Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of Notes

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            <s xml:id="echoid-s3200" xml:space="preserve">Itaque quoniam duæ lineæ K l, l m ſe ſe tangentes, duabus
              <lb/>
            lineis ſe ſe tangentibus a b, b c æquidiſtant; </s>
            <s xml:id="echoid-s3201" xml:space="preserve">nec ſunt in eo-
              <lb/>
            dem plano: </s>
            <s xml:id="echoid-s3202" xml:space="preserve">angulus
              <emph style="sc">K</emph>
            l m æqualis eſt angulo a b c: </s>
            <s xml:id="echoid-s3203" xml:space="preserve">& </s>
            <s xml:id="echoid-s3204" xml:space="preserve">ita an
              <lb/>
              <note position="left" xlink:label="note-0126-01" xlink:href="note-0126-01a" xml:space="preserve">10. unde
                <lb/>
              cimi</note>
            gulus l m
              <emph style="sc">K</emph>
            , angulo b c a, & </s>
            <s xml:id="echoid-s3205" xml:space="preserve">m
              <emph style="sc">K</emph>
            lipſi c a b æqualis prob abi
              <lb/>
            tur. </s>
            <s xml:id="echoid-s3206" xml:space="preserve">triangulum ergo
              <emph style="sc">K</emph>
            l m eſt æquale, & </s>
            <s xml:id="echoid-s3207" xml:space="preserve">ſimile triang ulo
              <lb/>
            a b c. </s>
            <s xml:id="echoid-s3208" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s3209" xml:space="preserve">triangulo d e f. </s>
            <s xml:id="echoid-s3210" xml:space="preserve">Ducatur linea c g o, & </s>
            <s xml:id="echoid-s3211" xml:space="preserve">per ip
              <lb/>
            ſam, & </s>
            <s xml:id="echoid-s3212" xml:space="preserve">per c f ducatur planum ſecans priſma, cuius & </s>
            <s xml:id="echoid-s3213" xml:space="preserve">paral
              <lb/>
            lelogrammi a e communis ſectio ſit o p q. </s>
            <s xml:id="echoid-s3214" xml:space="preserve">tranſibit linea
              <lb/>
            f q per h, & </s>
            <s xml:id="echoid-s3215" xml:space="preserve">m p per n. </s>
            <s xml:id="echoid-s3216" xml:space="preserve">nam cum plana æquidiſtantia ſecen
              <lb/>
            tur à plano c q, communes eorum ſectiones c g o, m p, f q
              <lb/>
            ſibi ipſis æquidiſtabunt. </s>
            <s xml:id="echoid-s3217" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s3218" xml:space="preserve">æquidiſtant a b,
              <emph style="sc">K</emph>
            l, d e. </s>
            <s xml:id="echoid-s3219" xml:space="preserve">an-
              <lb/>
            guli ergo a o c,
              <emph style="sc">K</emph>
            p m, d q f inter ſe æquales ſunt: </s>
            <s xml:id="echoid-s3220" xml:space="preserve">& </s>
            <s xml:id="echoid-s3221" xml:space="preserve">ſunt
              <lb/>
              <note position="left" xlink:label="note-0126-02" xlink:href="note-0126-02a" xml:space="preserve">10. unde-
                <lb/>
              cimi</note>
            æquales qui ad puncta a k d conſtituuntur. </s>
            <s xml:id="echoid-s3222" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s3223" xml:space="preserve">reliqui
              <lb/>
            reliquis æquales; </s>
            <s xml:id="echoid-s3224" xml:space="preserve">& </s>
            <s xml:id="echoid-s3225" xml:space="preserve">triangula a c o, _K_ m p, d f q inter ſe ſimi
              <lb/>
            lia erunt. </s>
            <s xml:id="echoid-s3226" xml:space="preserve">Vtigitur ca ad a o, ita fd ad d q: </s>
            <s xml:id="echoid-s3227" xml:space="preserve">& </s>
            <s xml:id="echoid-s3228" xml:space="preserve">permutando
              <lb/>
              <note position="left" xlink:label="note-0126-03" xlink:href="note-0126-03a" xml:space="preserve">4. ſexti</note>
            ut c a ad fd, ita a o ad d q. </s>
            <s xml:id="echoid-s3229" xml:space="preserve">eſt autem c a æqualis fd. </s>
            <s xml:id="echoid-s3230" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s3231" xml:space="preserve">
              <lb/>
            a o ipſi d q. </s>
            <s xml:id="echoid-s3232" xml:space="preserve">eadem quoque ratione & </s>
            <s xml:id="echoid-s3233" xml:space="preserve">a o ipſi _K_ p æqualis
              <lb/>
            demonſtrabitur. </s>
            <s xml:id="echoid-s3234" xml:space="preserve">Itaque ſi triangula, a b c, d e f æqualia & </s>
            <s xml:id="echoid-s3235" xml:space="preserve">
              <lb/>
            ſimilia inter ſe aptétur,
              <lb/>
              <figure xlink:label="fig-0126-01" xlink:href="fig-0126-01a" number="83">
                <image file="0126-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0126-01"/>
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            cadet linea f q in lineam
              <lb/>
            c g o. </s>
            <s xml:id="echoid-s3236" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s3237" xml:space="preserve">centrũ gra
              <lb/>
              <note position="left" xlink:label="note-0126-04" xlink:href="note-0126-04a" xml:space="preserve">per 5. pe-
                <lb/>
              titionem
                <lb/>
              Archime
                <lb/>
              dis.</note>
            uitatis h in g centrũ ca-
              <lb/>
            det. </s>
            <s xml:id="echoid-s3238" xml:space="preserve">trãſibit igitur linea
              <lb/>
            f q per h: </s>
            <s xml:id="echoid-s3239" xml:space="preserve">& </s>
            <s xml:id="echoid-s3240" xml:space="preserve">planum per
              <lb/>
            c o & </s>
            <s xml:id="echoid-s3241" xml:space="preserve">c f ductũ per axẽ
              <lb/>
            g h ducetur: </s>
            <s xml:id="echoid-s3242" xml:space="preserve">idcircoq; </s>
            <s xml:id="echoid-s3243" xml:space="preserve">li
              <lb/>
            neam m p etiã per n trã
              <lb/>
            ſire neceſſe erit. </s>
            <s xml:id="echoid-s3244" xml:space="preserve">Quo-
              <lb/>
            niam ergo ſh, c g æqua-
              <lb/>
            les ſunt, & </s>
            <s xml:id="echoid-s3245" xml:space="preserve">æquidiſtãtes:
              <lb/>
            </s>
            <s xml:id="echoid-s3246" xml:space="preserve">itemq; </s>
            <s xml:id="echoid-s3247" xml:space="preserve">h q, g o; </s>
            <s xml:id="echoid-s3248" xml:space="preserve">rectæ li-
              <lb/>
            neæ, quæ ipſas cónectũt
              <lb/>
            c m f, g n h, o p q æqua-
              <lb/>
            les & </s>
            <s xml:id="echoid-s3249" xml:space="preserve">æquidiſtãtes erũt.</s>
            <s xml:id="echoid-s3250" xml:space="preserve"/>
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