Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

< >
[1. None]
[2. ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBRI DVO. A FEDERICO COMMANDINO VRBINATE IN PRISTINVM NITOREM RESTITVTI, ET COMMENTARIIS ILLVSTRATI.]
[3. CVM PRIVILEGIO IN ANNOS X. BONONIAE,]
[4. M D LXV.]
[5. RANVTIO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.]
[6. Federicus Commandinus.]
[7. ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBER PRIMVS. CVM COMMENTARIIS FEDERICI COMMANDINI VRBINATIS. POSITIO.]
[8. PROPOSITIO I.]
[9. PROPOSITIO II.]
[10. PROPOSITIO III.]
[11. PROPOSITIO IIII.]
[12. PROPOSITIO V.]
[13. PROPOSITIO VI.]
[14. PROPOSITIO VII.]
[15. POSITIO II.]
[16. COMMENTARIVS.]
[17. PROPOSITIO VIII.]
[18. COMMENTARIVS.]
[19. PROPOSITIO IX.]
[20. COMMENTARIVS.]
[21. ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBER SECVNDVS. CVM COMMENTARIIS FEDERICI COMMANDINI VRBINATIS. PROPOSITIO I.]
[22. PROPOSITIO II.]
[23. COMMENTARIVS.]
[24. PROPOSITIO III.]
[25. PROPOSITIO IIII.]
[26. COMMENTARIVS.]
[27. PROPOSITIO V.]
[28. COMMENTARIVS.]
[29. PROPOSITIO VI.]
[30. COMMENTARIVS.]
< >
page |< < (37) of 213 > >|
DE IIS QVAE VEH. IN AQVA.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="41">
          <pb o="37" file="0073" n="73" rhead="DE IIS QVAE VEH. IN AQVA."/>
          <p>
            <s xml:space="preserve">Cum ergo tres portiones ſint a p o i, a ei, atd, con-
              <lb/>
              <anchor type="note" xlink:label="note-0073-01a" xlink:href="note-0073-01"/>
            tentæ rectis lineis, & </s>
            <s xml:space="preserve">rectãgulorum conorum ſectionibus;
              <lb/>
            </s>
            <s xml:space="preserve">rectæq;</s>
            <s xml:space="preserve">, ſimiles, & </s>
            <s xml:space="preserve">inæquales, quæ contingunt ſe ſe ſuper
              <lb/>
            unam quamque baſim.</s>
            <s xml:space="preserve">] _Poſt ea uerba, ſuper unamquanque_
              <lb/>
            _baſim, in trans latione aliqua deſiderari uidentur. </s>
            <s xml:space="preserve">Ad borum autem_
              <lb/>
            _demonſtrationem non nulla præmittere oportet, quæ etiam ad alia,_
              <lb/>
            _quæ ſequuntur, neceſſaria erunt._</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="11">
            <note position="right" xlink:label="note-0073-01" xlink:href="note-0073-01a" xml:space="preserve">M</note>
          </div>
        </div>
        <div type="section" level="1" n="42">
          <head xml:space="preserve">LEMMA I.</head>
          <p style="it">
            <s xml:space="preserve">Sit recta linea a b, quam ſecent duæ lineæ inter ſeſe
              <lb/>
            æquidiſtantes a c, d e, ita ut quam proportionem ba-
              <lb/>
            bet a b ad b d, eandern haheat a c ad de. </s>
            <s xml:space="preserve">Dico li-
              <lb/>
            neam, quæ c b puncta coniungit, etiam per ipſum e
              <lb/>
            tr anſire.</s>
            <s xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:space="preserve">SI enim fieri poteſt, non tranſeat pere, ſed nel ſupra, uel infra.
              <lb/>
            </s>
            <s xml:space="preserve">tranſeat primum infra, ut per f. </s>
            <s xml:space="preserve">erunt triangula a b c, d b f inter ſe
              <lb/>
            ſimilia. </s>
            <s xml:space="preserve">quare ut a b ad b d, ita a c ad d f. </s>
            <s xml:space="preserve">ſed ut a b ad bd, ita
              <lb/>
              <anchor type="note" xlink:label="note-0073-02a" xlink:href="note-0073-02"/>
            erat a c ad d e. </s>
            <s xml:space="preserve">ergo d f ipſi d e æqualis erit, uidelicet pars to-
              <lb/>
              <anchor type="note" xlink:label="note-0073-03a" xlink:href="note-0073-03"/>
            ti, quod eſt
              <lb/>
              <anchor type="figure" xlink:label="fig-0073-01a" xlink:href="fig-0073-01"/>
            cbſurdum.
              <lb/>
            </s>
            <s xml:space="preserve">Idem ab-
              <lb/>
            ſurdum ſe
              <lb/>
            quetur, ſi
              <lb/>
            linea c b
              <lb/>
            ſupra e pú
              <lb/>
            ctum tran
              <lb/>
            ſire pona-
              <lb/>
            tur. </s>
            <s xml:space="preserve">quare
              <lb/>
            c b etiam
              <lb/>
            per e ne-
              <lb/>
            ceſſario tranſibit. </s>
            <s xml:space="preserve">quod oportebat demonſtrare.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <note position="right" xlink:label="note-0073-02" xlink:href="note-0073-02a" xml:space="preserve">4. ſexti.</note>
            <note position="right" xlink:label="note-0073-03" xlink:href="note-0073-03a" xml:space="preserve">9. quinti.</note>
            <figure xlink:label="fig-0073-01" xlink:href="fig-0073-01a">
              <image file="0073-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0073-01"/>
            </figure>
          </div>
        </div>
      </text>
    </echo>