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

List of thumbnails

< >
51
51 		52
52
53
53 		54
54
55
55 		56
56
57
57 		58
58
59
59 		60
60
< >
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