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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EPISTOL AE.
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291
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0291
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<
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">De eodem ſubiecto.</
head
>
<
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">AD EVNDEM.</
head
>
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<
s
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xml:space
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">QVod aliàs tibi dixi, verum eſt, quod neceſſarium nullo modo ſit, vt modulan-
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do, deſinat cantilena in eodem tono (quod Græci phthongum appel-
<
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lant) à quo incępit. </
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<
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xml:space
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">immo neceſſariò ſemper ferè, altius, aut depræſ-
<
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ſius terminatur, per differentiam alicuius interualli æqualis, vel multiplicis ipſi com
<
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mati ſeſquioctuageſimæ, quod quidem comma, quamuis cantabile non ſit, inſenſi-
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biliter tamen generatur, & toties ab aliqua parte ipſius cantilenæ poſſet
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com-
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ma gcnerari, verſus acutum, vel graue, quod in fine ipſius cantilenę, vocis phtongus
<
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reperiatur diſtans à primo per interuallum alicuius toni ſeſquinoni, ſeu ſeſquioctaui
<
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plus, minúsue, vt in ſubſcripto exemplo clarè videre potes in prima figura, vbi ſu-
<
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perius à
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primę cellulæ ad
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ſecundæ, intereſt vnum
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, eo quod progrediens
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ſuperius in prima cellula ipſius cantilenæ à quarta ad quintam cum tenore, aſcendit
<
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per tonum ſeſquioctauum, à prima cellula deinde ad ſecundam, tenor aſcendit ſimi-
<
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liter per tonum ſeſquioctauum cum tranſeat à quinta ad quartam, quod facit cum
<
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ſuperiori, in ſecunda cellula poſtea, cum ſuperius deſcendat à maiori ſexta ad quin
<
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tam, quod facit cum baſſu, ſeu à quarta ad tertiam minorem, quod facit cum teno-
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re, </
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<
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gum, vbi prius erat in prima cellula, ſed reperitur per
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altius,
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eſt differentia inter
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&
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, vt alias tibi
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.</
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<
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">Progrediendo igitur hoc modo, videbis quod cum tenor à ſecunda cellula ad ter
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tiam tranſeat à tertia minori ad quartam, quod facit cum ſuperiori, deſcendit per
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tonum ſeſquinonum, vnde in tertia cellula altius remanet quam in prima per
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comma, in qua tertia cellula, cum iterum tranſeat ſuperius à quarta ad quintam,
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facit cum tenore, eleuatur per tonum ſeſquioctauum, proſequendo deinde tali ordi
<
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ne, vidc
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bis in quarta cellula cantilenam auctam per duo commata, in ſexta,
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cel-
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lula per tria commata, in octaua verò per .4. commata, vnde hac merhodo, ſi can-
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tilena prolixior debito eſſet, vel ſi talia interualla frequentiora reperirentur, poſſet
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cantilena à principio ad finem differre per .9. commata, & plus etiam, quæ quidem
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