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

Page concordance

< >
Scan Original
71 359
72 360
73 361
74 362
75 363
76 364
77 365
78 366
79
80
81
82 367
83 368
84 369
85 370
86 371
87 372
88 373
89 374
90 375
91 376
92
93
94
95 377
96 378
97 379
98 380
99 381
100 382
< >
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