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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          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div533" type="section" level="3" n="11">
              <div xml:id="echoid-div538" type="letter" level="4" n="4">
                <p>
                  <s xml:id="echoid-s3451" xml:space="preserve">
                    <num value="60">
                      <pb o="277" rhead="EPISTOL AE." n="289" file="0289" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0289"/>
                    60.</num>
                  ) per .21. deinde
                    <reg norm="productum" type="context">productũ</reg>
                  etiam multiplicare per
                    <var>.b.c.</var>
                  (hoc eſt .60.) breuius erit
                    <lb/>
                  multiplicare totum numerum .3600. per .21. cętera verò facere, vt diximus.</s>
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                <p>
                  <s xml:id="echoid-s3452" xml:space="preserve">Sed
                    <reg norm="vnaquæque" type="simple">vnaquæq;</reg>
                  iſtarum operationum, aliquid imperfectionis patitur, eo quod
                    <reg norm="cum" type="context">cũ</reg>
                    <lb/>
                  aliquis cuperet quadratum perfectum ſuperficiale habere,
                    <reg norm="abſque" type="simple">abſq;</reg>
                  aliquo defectu, vel
                    <lb/>
                  exceſfu, aliquid aliud adhuc facere oporteret, hoc eſt, inuentum cum fuerit quadra
                    <lb/>
                  tum
                    <var>.e.f.</var>
                  cum ſuis radicibus
                    <var>.e.g.</var>
                  et
                    <var>.g.f.</var>
                  pedum .275. vnaquaque, vt in dicto exemplo
                    <lb/>
                  factum eſt, oportebit
                    <reg norm="numerum" type="context">numerũ</reg>
                  quærere minorem ipſo .275. ſed proximiorem men-
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                  furabilem ab .3. & ab .7. quod facilè fiet ſi diuiſerimus .275. per .21. detrahendo fra-
                    <lb/>
                  cta diuiſionis ab ipſo .275. quæ quidem fracta in hoc exemplo ſunt .2. vnde remane-
                    <lb/>
                  bit .273. pro numero laterum quadrati ſuperficialis, in quo poſſent locari .3549. ho-
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                  mines, eo ordine quo ſupra dictum eſt, quorum ſcilicet vnuſquiſque obtineat .21.
                    <lb/>
                  pedes ſuperſiciales.</s>
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            <div xml:id="echoid-div542" type="section" level="3" n="12">
              <div xml:id="echoid-div542" type="letter" level="4" n="1">
                <head xml:id="echoid-head412" xml:space="preserve">DE INTERVALLIS MVSICIS.</head>
                <head xml:id="echoid-head413" style="it" xml:space="preserve">Cypriano Rorè Muſico celeberrimo.</head>
                <p>
                  <s xml:id="echoid-s3453" xml:space="preserve">
                    <emph style="sc">OPinio</emph>
                  Hectoris Euſonij Cypriane mi dilectiſſime, vera non eſt, quod ali
                    <lb/>
                  quisrectè poſſit intelligere rationes conſonantiarum muſicæ, ablque co
                    <lb/>
                  gnitione illarum mediante ipſo ſenſu, imo nemo
                    <reg norm="pont" type="context">põt</reg>
                  calere
                    <reg norm="theoriam" type="context">theoriã</reg>
                  mu
                    <lb/>
                  ſices, niſi aliquo
                    <reg norm="mon" type="context">mõ</reg>
                  verſatus ſit in praxi. </s>
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                    <reg norm="Quando" type="wordlist">Qũo</reg>
                  enim cognoſci
                    <reg norm="poterunt" type="context">poterũt</reg>
                    <lb/>
                  quid nam ſint diapaſon, diapente, diateſſeron, ditonus, ſemiditonus, hexacordum
                    <lb/>
                  maius, aut minus, & conſonantiæ ex ijs cum diapaſon compoſitæ, abſque earum
                    <lb/>
                  praxi? </s>
                  <s xml:id="echoid-s3455" xml:space="preserve">vnde ſequetur
                    <reg norm="neque" type="simple">neq;</reg>
                  etiam cognoſci poſſe interualla diſſonantia. </s>
                  <s xml:id="echoid-s3456" xml:space="preserve">Et purus
                    <lb/>
                  practicus non intelliget quid ſit octaua, quinta, quarta, tertia maior, tertia minor,
                    <lb/>
                  ſexta maior, ſexta minor, decima maior, decima minor, vndecima, duode-
                    <lb/>
                  cima, decimatertia maior, aut minor, aut decimaquinta, & aliæ, ita vt ad
                    <lb/>
                  comparandam perfectionem muſicæ neceſſarium ſit, & thęoriam & praxim ad-
                    <lb/>
                  diſcere. </s>
                  <s xml:id="echoid-s3457" xml:space="preserve">Cum pręterea Ludouicus Folianus apertè monſtrarit (etiam ſi id à diato-
                    <lb/>
                  nico ſintono Ptolomei deſumpſerit) reperiri duos tonos, maiorem, & minorem, id-
                    <lb/>
                  eſt ſeſquioctauum, & ſeſquinonum, & tria ſemitonia, maius, minus, & mini-
                    <lb/>
                  mum, ideſt ſeſquiquintumdecimum, qui eſt maius, ſeſquiuigeſimum quartum id-
                    <lb/>
                  eſt minimum, & mediocre, vt .27. ad .25. quæ proportio ſuperbipartiens vigeſi-
                    <lb/>
                  maſquintas appellatur, & cum cognouerit ſemiditonum conſonantem eſſe ſeſqui-
                    <lb/>
                  quintum, ditonum ſeſquiquartum, & hexachordum minus, vt .8. ad .5. quæ propor-
                    <lb/>
                  tio dicitur ſupertripartiens quintas, & hexachordum maius, vt .5. ad .3. hęc autem vo
                    <lb/>
                  catur ſuperbipartienstertias; </s>
                  <s xml:id="echoid-s3458" xml:space="preserve">omnium ſimplicium conſonantiarum cognitioni, ex-
                    <lb/>
                  tremam impoſuit manum. </s>
                  <s xml:id="echoid-s3459" xml:space="preserve">Et quia tibi etiam oſtendere promiſi in modulationibus </s>
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