Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
91 40
92
93 41
94
95 42
96
97 43
98
99 44
100
101 43
102
103
104
105
106
107
108
109
110
111
112
113 1
114
115 2
116
117 3
118
119 4
120
< >
page |< < of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div199" type="section" level="1" n="65">
          <p>
            <s xml:id="echoid-s3043" xml:space="preserve">
              <pb file="0120" n="120" rhead="FED. COMMANDINI"/>
            triangulum m k φ triangulo n k φ. </s>
            <s xml:id="echoid-s3044" xml:space="preserve">ergo anguli l z k, o z k,
              <lb/>
            m φ k, n φ k æquales ſunt, ac recti. </s>
            <s xml:id="echoid-s3045" xml:space="preserve">quòd cum etiam recti
              <lb/>
            ſint, qui ad k; </s>
            <s xml:id="echoid-s3046" xml:space="preserve">æquidiſtabunt lineæ l o, m n axi b d. </s>
            <s xml:id="echoid-s3047" xml:space="preserve">& </s>
            <s xml:id="echoid-s3048" xml:space="preserve">ita.
              <lb/>
            </s>
            <s xml:id="echoid-s3049" xml:space="preserve">
              <note position="left" xlink:label="note-0120-01" xlink:href="note-0120-01a" xml:space="preserve">28. primi.</note>
            demonſtrabuntur l m, o n ipſi a c æquidiſtare. </s>
            <s xml:id="echoid-s3050" xml:space="preserve">Rurſus ſi
              <lb/>
            iungantur a l, l b, b m, m c, c n, n d, d o, o a: </s>
            <s xml:id="echoid-s3051" xml:space="preserve">& </s>
            <s xml:id="echoid-s3052" xml:space="preserve">bifariam di
              <lb/>
            uidantur: </s>
            <s xml:id="echoid-s3053" xml:space="preserve">à centro autem k ad diuiſiones ductæ lineæ pro-
              <lb/>
            trahantur uſque ad ſectionem in puncta p q r s t u x y: </s>
            <s xml:id="echoid-s3054" xml:space="preserve">& </s>
            <s xml:id="echoid-s3055" xml:space="preserve">po
              <lb/>
            ſtremo p y, q x, r u, s t, q r, p s, y t, x u coniungantur. </s>
            <s xml:id="echoid-s3056" xml:space="preserve">Simili-
              <lb/>
            ter oſtendemus lineas
              <lb/>
              <figure xlink:label="fig-0120-01" xlink:href="fig-0120-01a" number="76">
                <image file="0120-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0120-01"/>
              </figure>
            p y, q x, r u, s t axi b d æ-
              <lb/>
            quidiſtantes eſſe: </s>
            <s xml:id="echoid-s3057" xml:space="preserve">& </s>
            <s xml:id="echoid-s3058" xml:space="preserve">q r,
              <lb/>
            p s, y t, x u æquidiſtan-
              <lb/>
            tesipſi a c. </s>
            <s xml:id="echoid-s3059" xml:space="preserve">Itaque dico
              <lb/>
            harum figurarum in el-
              <lb/>
            lipſi deſcriptarum cen-
              <lb/>
            trum grauitatis eſſe pũ-
              <lb/>
            ctum k, idem quod & </s>
            <s xml:id="echoid-s3060" xml:space="preserve">el
              <lb/>
            lipſis centrum. </s>
            <s xml:id="echoid-s3061" xml:space="preserve">quadri-
              <lb/>
            lateri enim a b c d cen-
              <lb/>
            trum eſt k, ex decima e-
              <lb/>
            iuſdem libri Archime-
              <lb/>
            dis, quippe cũ in eo om
              <lb/>
            nes diametri cõueniãt.
              <lb/>
            </s>
            <s xml:id="echoid-s3062" xml:space="preserve">Sed in figura alb m c n
              <lb/>
              <note position="left" xlink:label="note-0120-02" xlink:href="note-0120-02a" xml:space="preserve">13. Archi
                <lb/>
              medis.</note>
            d o, quoniam trianguli
              <lb/>
            alb centrum grauitatis
              <lb/>
              <note position="left" xlink:label="note-0120-03" xlink:href="note-0120-03a" xml:space="preserve">Vltima.</note>
            eſt in linea l e: </s>
            <s xml:id="echoid-s3063" xml:space="preserve">trapezijq́; </s>
            <s xml:id="echoid-s3064" xml:space="preserve">a b m o centrum in linea e k: </s>
            <s xml:id="echoid-s3065" xml:space="preserve">trape
              <lb/>
            zij o m c d in k g: </s>
            <s xml:id="echoid-s3066" xml:space="preserve">& </s>
            <s xml:id="echoid-s3067" xml:space="preserve">trianguli c n d in ipſa g n: </s>
            <s xml:id="echoid-s3068" xml:space="preserve">erit magnitu
              <lb/>
            dinis ex his omnibus conſtantis, uidelicet totius figuræ cen
              <lb/>
            trum grauitatis in linea l n: </s>
            <s xml:id="echoid-s3069" xml:space="preserve">& </s>
            <s xml:id="echoid-s3070" xml:space="preserve">o b eandem cauſſam in linea
              <lb/>
            o m. </s>
            <s xml:id="echoid-s3071" xml:space="preserve">eſt enim trianguli a o d centrum in linea o h: </s>
            <s xml:id="echoid-s3072" xml:space="preserve">trapezij
              <lb/>
            a l n d in h k: </s>
            <s xml:id="echoid-s3073" xml:space="preserve">trapezij l b c n in k f: </s>
            <s xml:id="echoid-s3074" xml:space="preserve">& </s>
            <s xml:id="echoid-s3075" xml:space="preserve">trianguli b m c in fm.
              <lb/>
            </s>
            <s xml:id="echoid-s3076" xml:space="preserve">cum ergo figuræ a l b m c n d o centrum grauitatis ſit in li-
              <lb/>
            nea l n, & </s>
            <s xml:id="echoid-s3077" xml:space="preserve">in linea o m; </s>
            <s xml:id="echoid-s3078" xml:space="preserve">erit centrum ipſius punctum k, </s>
          </p>
        </div>
      </text>
    </echo>