Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

Page concordance

< >
Scan Original
281 269
282 270
283 271
284 272
285 273
286 274
287 275
288 276
289 277
290 278
291 279
292 280
293 281
294 288
295 283
296 284
297 285
298 286
299 287
300 288
301 289
302 290
303 291
304 292
305 293
306 294
307 295
308 296
309 297
310 298
< >
page |< < (283) of 445 > >|
    <echo version="1.0">
      <text type="book" xml:lang="la">
        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div544" type="section" level="3" n="13">
              <div xml:id="echoid-div544" type="letter" level="4" n="1">
                <p>
                  <s xml:id="echoid-s3499" xml:space="preserve">
                    <pb o="283" rhead="EPISTOL AE." n="295" file="0295" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0295"/>
                  ſeptima maiori, omnia ſibi inuicem ſunt proportionalia, idem etiam dico de reli-
                    <lb/>
                  quis partibus, cum relatæ fuerint ad ſua tota.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3500" xml:space="preserve">Nec alienum mihi videtur à propoſito inſtituto, ſpeculari modum generationis
                    <lb/>
                  ipſarum ſimplicium
                    <reg norm="conſonantiarum" type="context">conſonantiarũ</reg>
                  ; </s>
                  <s xml:id="echoid-s3501" xml:space="preserve">qui quidem modus fit ex quadam æquatione per
                    <lb/>
                  @uſſionum, ſeu æquali concurſu vndarum aeris, vel conterminatione earum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3502" xml:space="preserve">Nam, nulli dubium eſt, quin vniſonus ſit prima principalis
                    <reg norm="audituque" type="simple">audituq́</reg>
                  amiciſſima,
                    <lb/>
                  nec non magis propria conſonantia; </s>
                  <s xml:id="echoid-s3503" xml:space="preserve">& ſi intelligatur, vt punctus in linea, vel vnitas
                    <lb/>
                  in numero, quam immediate ſequitur diapaſon, ei ſimillima, poſt hanc verò diapen
                    <lb/>
                  te,
                    <reg norm="cæteræque" type="simple">cæteræq́;</reg>
                  . </s>
                  <s xml:id="echoid-s3504" xml:space="preserve">Videamus igitur ordinem concurſus percuſſionum terminorum, ſeu
                    <lb/>
                  vndarum aeris, vnde ſonus generatur.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3505" xml:space="preserve">Concipiatur igitur mente monochordus, hoc eſt chorda diſtenta, quæ cum diuiſa
                    <lb/>
                  fuerit in duas æquales partes à ponticulo, </s>
                  <s xml:id="echoid-s3506" xml:space="preserve">tunc
                    <reg norm="vnaquæque" type="simple">vnaquæq;</reg>
                  pars eundem ſonum pro-
                    <lb/>
                  feret, & ambæ formabunt vniſonum, quia eodem tempore, tot percuſſiones in aere
                    <lb/>
                  faciet vna partium illius chordæ, quot & altera: </s>
                  <s xml:id="echoid-s3507" xml:space="preserve">ita vt vndæ aeris ſimul eant, & æqua
                    <lb/>
                  liter concurrant, abſque ulla interſectione, vel fractione illarum inuicem.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3508" xml:space="preserve">Sed cum ponticulus ita diuiſerit chordam, vt relicta ſit eius tertia pars ab vno la-
                    <lb/>
                  tere, ab alio vero, duę tertię, </s>
                  <s xml:id="echoid-s3509" xml:space="preserve">tunc maior pars, dupla erit minori, &
                    <reg norm="ſonabunt" type="context">ſonabũt</reg>
                  ipſam dia
                    <lb/>
                  paſon conſonantiam, percuſſiones vero terminorum ipſius, tali proportione ſe inui-
                    <lb/>
                  cem habebunt, ut in qualibet ſecunda percuſſione minoris portionis ipſius chordæ,
                    <lb/>
                  maior percutiet, ſeu concurret cum minori, eodem temporis inſtanti, cum ne-
                    <lb/>
                  mo ſit qui neſciat, quod quo longior eſt chorda, etiam tardius moueatur, </s>
                  <s xml:id="echoid-s3510" xml:space="preserve">quare
                    <lb/>
                  cum longior dupla ſit breuiori, & eiuſdem intenſionis tam vna quam altera, tunc eo
                    <lb/>
                  tempore, quo longior vnum interuallum tremoris perfecerit, breuior duo interual-
                    <lb/>
                  la conficiet.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3511" xml:space="preserve">Cum autem ponticulus ita diuiſerit chordam, ut ab uno latere relinquantur duæ
                    <lb/>
                  quintæ partes, ab alio verò tres quintæ, ex quibus partibus generatur conſonantia
                    <lb/>
                  diapente; </s>
                  <s xml:id="echoid-s3512" xml:space="preserve">tunc clarè patet, quod eadem proportione tardius erit vnum interuallu
                    <unsure/>
                  m
                    <lb/>
                  tremoris maioris portionis, vno interuallo tremoris minoris portionis, quam ma-
                    <lb/>
                  i
                    <unsure/>
                  or portio habet ad minorem; </s>
                  <s xml:id="echoid-s3513" xml:space="preserve">hoc eſt tempus maioris interualli ad tempus minoris
                    <lb/>
                  erit
                    <reg norm="ſeſquialterum" type="context">ſeſquialterũ</reg>
                  quare non
                    <reg norm="conuenient" type="context">cõuenient</reg>
                  ſimul, niſi perfectis tribus interuallis mino-
                    <lb/>
                  ris portionis, & duobus maioris; </s>
                  <s xml:id="echoid-s3514" xml:space="preserve">ita quod eadem proportio erit numeri interuallo-
                    <lb/>
                  rum minoris portionis ad interualla maioris, quæ longitudinis maioris portionis ad
                    <lb/>
                  longitudinem minoris; </s>
                  <s xml:id="echoid-s3515" xml:space="preserve">vnde productum numeri portionis minoris ipſius chordæ
                    <lb/>
                  in numerum interuallorum motus ipſius portionis, æquale erit producto numeri
                    <lb/>
                  portionis maioris in numerum interuallorum ipſius maioris portionis; </s>
                  <s xml:id="echoid-s3516" xml:space="preserve">quæ quidem
                    <lb/>
                  producta ita ſe habebunt, vt in diapaſon, ſit binarius numerus; </s>
                  <s xml:id="echoid-s3517" xml:space="preserve">in diapente verò
                    <lb/>
                  ſenarius; </s>
                  <s xml:id="echoid-s3518" xml:space="preserve">in diateſſaron duodenarius, in hexachordo maiori quindenarius; </s>
                  <s xml:id="echoid-s3519" xml:space="preserve">in di-
                    <lb/>
                  tono vicenarius, in ſemiditono tricenarius, demum in hexachordo minori quadra
                    <lb/>
                  genarius: </s>
                  <s xml:id="echoid-s3520" xml:space="preserve">qui quidem numeri non abſque mirabili analogia conueniunt inuicem.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3521" xml:space="preserve">Voluptas autem, quam auditui afferunt conſonantiæ fit, quia leniuntur ſenſus,
                    <lb/>
                  quemadmodum
                    <reg norm="contra" type="context">cõtra</reg>
                  , dolor qui à diſſonantijs oritur, ab aſperitate naſcitur, id quod
                    <lb/>
                  facilè vide
                    <unsure/>
                  re poteris cum conchordantur organorum fiſtulæ.</s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum