Biancani, Giuseppe, Aristotelis loca mathematica, 1615

Page concordance

< >
Scan Original
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
< >
page |< < of 355 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.004621">
                <pb pagenum="266" xlink:href="009/01/266.jpg"/>
              eſt. </s>
              <s id="s.004622">idem quærit etiam problemate 42. Hæc de ratione multiplici, & ſuper­
                <lb/>
              particulari dicta ſunt ex veterum ſententia: recentiores enim muſicæ de­
                <lb/>
              prauatores plures alias rationes perperam inter harmonicas intruſerunt.</s>
            </p>
            <p type="main">
              <s id="s.004623">
                <arrow.to.target n="marg379"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.004624">
                <margin.target id="marg379"/>
              388</s>
            </p>
            <p type="main">
              <s id="s.004625">Probl. 35.
                <emph type="italics"/>
              (Cur Diapaſon conſonantia omnium pulcherrima eſt? </s>
              <s id="s.004626">An quod
                <lb/>
              integris terminis huius proportiones continentur: cæterarum autem non integris?
                <lb/>
              </s>
              <s id="s.004627">cùm enim Nete dupla ad hypaten ſit, quocunque in genere Nete duo tenuerit, hy­
                <lb/>
              pate vnum habebit; & vbi hypate duo, Nete quatuor reſonabit, & ita deinceps.
                <lb/>
              </s>
              <s id="s.004628">At verò eadem Nete meſes ſeſquialtera eſt: proportio
                <expan abbr="namq;">namque</expan>
              ſeſquialtera, qua
                <expan abbr="cõ-ſonantia">con­
                  <lb/>
                ſonantia</expan>
              diapente concluditur, non integris numeris poſita eſt: maior enim mino­
                <lb/>
              rem intra ſe continet totum, & partem eius dimidiam. </s>
              <s id="s.004629">quamobrem non integri
                <lb/>
              cùm integris comparantur, ſed partes ſuperſunt. </s>
              <s id="s.004630">Conſonantia quoque Diateſſa­
                <lb/>
              ron proportione ſeſquitertia continetur, quæ terminis conſtat, quorum maior mi­
                <lb/>
              norem totum continet, & inſuper tertiam eius partem. </s>
              <s id="s.004631">An quod ex amba­
                <lb/>
              bus conſiſtit, perfectiſſima eſt? </s>
              <s id="s.004632">& quoniam modulandi menſuram hæc tenet, meri­
                <lb/>
              tò omnium elegantiſſima)
                <emph.end type="italics"/>
              Proportio conſonantiæ Diapaſon eſt ſicuti 2. ad 1.
                <lb/>
              vbi vides vtrunque terminum eſſe integrum, quia maior minorem bis inte­
                <lb/>
              grè continet. </s>
              <s id="s.004633">proportio verò conſonantiæ Diapente, eſt ſicuti 3. ad 2. vbi
                <lb/>
              maior terminus minorem non integrè continet, ſed ſemel, & adhuc
                <expan abbr="dimidiũ">dimidium</expan>
                <lb/>
              illius. </s>
              <s id="s.004634">proportio
                <expan abbr="deniq́">denique</expan>
              ; Diateſſaron eſt ſicuti 4. ad 3. vbi maior
                <expan abbr="minorẽ">minorem</expan>
              non
                <lb/>
              integrè continet, ſed ſemel, & adhuc tertiam ipſius partem: breuiter deno­
                <lb/>
              minationes
                <expan abbr="harũ">harum</expan>
                <expan abbr="proportionũ">proportionum</expan>
              ſunt hi, 2/1. 1 1/2. 1 1/3. vbi vides,
                <expan abbr="primũ">primum</expan>
              , qui eſt
                <lb/>
              Diapaſon conſtare ex integris numeris. </s>
              <s id="s.004635">ſecundum verò, & tertium, qui ſunt
                <lb/>
              Diapente, & Diateſſaron exintegro cum fractione. </s>
              <s id="s.004636">maior autem perfectio
                <lb/>
              eſt integritas, quam fractio, aut diuiſio. </s>
              <s id="s.004637">propterea perfectior reliquis eſt
                <lb/>
              conſonantia Diapaſon: & Diapente adhuc perfectior, quam Diateſſaron,
                <lb/>
              quia illius numeri minorem habent fractionem, quam huius. </s>
              <s id="s.004638">Aliter reſpon­
                <lb/>
              det poſtea dicens, Diapaſon perfectam eſſe adeò conſonantiam; quoniam
                <lb/>
              ex duabus Diapente, & Diateſſaron conſtat, vt ſupra ex diuiſione mono­
                <lb/>
              chordij, & in præcedenti etiam problemate patuit. </s>
              <s id="s.004639">quæ ratio, quantum va­
                <lb/>
              leat, alij viderint. </s>
              <s id="s.004640">Reſpondet tandem Diapaſon ideò perfectiſſimam eſſe,
                <lb/>
              quia ipſa ſit modulandi menſura, ideſt, quia intra terminos huius
                <expan abbr="conſonã-tiæ">conſonan­
                  <lb/>
                tiæ</expan>
              omnes aliæ ſimplices conſonantiæ continentur, vt ſupra initio explica­
                <lb/>
              ui. </s>
              <s id="s.004641">meritò igitur omnium elegantiſſima eſt. </s>
              <s id="s.004642">In græco textu ſuperſunt
                <expan abbr="nō-nulla">non­
                  <lb/>
                nulla</expan>
              , quæ meritò Gaza omiſit, cum nullo pacto cùm præcedentibus cohæ­
                <lb/>
              reant. </s>
              <s id="s.004643">Verba illa
                <emph type="italics"/>
              (Cum enim nete ad hypatem dupla ſit, quocunque in genere
                <lb/>
              duo tenuerit, hypate vnŭμ habebit &c.)
                <emph.end type="italics"/>
              Videntur
                <foreign lang="grc">νστερογ πρωτερον·</foreign>
              cum debuiſ­
                <lb/>
              ſet dicere, hypatem duplam eſſe ipſius netes, vt ſupra patuit ex diuiſione
                <lb/>
              regulæ harmonicæ. </s>
              <s id="s.004644">Fortè vult dicere neten eſſe duplò acutiorem,
                <expan abbr="quã">quam</expan>
              hy­
                <lb/>
              pate: vel fuit memoriæ lapſus. </s>
              <s id="s.004645">quod ait
                <emph type="italics"/>
              (At verò eadem nete Meſes ſeſqui­
                <lb/>
              altera eſt)
                <emph.end type="italics"/>
              vult dicere Meſen ad neten habere ſeſquialteram proportionem,
                <lb/>
              quamuis inuersè loquatur: qua ratione verò Meſe ad netem ſeſquialtera
                <lb/>
              ſit, ex diuiſione monochordij initio tradita ſatis patere poteſt.</s>
            </p>
            <p type="main">
              <s id="s.004646">
                <arrow.to.target n="marg380"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.004647">
                <margin.target id="marg380"/>
              389</s>
            </p>
            <p type="main">
              <s id="s.004648">Probl. 36.
                <emph type="italics"/>
              (Cur ſi neruus medius ex ſuo intentionis modo dimotus fuerit, cæte­
                <lb/>
              ris
                <expan abbr="quoq;">quoque</expan>
              omnes nerui, ſonos diſſonos reddent: ſed ſi, immoto illo manente, ali­
                <lb/>
              quis ex cæteris dimotus fuerit, ſolus hic, qui modo ſuo caruerit, aberrabit? </s>
              <s id="s.004649">An,
                <lb/>
              quod ratio concinendi, aptaneruorum omnium intentione continetur, quæ non niſ
                <emph.end type="italics"/>
              i </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum