Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of Notes

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            <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/>
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            <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"/>
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            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-
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            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>
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