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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60.</
num
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) per .21. deinde
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etiam multiplicare per
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(hoc eſt .60.) breuius erit
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multiplicare totum numerum .3600. per .21. cętera verò facere, vt diximus.</
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<
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iſtarum operationum, aliquid imperfectionis patitur, eo quod
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aliquis cuperet quadratum perfectum ſuperficiale habere,
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aliquo defectu, vel
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exceſfu, aliquid aliud adhuc facere oporteret, hoc eſt, inuentum cum fuerit quadra
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tum
<
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>.e.f.</
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>
cum ſuis radicibus
<
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>.e.g.</
var
>
et
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>.g.f.</
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>
pedum .275. vnaquaque, vt in dicto exemplo
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factum eſt, oportebit
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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-
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cta diuiſionis ab ipſo .275. quæ quidem fracta in hoc exemplo ſunt .2. vnde remane-
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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.
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pedes ſuperſiciales.</
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<
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xml:space
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">DE INTERVALLIS MVSICIS.</
head
>
<
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style
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it
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xml:space
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">Cypriano Rorè Muſico celeberrimo.</
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<
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Hectoris Euſonij Cypriane mi dilectiſſime, vera non eſt, quod ali
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quisrectè poſſit intelligere rationes conſonantiarum muſicæ, ablque co
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gnitione illarum mediante ipſo ſenſu, imo nemo
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calere
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mu
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ſices, niſi aliquo
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verſatus ſit in praxi. </
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Quando
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enim cognoſci
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quid nam ſint diapaſon, diapente, diateſſeron, ditonus, ſemiditonus, hexacordum
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maius, aut minus, & conſonantiæ ex ijs cum diapaſon compoſitæ, abſque earum
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praxi? </
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<
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etiam cognoſci poſſe interualla diſſonantia. </
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<
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practicus non intelliget quid ſit octaua, quinta, quarta, tertia maior, tertia minor,
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ſexta maior, ſexta minor, decima maior, decima minor, vndecima, duode-
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cima, decimatertia maior, aut minor, aut decimaquinta, & aliæ, ita vt ad
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comparandam perfectionem muſicæ neceſſarium ſit, & thęoriam & praxim ad-
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diſcere. </
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<
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">Cum pręterea Ludouicus Folianus apertè monſtrarit (etiam ſi id à diato-
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nico ſintono Ptolomei deſumpſerit) reperiri duos tonos, maiorem, & minorem, id-
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eſt ſeſquioctauum, & ſeſquinonum, & tria ſemitonia, maius, minus, & mini-
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mum, ideſt ſeſquiquintumdecimum, qui eſt maius, ſeſquiuigeſimum quartum id-
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eſt minimum, & mediocre, vt .27. ad .25. quæ proportio ſuperbipartiens vigeſi-
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maſquintas appellatur, & cum cognouerit ſemiditonum conſonantem eſſe ſeſqui-
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quintum, ditonum ſeſquiquartum, & hexachordum minus, vt .8. ad .5. quæ propor-
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tio dicitur ſupertripartiens quintas, & hexachordum maius, vt .5. ad .3. hęc autem vo
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catur ſuperbipartienstertias; </
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<
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">omnium ſimplicium conſonantiarum cognitioni, ex-
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tremam impoſuit manum. </
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<
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