Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Reg.
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                  1. Si ſervetur tum Medii denſitas in
                    <emph type="italics"/>
                  A,
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                  tum velocitas qua­
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                    <arrow.to.target n="note217"/>
                  cum corpus projicitur, & mutetur angulus
                    <emph type="italics"/>
                  NAH
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                  ; manebunt lon­
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                  gitudines
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                  AH, AI, HX.
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                  Ideoque ſi longitudines illæ in aliquo
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                  caſu inveniantur, Hyperbola deinceps ex dato quovis angulo
                    <emph type="italics"/>
                  NAH
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                    <lb/>
                  expedite determinari poteſt. </s>
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                <p type="margin">
                  <s>
                    <margin.target id="note217"/>
                  LIBER
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                  SECUNDUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Reg.
                    <emph.end type="italics"/>
                  2. Si ſervetur tum angulus
                    <emph type="italics"/>
                  NAH,
                    <emph.end type="italics"/>
                  tum Medii denſitas
                    <lb/>
                  in
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  & mutetur velocitas quacum corpus projicitur; ſervabitur
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                  longitudo
                    <emph type="italics"/>
                  AH,
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                  & mutabitur
                    <emph type="italics"/>
                  AI
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                  in duplicata ratione velocitatis
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                  reciproce. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Reg.
                    <emph.end type="italics"/>
                  3. Si tam angulus
                    <emph type="italics"/>
                  NAH
                    <emph.end type="italics"/>
                  quam corporis velocitas in
                    <emph type="italics"/>
                  A,
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                    <lb/>
                  gravitaſque acceleratrix ſervetur, & proportio reſiſtentiæ in
                    <emph type="italics"/>
                  A
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                  ad
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                    <figure id="id.039.01.269.1.jpg" xlink:href="039/01/269/1.jpg" number="156"/>
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                  gravitatem motricem augeatur in ratione quacunque: augebitur
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                  proportio
                    <emph type="italics"/>
                  AH
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                  ad
                    <emph type="italics"/>
                  AI
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                  in eadem ratione, manente Parabolæ late­
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                  re recto, eique proportionali longitudine (
                    <emph type="italics"/>
                  AHq/AI
                    <emph.end type="italics"/>
                  ); & propterea mi­
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                  nuetur
                    <emph type="italics"/>
                  AH
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                  in eadem ratione, &
                    <emph type="italics"/>
                  AI
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                  minuetur in ratione illa du­
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                  plicata. </s>
                  <s>Augetur vero proportio reſiſtentiæ ad pondus, ubi vel gra­
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                  vitas ſpecifica ſub æquali magnitudine fit minor, vel Medii denſi­
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                  tas major, vel reſiſtentia, ex magnitudine diminuta, diminuitur in
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                  minore ratione quam pondus. </s>
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