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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[284] Pro Lunæ ortu. Ad lati .45.
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[286] Pro Lunæ occaſu. Ad lati .45.
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                  <s xml:id="echoid-s3459" xml:space="preserve">
                    <pb o="278" rhead="IO. BAPT. BENED." n="290" file="0290" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0290"/>
                  hæc omnia interualla ſeruari, ideo ad te mitto ſeptem hic ſubſcripta exempla, in
                    <lb/>
                  quorum primo, & ſecundo, inter dieſim, et
                    <var>.b.</var>
                  in ſuperiori, agnoſces interuallum mi
                    <lb/>
                  nimi ſemitonij, & ſi ibi ſit dieſis, tanquam terminus ad quem, et
                    <var>.b.</var>
                  tanquam termi-
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                  nus à quo: </s>
                  <s xml:id="echoid-s3460" xml:space="preserve">quod autem inter dieſim et
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                  ſit ſemitonium minimum, facilè agnoſces
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                  ſi ſubtraxeris
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                    <reg norm="minorem" type="context">minorẽ</reg>
                  à maiori,
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                  facit ſuperius
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                  inferiori, ideſt
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                  baſſu.</s>
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                  <s xml:id="echoid-s3461" xml:space="preserve">Qua quidem modulatione tu etiam vſus es in cantilena illa, quæ Galica lingua
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                  incipit. </s>
                  <s xml:id="echoid-s3462" xml:space="preserve">Hellas comment. </s>
                  <s xml:id="echoid-s3463" xml:space="preserve">Eadem, ego quoque in meis cantilenis latino ſermo-
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                  ne compoſitis, quæ Moreta vocantur aliquando vſus ſum.</s>
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                <p>
                  <s xml:id="echoid-s3464" xml:space="preserve">Sed in tertio exemplo inuenies ſemitonium maius, neceſſariò genitum in ſupe-
                    <lb/>
                  riori, ſi ſextam maiorem cum baſſu eſſicere volueris, quia tenor, à ditono cum
                    <lb/>
                  ſuperiori ad diapentem, & ad vniſonum cum baſſu procedit, vbi quieſcit, progre-
                    <lb/>
                  diendo poſtea baſſus ad ſemiditonum cum tenore, </s>
                  <s xml:id="echoid-s3465" xml:space="preserve">tunc ſi à proportione huius ſep-
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                  timæ, quæ eſt vt .9. ad .5. hoc eſt ſuperquadripartiensquintas demptum fuerit hexa-
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                  chordum maius, ſeu ſexta maior, quæ eſt vt .5. ad .3. remanebit proportio .27. ad .25.
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                  quæ maior eſt quam .32. ad .30.</s>
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                  <s xml:id="echoid-s3466" xml:space="preserve">In quarto
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                  habebis ſemitonium minus in ſuperiori, quod quidem remanet
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                  ex ſubtractione ditoni
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                  ab diateſſaron
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                  à ſuperiori cum tenore.</s>
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                  <s xml:id="echoid-s3467" xml:space="preserve">In quinto exemplo videbis tonum minorem, & tonum maiorem ſucceſſiuè vnum
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                  poſt alium in tenore, detrahendo primo
                    <reg norm="ſemiditonum" type="context">ſemiditonũ</reg>
                  à diateſſaron, quod ſuperius fa-
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                  cit cum tenore, vel detrahendo diapente ab hexachordo maiori, quod facit tenor
                    <lb/>
                  cum baſſu, vnde remanet tonus minor ſeſquinonus, detrahendo poſtea diateſſaron
                    <lb/>
                  à diapente, quod ſuperius facit cum tenore, remanebit tonus maior ſeſquioctauus.</s>
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                <p>
                  <s xml:id="echoid-s3468" xml:space="preserve">In ſexto exemplo deinde videbis tenorem aſcendere per duos tonos minores ſuc
                    <lb/>
                  ceſſiuè vnum poſt alium in tenore, ſi
                    <reg norm="demp" type="context">dẽp</reg>
                  ſeris
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                  à diateſſaron
                    <reg norm="cum" type="context">cũ</reg>
                  ſuperiori.</s>
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                <p>
                  <s xml:id="echoid-s3469" xml:space="preserve">In .7.
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                  demum videbis
                    <reg norm="ſuperiorem" type="context">ſuperiorẽ</reg>
                  aſcendere per duos tonos maiores ſucceſ-
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                  ſiuè
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                  poſt
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                  , ſi dempſeris diateſſaron à diapente, quod facittenor
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                  ſuperiori.</s>
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