Marci of Kronland, Johannes Marcus, De proportione motus figurarum recti linearum et circuli quadratura ex motu, 1648

Page concordance

< >
Scan Original
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
< >
page |< < of 145 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="063/01/060.jpg"/>
            <p type="main">
              <s>
                <emph type="center"/>
                <emph type="italics"/>
              ALIA QVADRATVRA CIRCVLI
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
                <emph type="italics"/>
              per motum.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>DVcatur à contactu G per centrum figuræ E linea GL æ­
                <lb/>
              qualis GB: & ex L ad eam perpendicularis LM ſecans B
                <lb/>
              C in M:
                <expan abbr="eritq;">eritque</expan>
              LM æqualis BM. </s>
              <s>Si enim iungatur recta BL,
                <lb/>
              duo anguli GBL. GLB, ac proinde reſidui MBL. MLB ſunt
                <lb/>
              æquales. </s>
              <s>Centro
                <expan abbr="itaq;">itaque</expan>
              M, interuallo ML deſcribatur arcus LB
                <lb/>
              ſecans
                <expan abbr="lineã">lineam</expan>
              motûs reflexi GK in O: ex O verò demittantur per
                <lb/>
              pendiculares ON. OP. </s>
              <s>Quoniam
                <expan abbr="itaq;">itaque</expan>
              punctum G à plagâ re­
                <lb/>
              ciprocâ ex H per lineam agitur GL per 5 theorema: impulſus
                <lb/>
              verò reſiduus in FE per lineam GB per lemma 2. </s>
              <s>
                <expan abbr="Eſtq;">Eſtque</expan>
              motus
                <lb/>
              medius GK, erit per problem. propoſitionis 35 de propor. mo­
                <lb/>
              tûs, vt OP ad ON, ita impulſus in GB ad impulſum in GL, æ­
                <lb/>
              qualem impulſui in H. </s>
              <s>Et ſi quidem ON eſt ſemiſſis OP, erit
                <lb/>
              impulſus in OP ad impulſum in ON ut 4 ad 2. ſupponamus ve­
                <lb/>
              rò ſpatium decurſum ab E, ad ſpatium decurſum ab H eſſe in
                <lb/>
              ſeſquialterâ ratione, hoc eſt ut 3 ad 2. </s>
              <s>Igitur ſi circulus H acci­
                <lb/>
              piat impulſum ut 3, movebitur ad idem interuallum cum qua­
                <lb/>
              drato ABCD per corollarium 2 Axiomatis 1 & poſitionem 4. </s>
              <lb/>
              <s>Etſi fiat ut 4 ad 3 ita ABCD ad aliud; inventum erit quadra­
                <lb/>
              tum dato circulo H æquale. </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
                <emph type="italics"/>
              COROLL ARIVM
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
              Eadem ratione inveniemus quadratum æquale ſectionibus
                <lb/>
              conicis,
                <expan abbr="atq;">atque</expan>
              adeo illarum fruſtis; ſi loco circuli hu­
                <lb/>
              iuſmodi figuras ſubſtituamus.
                <emph.end type="center"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum