Vitruvius, De architectura libri decem, 1567

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            <p style="it">
              <s xml:id="echoid-s1543" xml:space="preserve">
                <pb o="14" file="514.01.046" n="46" rhead="LIBER"/>
              conſenſus duarum ſcientiarum inter ſe, mox multarum, Muſice, medicinaq́; </s>
              <s xml:id="echoid-s1544" xml:space="preserve">ſcientiæ, uel artes ſunt. </s>
              <s xml:id="echoid-s1545" xml:space="preserve">Medi-
                <lb/>
              ci munus est ſanitatem inducere ubinon eſt, aut conſeruare ubiest, Muſici quatenus Muſici est modulando au
                <lb/>
              ditores delectare, his muneribus differunt, ſed quibuſdam rationibus conueniunt inter ſe, conuenientia ex
                <lb/>
              conmuni quadam regula proficiſcitur: </s>
              <s xml:id="echoid-s1546" xml:space="preserve">nam dum Medicus conſiderat elationem, & </s>
              <s xml:id="echoid-s1547" xml:space="preserve">depreſſionem arteriarum,
                <lb/>
              & </s>
              <s xml:id="echoid-s1548" xml:space="preserve">pulſus, uelocitatem, & </s>
              <s xml:id="echoid-s1549" xml:space="preserve">moram, œqualitatem, & </s>
              <s xml:id="echoid-s1550" xml:space="preserve">inœqualitatem, cum Muſicis ratione conuenit, Muſicus
                <lb/>
              enim eaſdem res in uocibus ſpeculatur: </s>
              <s xml:id="echoid-s1551" xml:space="preserve">nam uelocitas, tarditas, altitudo, depreſſio, æqualitas, & </s>
              <s xml:id="echoid-s1552" xml:space="preserve">huiuſmo-
                <lb/>
              di communes termini ſunt, qui ad res multas diſpares accommodari poſſunt, ideò nullum eſt incommodum artifi
                <lb/>
              ees in rationibus conſentire, qui postea in operibus ſunt differentes. </s>
              <s xml:id="echoid-s1553" xml:space="preserve">idq́ oritur ex ui principiorum, quœ cum
                <lb/>
              communia ſint, & </s>
              <s xml:id="echoid-s1554" xml:space="preserve">uniuerſalia, abſque ullo diſcrimine res multas amplectuntur. </s>
              <s xml:id="echoid-s1555" xml:space="preserve">A equalitas igitur tempori,
                <lb/>
              loco, numero, magnitudini aptari potest. </s>
              <s xml:id="echoid-s1556" xml:space="preserve">idem iudicium de reliquis: </s>
              <s xml:id="echoid-s1557" xml:space="preserve">nil igitur mirum, ſi ratio eadem plures
                <lb/>
                <note position="left" xlink:label="note-514.01.046-01" xlink:href="note-514.01.046-01a" xml:space="preserve">10</note>
              iuuat artifices, qui in operibus diuerſis diſſentiunt, aliud enim ratio, aliud est opus, ratio doctis, opus exper-
                <lb/>
              tis tribuitur. </s>
              <s xml:id="echoid-s1558" xml:space="preserve">Angulos facilè coaleſcere a Geometria ſumit Medicus, circulum non item. </s>
              <s xml:id="echoid-s1559" xml:space="preserve">hinc ea ratione du-
                <lb/>
              citur, ut uulnera, quæ in orbemtendunt, difficillimæ curœ iudicet, angularia facile ſanet. </s>
              <s xml:id="echoid-s1560" xml:space="preserve">At ſi uulnus me-
                <lb/>
              deri oportuerit, non accedet Geometra, ſed Medicus.</s>
              <s xml:id="echoid-s1561" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s1562" xml:space="preserve">
                <emph style="sc">Similiter</emph>
              cum Aſtrologis, & </s>
              <s xml:id="echoid-s1563" xml:space="preserve">Muſicis eſt diſputatio communis de Sympathia ſtellarum, & </s>
              <s xml:id="echoid-s1564" xml:space="preserve">ſym
                <lb/>
              phoniarum in quadratis, & </s>
              <s xml:id="echoid-s1565" xml:space="preserve">trigonis, diateſſaron & </s>
              <s xml:id="echoid-s1566" xml:space="preserve">diapente: </s>
              <s xml:id="echoid-s1567" xml:space="preserve">cum Geometris de uiſu qui λóγos
                <lb/>
              appellatur, cæterisq́; </s>
              <s xml:id="echoid-s1568" xml:space="preserve">omnibus doctrinis multæ res, uel omnes communes ſunt duntaxat ad diſputan-
                <lb/>
              dum, operum uerò ingreſſus, qui manu, ac tractationibus, ad elegantiam perducuntur, ipſorum
                <lb/>
              ſunt, qui propriè una arte ad faciendum ſuntinſtituti.</s>
              <s xml:id="echoid-s1569" xml:space="preserve"/>
            </p>
            <p style="it">
              <s xml:id="echoid-s1570" xml:space="preserve">Cum Aſtronomi ſibi proponant oſtendere qua ratione cœlestia illa, ac lucentia mundi corpora conſentiant in
                <lb/>
                <note position="left" xlink:label="note-514.01.046-02" xlink:href="note-514.01.046-02a" xml:space="preserve">20</note>
              ter ſe, conſpirentq́; </s>
              <s xml:id="echoid-s1571" xml:space="preserve">in demittentis ad centrum uirtutibus, & </s>
              <s xml:id="echoid-s1572" xml:space="preserve">influxibus, ſelegerunt quaſdam figuras Geome-
                <lb/>
              tricas inter ſe ratione, comparationeq́; </s>
              <s xml:id="echoid-s1573" xml:space="preserve">reſpondentes, triquetram, quadratam, exagonam. </s>
              <s xml:id="echoid-s1574" xml:space="preserve">In his admira-
                <lb/>
              bilesrationes, & </s>
              <s xml:id="echoid-s1575" xml:space="preserve">uires inuenere. </s>
              <s xml:id="echoid-s1576" xml:space="preserve">Quod ut manifeſtum ſit, lucidius explicabo. </s>
              <s xml:id="echoid-s1577" xml:space="preserve">Angulorum menſuræ, & </s>
              <s xml:id="echoid-s1578" xml:space="preserve">
                <lb/>
              comparationes ſumuntur ex parte circumferentiæ, quæ illis angulis continetur. </s>
              <s xml:id="echoid-s1579" xml:space="preserve">maiores ſunt anguli, quorum
                <lb/>
              lineæ maiorem circuli portionem amplectuntur, minores, qui minorem. </s>
              <s xml:id="echoid-s1580" xml:space="preserve">Antiqui prœterea rem omnem inte-
                <lb/>
              gram diuiduam, & </s>
              <s xml:id="echoid-s1581" xml:space="preserve">menſurabilem uocabant Aſſem: </s>
              <s xml:id="echoid-s1582" xml:space="preserve">quem duodenas in partes diuidebant, has uncias nomina
                <lb/>
              bant. </s>
              <s xml:id="echoid-s1583" xml:space="preserve">unapars uncia dicebatur, duæſextans; </s>
              <s xml:id="echoid-s1584" xml:space="preserve">nam ſex uicibus binœ Aſſem conſtituebant, tres quadran-
                <lb/>
              tem uocabant, duodecim enim ex tribus quadrantibus efficiuntur: </s>
              <s xml:id="echoid-s1585" xml:space="preserve">quatuor uerſauice trientem: </s>
              <s xml:id="echoid-s1586" xml:space="preserve">quinque quicun
                <lb/>
              cem nulla ratione habita ad aſſem, quoniam nulla quinarij aſſumptione aſſis perficitur. </s>
              <s xml:id="echoid-s1587" xml:space="preserve">Sex uerò ſemiſſem,
                <lb/>
              quaſi dimidiatum aſſem dicebãt: </s>
              <s xml:id="echoid-s1588" xml:space="preserve">ſeptem ſeptuncem, eadem ratione, qua dixere quincuncem, octo beſſem, duas
                <lb/>
                <note position="left" xlink:label="note-514.01.046-03" xlink:href="note-514.01.046-03a" xml:space="preserve">30</note>
              enim ſenis addebant, nouem dodrantem, decem dextantem, undecim, deuncem, quoniam nulla erat earum
                <lb/>
              partium multiplicatio, quœ aſſem perficeret, nam ſemel ſumptœ non accedebant ad ſummam: </s>
              <s xml:id="echoid-s1589" xml:space="preserve">plures, ultra aſ
                <lb/>
              ſem perueniebant. </s>
              <s xml:id="echoid-s1590" xml:space="preserve">his stabilitis fingamus quadrantem circuli in duodenas partes eſſe diuiſum, qualium totus
                <lb/>
              orbis est quadraginta octo. </s>
              <s xml:id="echoid-s1591" xml:space="preserve">rectus, & </s>
              <s xml:id="echoid-s1592" xml:space="preserve">œqualis quadrantis angulus duodecim occupabit: </s>
              <s xml:id="echoid-s1593" xml:space="preserve">trigoni ſexdecim:
                <lb/>
              </s>
              <s xml:id="echoid-s1594" xml:space="preserve">exagoni octo. </s>
              <s xml:id="echoid-s1595" xml:space="preserve">quadrati igitur angulus, quoniam rectus eſt, integerq́ dicetur Aſſis, Trianguli, quoniam ma-
                <lb/>
              ior tertia parte, quemadmodum in diagrammate uidetur, ſemel continebit rectum, & </s>
              <s xml:id="echoid-s1596" xml:space="preserve">integrum, & </s>
              <s xml:id="echoid-s1597" xml:space="preserve">amplius
                <lb/>
              quadrantem, hoc eſt, partem tertiam, & </s>
              <s xml:id="echoid-s1598" xml:space="preserve">inter hos duos angulos ratio ſeſquitertia cadet. </s>
              <s xml:id="echoid-s1599" xml:space="preserve">exagoni uero angu-
                <lb/>
              lus, quoniam dimidio minor est angulo trigoni ( octo enim partes continet, ex ſexdecim ) ideò ad ipſum com
                <lb/>
              paratus angulum exagoni oſtendet rationem duplam, ſed inter quadrati angulum, & </s>
              <s xml:id="echoid-s1600" xml:space="preserve">exagoni eſt proportio
                <lb/>
              ſeſquialtera; </s>
              <s xml:id="echoid-s1601" xml:space="preserve">quæ fit, cum quid integrum continet, & </s>
              <s xml:id="echoid-s1602" xml:space="preserve">amplius dimidiam partem, quemadmodum octo pars
                <lb/>
                <note position="left" xlink:label="note-514.01.046-04" xlink:href="note-514.01.046-04a" xml:space="preserve">40</note>
              beſſalis continetur ab aſſe ſemel, & </s>
              <s xml:id="echoid-s1603" xml:space="preserve">trientem: </s>
              <s xml:id="echoid-s1604" xml:space="preserve">& </s>
              <s xml:id="echoid-s1605" xml:space="preserve">hoc eſt, quod ad Aſtrologiam pertinet in figuris, aſpecti-
                <lb/>
              busq́; </s>
              <s xml:id="echoid-s1606" xml:space="preserve">ſyderum conſideratum, & </s>
              <s xml:id="echoid-s1607" xml:space="preserve">ſympathia hoc eſt conſenſu. </s>
              <s xml:id="echoid-s1608" xml:space="preserve">quod uerò ad Muſicen ſpectat illud est, quod
                <lb/>
                <figure xlink:label="fig-514.01.046-01" xlink:href="fig-514.01.046-01a" number="6">
                  <variables xml:id="echoid-variables1" xml:space="preserve">12 3 16</variables>
                </figure>
                <note position="left" xlink:label="note-514.01.046-05" xlink:href="note-514.01.046-05a" xml:space="preserve">50</note>
              Muſicus huiuſmodi proportiones, & </s>
              <s xml:id="echoid-s1609" xml:space="preserve">concentus conſiderat, ſed non in figuris, uerum in uocibus, & </s>
              <s xml:id="echoid-s1610" xml:space="preserve">earum
                <lb/>
              interuallis: </s>
              <s xml:id="echoid-s1611" xml:space="preserve">harmonia est uocum diſtantium iucundus concentus. </s>
              <s xml:id="echoid-s1612" xml:space="preserve">ex his ſimplices quidam ſunt, quidam com-
                <lb/>
              poſiti, ſimplicium nomina hæc ſunt, Diapaſon, Diapente, & </s>
              <s xml:id="echoid-s1613" xml:space="preserve">Diateſſaron: </s>
              <s xml:id="echoid-s1614" xml:space="preserve">uocabula compoſitorum ſunt, diſdia-
                <lb/>
                <note position="left" xlink:label="note-514.01.046-06" xlink:href="note-514.01.046-06a" xml:space="preserve">60</note>
              </s>
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