Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/250.jpg" pagenum="222"/>
                    <arrow.to.target n="note198"/>
                  de datur punctum
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  per quod Hyperbola, Aſymptoris
                    <emph type="italics"/>
                  CH, CD,
                    <emph.end type="italics"/>
                    <lb/>
                  deſcribi debet; ut & ſpatium
                    <emph type="italics"/>
                  ABGD,
                    <emph.end type="italics"/>
                  quod corpus incipiendo
                    <lb/>
                  motum ſuum cum velocitate illa
                    <emph type="italics"/>
                  AB,
                    <emph.end type="italics"/>
                  tempore quovis
                    <emph type="italics"/>
                  AD,
                    <emph.end type="italics"/>
                  in Me­
                    <lb/>
                  dio ſimilari reſiſtente deſcribere poteſt. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note198"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO VI. THEOREMA IV.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corpora Spherica homogemea & æqualia, reſiſtentiis in duplicata
                    <lb/>
                  ratione velocitatum impedita, & ſolis viribus inſitis incitata,
                    <lb/>
                  temporibus quæ ſunt reciproce ut velocitates ſub initio, deſcri­
                    <lb/>
                  bunt ſemper æqualia ſpatia, & amittunt partes velocitatum pro­
                    <lb/>
                  portionales totis.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Aſymptotis rectangulis
                    <emph type="italics"/>
                  CD,
                    <lb/>
                    <figure id="id.039.01.250.1.jpg" xlink:href="039/01/250/1.jpg" number="150"/>
                    <lb/>
                  CH
                    <emph.end type="italics"/>
                  deſcripta Hyperbola qua­
                    <lb/>
                  vis
                    <emph type="italics"/>
                  BbEe
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                  ſecante perpendicula
                    <lb/>
                    <emph type="italics"/>
                  AB, ab, DE, de,
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  B, b, E, e,
                    <emph.end type="italics"/>
                    <lb/>
                  exponantur velocitates initi­
                    <lb/>
                  ales per perpendicula
                    <emph type="italics"/>
                  AB,
                    <lb/>
                  DE,
                    <emph.end type="italics"/>
                  & tempora per lineas
                    <lb/>
                    <emph type="italics"/>
                  Aa, Dd.
                    <emph.end type="italics"/>
                  Eſt ergo ut
                    <emph type="italics"/>
                  Aa
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  Dd
                    <emph.end type="italics"/>
                  ita (per Hypotheſin)
                    <emph type="italics"/>
                  DE
                    <emph.end type="italics"/>
                    <lb/>
                  ad
                    <emph type="italics"/>
                  AB,
                    <emph.end type="italics"/>
                  & ita (ex natura Hy­
                    <lb/>
                  perbolæ)
                    <emph type="italics"/>
                  CA
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  CD
                    <emph.end type="italics"/>
                  ; & com­
                    <lb/>
                  ponendo, ita
                    <emph type="italics"/>
                  Ca
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  Cd.
                    <emph.end type="italics"/>
                  Ergo
                    <lb/>
                  areæ
                    <emph type="italics"/>
                  ABba, DEed,
                    <emph.end type="italics"/>
                  hoc eſt, ſpatia deſcripta æquamtur inter ſe,
                    <lb/>
                  & velocitates primæ
                    <emph type="italics"/>
                  AB, DE
                    <emph.end type="italics"/>
                  ſunt ultimis
                    <emph type="italics"/>
                  ab, de,
                    <emph.end type="italics"/>
                  & propterea
                    <lb/>
                  (dividendo) partibus etiam ſuis amiſſis
                    <emph type="italics"/>
                  AB-ab, DE-de
                    <emph.end type="italics"/>
                  pro­
                    <lb/>
                  portionales.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO VII. THEOREMA V.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corpora Sphærica quibus reſiſtitur in duplicata ratione velocitatum,
                    <lb/>
                  temporibus quæ ſunt ut motus primi directe & reſiſtentiæ pri­
                    <lb/>
                  mæ inverſe, amittent partes motuum proportionales totis, &
                    <lb/>
                  ſpatia deſcribent temporibus iſtis in velocitates primas ductis
                    <lb/>
                  proportionalia.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Namque motuum partes amiſſæ ſunt ut reſiſtentiæ & tempora </s>
                </p>
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