Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

List of thumbnails

< >
71
71 (359) 		72
72 (360)
73
73 (361) 		74
74 (362)
75
75 (363) 		76
76 (364)
77
77 (365) 		78
78 (366)
79
79 		80
80
< >
page |< < (363) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div66" type="section" level="1" n="30">
          <p>
            <s xml:id="echoid-s1291" xml:space="preserve">
              <pb o="363" file="0071" n="75" rhead="DE CIRCULI MAGNIT. INVENTA."/>
            goni A C D. </s>
            <s xml:id="echoid-s1292" xml:space="preserve">Exceſſus igitur perimetrorum eſt H I; </s>
            <s xml:id="echoid-s1293" xml:space="preserve">cujus
              <lb/>
            triens I K adjiciatur ipſi G I. </s>
            <s xml:id="echoid-s1294" xml:space="preserve">Dico totâ G K majorem eſſe
              <lb/>
            circuli A B circumferentiam. </s>
            <s xml:id="echoid-s1295" xml:space="preserve">Inſcribatur enim circulo tertium
              <lb/>
            polygonum æquilaterum A L E M C, quod ſit duplo nu-
              <lb/>
            mero laterum polygoni A E C B D F. </s>
            <s xml:id="echoid-s1296" xml:space="preserve">Et ſuper lineis G H,
              <lb/>
            H I, I K, triangula conſtituantur quorum communis vertex
              <lb/>
            N, altitudo autem æqualis ſemidiametro circuli A B. </s>
            <s xml:id="echoid-s1297" xml:space="preserve">Igi-
              <lb/>
            tur quoniam G H baſis æqualis eſt perimetro polygoni
              <lb/>
            A C D, erit triangulum G N H æquale polygono, cui bis
              <lb/>
            totidem ſunt latera, hoc eſt, polygono A E C B D F. </s>
            <s xml:id="echoid-s1298" xml:space="preserve">Hoc
              <lb/>
            enim patet, ductis ex centro rectis O A & </s>
            <s xml:id="echoid-s1299" xml:space="preserve">O E, quarum
              <lb/>
            hæc ſecet A C in P. </s>
            <s xml:id="echoid-s1300" xml:space="preserve">Nam triangulum quidem A E O æ-
              <lb/>
            quale eſt triangulo baſin habenti A P & </s>
            <s xml:id="echoid-s1301" xml:space="preserve">altitudinem radii
              <lb/>
            O E. </s>
            <s xml:id="echoid-s1302" xml:space="preserve">Quanta autem pars eſt triangulum A E O polygo-
              <lb/>
            ni A E C B D F, eadem eſt recta A P perimetri A C D.
              <lb/>
            </s>
            <s xml:id="echoid-s1303" xml:space="preserve">Itaque polygonum A E C B D F æquabitur triangulo cu-
              <lb/>
            jus baſis æqualis perimetro A C D, altitudo autem radio
              <lb/>
            E O: </s>
            <s xml:id="echoid-s1304" xml:space="preserve">hoc eſt, triangulo G N H. </s>
            <s xml:id="echoid-s1305" xml:space="preserve">Eâdem ratione, quo-
              <lb/>
            niam baſis G I eſt æqualis polygoni A E C B D F
              <lb/>
            perimetro, & </s>
            <s xml:id="echoid-s1306" xml:space="preserve">altitudo trianguli G N I æqualis radio circu-
              <lb/>
            li, erit triangulum G N I æquale polygono A L E M C. </s>
            <s xml:id="echoid-s1307" xml:space="preserve">
              <lb/>
            Itaque triangulum H N I æquale exceſſui polygoni
              <lb/>
            A L E M C ſupra polygonum A E C B D F. </s>
            <s xml:id="echoid-s1308" xml:space="preserve">Trianguli
              <lb/>
            autem H N I ſubtriplum eſt ex conſtr triangulum I N K. </s>
            <s xml:id="echoid-s1309" xml:space="preserve">
              <lb/>
            Ergo hoc æquale erit dicti exceſſus trienti. </s>
            <s xml:id="echoid-s1310" xml:space="preserve">Quare totum tri-
              <lb/>
            angulum G N K minus erit circulo A B . </s>
            <s xml:id="echoid-s1311" xml:space="preserve">Altitudo
              <note symbol="*" position="right" xlink:label="note-0071-01" xlink:href="note-0071-01a" xml:space="preserve">per 5. huj.</note>
            trianguli æqualis eſt circuli ſemidiametro. </s>
            <s xml:id="echoid-s1312" xml:space="preserve">Ergo evidens eſt
              <lb/>
            rectam G K totâ circuli circumferentiâ minorem eſſe. </s>
            <s xml:id="echoid-s1313" xml:space="preserve">Quod
              <lb/>
            erat oſtendendum.</s>
            <s xml:id="echoid-s1314" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1315" xml:space="preserve">Hinc manifeſtum eſt, ſi à feſquitertio laterum polygoni
              <lb/>
            circulo inſcripti auferatur triens laterum polygoni alterius
              <lb/>
            inſcripti ſubduplo laterum numero, reliquum circumferen-
              <lb/>
            tiâ minus eſſe. </s>
            <s xml:id="echoid-s1316" xml:space="preserve">Idem enim eſt, ſive perimetro majori adda-
              <lb/>
            tur {1/3} exceſſus quo ipſa ſuperat perimetrum minorem, ſive
              <lb/>
            addatur {1/3} perimetri majoris contraque auferatur {1/3} perimetri
              <lb/>
            minoris. </s>
            <s xml:id="echoid-s1317" xml:space="preserve">Hinc autem fit ſeſquitertium majoris perimetri </s>
          </p>
        </div>
      </text>
    </echo>
Impressum