Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Page concordance

< >
Scan Original
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/084.jpg" pagenum="56"/>
                    <arrow.to.target n="note32"/>
                  latera recta principalia ſunt æqualia, velocitas corporis eſt reciproce
                    <lb/>
                  ut perpendiculum demiſſum ab umbilico ad tangentem. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note32"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  6. In Parabola, velocitas eſt reciproce in ſubduplicata ra­
                    <lb/>
                  tione diſtantiæ corporis ab umbilico figuræ; in Ellipſi magis varia­
                    <lb/>
                  tur, in Hyperbola minus, quam in hac ratione. </s>
                  <s>Nam (per Corol. </s>
                  <s>
                    <lb/>
                  2. Lem. </s>
                  <s>XIV.) perpendiculum demiſſum ab umbilico ad tangentem
                    <lb/>
                  Parabolæ eſt in ſubduplicata ratione diſtantiæ. </s>
                  <s>In Hyperbola per­
                    <lb/>
                  pendiculum minus variatur, in Ellipſi magis. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  7. In Parabola, velocitas corporis ad quamvis ab umbili­
                    <lb/>
                  co diſtantiam, eſt ad velocitatem corporis revolventis in Circulo
                    <lb/>
                  ad eandem a centro diſtantiam, in ſubduplicata ratione numeri bi­
                    <lb/>
                  narii ad unitatem; in Ellipſi minor eſt, in Hyperbola major quam
                    <lb/>
                  in hac ratione. </s>
                  <s>Nam per hujus Corollarium ſecundum, velocitas
                    <lb/>
                  in vertice Parabolæ eſt in hac ratione, & per Corollaria ſexta hu­
                    <lb/>
                  jus & Propoſitionis quartæ, ſervatur eadem proportio in omnibus
                    <lb/>
                  diſtantiis. </s>
                  <s>Hinc etiam in Parabola velocitas ubique æqualis eſt ve­
                    <lb/>
                  locitati corporis revolventis in Circulo ad dimidiam diſtantiam, in
                    <lb/>
                  Ellipſi minor eſt, in Hyperbola major. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  8. Velocitas gyrantis in Sectione quavis Conica eſt ad ve­
                    <lb/>
                  locitatem gyrantis in Circulo in diſtantia dimidii lateris recti princi­
                    <lb/>
                  palis Sectionis, ut diſtantia illa ad perpendiculum ab umbilico in
                    <lb/>
                  tangentem Sectionis demiſſum. </s>
                  <s>Patet per Corollarium quintum. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  9. Unde cum (per Corol. </s>
                  <s>6. Prop. </s>
                  <s>IV.) velocitas gyrantis
                    <lb/>
                  in hoc Circulo ſit ad velocitatem gyrantis in Circulo quovis alio,
                    <lb/>
                  reciproce in ſubduplicata ratione diſtantiarum; fiet ex æquo velo­
                    <lb/>
                  citas gyrantis in Conica ſectione ad velocitatem gyrantis in Circulo
                    <lb/>
                  in eadem diſtantia, ut media proportionalis inter diſtantiam illam
                    <lb/>
                  communem & ſemiſſem principalis lateris recti ſectionis, ad per­
                    <lb/>
                  pendiculum ab umbilico communi in tangentem ſectionis de­
                    <lb/>
                  miſſum. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XVII. PROBLEMA. IX.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Poſito quod vis centripeta ſit reciproce proportionalis quadrato diſtan­
                    <lb/>
                  ſtantiæ loeorum a centro, & quod vis illius quantitas abſoluta ſit
                    <lb/>
                  cognita; requiritur Linea quam corpus deſcribit, de loco dato, cum
                    <lb/>
                  data velocitate, ſecundum datam rectam egrediens.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Vis centripeta tendens ad punctum
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  ea ſit qua corpus
                    <emph type="italics"/>
                  p
                    <emph.end type="italics"/>
                  in or­
                    <lb/>
                  bita quavis data
                    <emph type="italics"/>
                  pq
                    <emph.end type="italics"/>
                  gyretur, & cognoſcatur hujus velocitas in loco
                    <emph type="italics"/>
                  p.
                    <emph.end type="italics"/>
                  </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum