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]

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page |< < (279) of 445 > >|
EPISTOL AE.
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                <pb o="279" rhead="EPISTOL AE." n="291" file="0291" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0291"/>
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            <div xml:id="echoid-div544" type="section" level="3" n="13">
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                <head xml:id="echoid-head414" style="it" xml:space="preserve">De eodem ſubiecto.</head>
                <head xml:id="echoid-head415" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3470" xml:space="preserve">QVod aliàs tibi dixi, verum eſt, quod neceſſarium nullo modo ſit, vt modulan-
                    <lb/>
                  do, deſinat cantilena in eodem tono (quod Græci phthongum appel-
                    <lb/>
                  lant) à quo incępit. </s>
                  <s xml:id="echoid-s3471" xml:space="preserve">immo neceſſariò ſemper ferè, altius, aut depræſ-
                    <lb/>
                  ſius terminatur, per differentiam alicuius interualli æqualis, vel multiplicis ipſi com
                    <lb/>
                  mati ſeſquioctuageſimæ, quod quidem comma, quamuis cantabile non ſit, inſenſi-
                    <lb/>
                  biliter tamen generatur, & toties ab aliqua parte ipſius cantilenæ poſſet
                    <reg norm="dictum" type="context">dictũ</reg>
                  com-
                    <lb/>
                  ma gcnerari, verſus acutum, vel graue, quod in fine ipſius cantilenę, vocis phtongus
                    <lb/>
                  reperiatur diſtans à primo per interuallum alicuius toni ſeſquinoni, ſeu ſeſquioctaui
                    <lb/>
                  plus, minúsue, vt in ſubſcripto exemplo clarè videre potes in prima figura, vbi ſu-
                    <lb/>
                  perius à
                    <var>.g.</var>
                  primę cellulæ ad
                    <var>.g.</var>
                  ſecundæ, intereſt vnum
                    <reg norm="comma" type="context">cõma</reg>
                  , eo quod progrediens
                    <lb/>
                  ſuperius in prima cellula ipſius cantilenæ à quarta ad quintam cum tenore, aſcendit
                    <lb/>
                  per tonum ſeſquioctauum, à prima cellula deinde ad ſecundam, tenor aſcendit ſimi-
                    <lb/>
                  liter per tonum ſeſquioctauum cum tranſeat à quinta ad quartam, quod facit cum
                    <lb/>
                  ſuperiori, in ſecunda cellula poſtea, cum ſuperius deſcendat à maiori ſexta ad quin
                    <lb/>
                  tam, quod facit cum baſſu, ſeu à quarta ad tertiam minorem, quod facit cum teno-
                    <lb/>
                  re, </s>
                  <s xml:id="echoid-s3472" xml:space="preserve">tunc deſcendit per tonum ſeſquinonum, ita quod non reuertitur ad
                    <reg norm="eundem" type="context">eundẽ</reg>
                    <reg norm="phthon" type="context">phthõ</reg>
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                  gum, vbi prius erat in prima cellula, ſed reperitur per
                    <reg norm="vnum" type="context">vnũ</reg>
                    <reg norm="coomma" type="context">coõma</reg>
                  altius,
                    <reg norm="quod" type="wordlist">qđ</reg>
                    <reg norm="quidem" type="context">quidẽ</reg>
                    <lb/>
                    <reg norm="comma" type="context">cõma</reg>
                  eſt differentia inter
                    <reg norm="tonum" type="context">tonũ</reg>
                    <reg norm="ſeſquioctauum" type="context">ſeſquioctauũ</reg>
                  &
                    <reg norm="ſeſquinonum" type="context">ſeſquinonũ</reg>
                  , vt alias tibi
                    <reg norm="demonſtraui" type="context">demõſtraui</reg>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s3473" xml:space="preserve">Progrediendo igitur hoc modo, videbis quod cum tenor à ſecunda cellula ad ter
                    <lb/>
                  tiam tranſeat à tertia minori ad quartam, quod facit cum ſuperiori, deſcendit per
                    <lb/>
                  tonum ſeſquinonum, vnde in tertia cellula altius remanet quam in prima per
                    <reg norm="vnum" type="context">vnũ</reg>
                    <lb/>
                  comma, in qua tertia cellula, cum iterum tranſeat ſuperius à quarta ad quintam,
                    <reg norm="quod" type="simple">ꝙ</reg>
                    <lb/>
                  facit cum tenore, eleuatur per tonum ſeſquioctauum, proſequendo deinde tali ordi
                    <lb/>
                  ne, vidc
                    <unsure/>
                  bis in quarta cellula cantilenam auctam per duo commata, in ſexta,
                    <reg norm="autem" type="wordlist">aũt</reg>
                  cel-
                    <lb/>
                  lula per tria commata, in octaua verò per .4. commata, vnde hac merhodo, ſi can-
                    <lb/>
                  tilena prolixior debito eſſet, vel ſi talia interualla frequentiora reperirentur, poſſet
                    <lb/>
                  cantilena à principio ad finem differre per .9. commata, & plus etiam, quæ quidem
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0291-01a" xlink:href="fig-0291-01"/>
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