autem ſubſtituendo æquabilem arearum deſcriptionem
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                  pro æquabili motu, & diſtantias corporum a centris pro radiis uſur­
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                  pando. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  9. Ex eadem demonſtratione conſequitur etiam; quod ar­
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                  cus, quem corpus in circulo data vi centripeta uniformiter revolven­
                    <lb/>
                  do tempore quovis deſcribit, medius eſt proportionalis inter dia­
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                  metrum circuli, & deſcenſum corporis eadem data vi eodem que tem­
                    <lb/>
                  pore cadendo confectum. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Scholium.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Caſus Corollarii ſexti obtinet in corporibus cæleſtibus, (ut ſeor­
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                  ſum collegerunt etiam noſtrates
                    <emph type="italics"/>
                  Wrennus, Hookius
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Hallæus
                    <emph.end type="italics"/>
                  ) &
                    <lb/>
                  propterea quæ ſpectant ad vim centripetam decreſcentem in dupli­
                    <lb/>
                  cata ratione diſtantiarum a centris, decrevi fuſius in ſequentibus
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                  exponere. </s>
                </p>
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