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]

Table of contents

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[4.28.] Occultam fuiße grauisſimo Stagirit & canſam ſcintilla-tionis ſtellarum. CAP. XXVIII.
[4.29.] Daricontinuum infinitum motum ſuper rectam at que finitam lineam. CAP. XXIX.
[4.30.] Non eſſe ſolis calorem à motu localι ipſius corporis ſolaris, ut Ariſtoteli placuit. CAP. XXX.
[4.31.] Vnde caloris ſolis prode at incrementum & state, et byeme decrementum. CAP. XXXI.
[4.32.] Nullum corpus ſenſus expers à ſono offendi, præterquam Aristoteles crediderit. CAP. XXXII.
[4.33.] Pytagoreorum opinionem de ſonitu corporum cælestium non fuiſſe ab Aristotele ſublatam. CAP. XXXIII.
[4.34.] Deraro et denſo nonnulla, minus diligenter à Peripateticis perpenſa. CAP. XXXIIII.
[4.35.] Motum rectum curuo poſſe comparari etiam diſentiente Ariſtotele. CAP. XXXV.
[4.36.] Minus ſufficienter exploſam fuiſſe ab Ariſtotele opinionem cre-dentium plures mundos exiſtere. CAP. XXXVI.
[4.37.] Anrectè loquutus ſit Phyloſopbus de extenſione luminis per uacuum. CAP. XXXVII.
[4.38.] An rectè phyloſophiœ penus Ariſtoteles ſenſerit de loco im-pellendo à pyramide. CAP. XXXVIII.
[4.39.] Examinatur quam ualida ſit ratio Aristotelis de inalterabilitate Cœli. CAP. XXXIX.
[5.] IN QVINTVM EVCLIDIS LIBRVM
[Item 5.1.]
[5.1.1.] Horum autem primum est.
[5.1.2.] SECVNDVM.
[5.1.3.] TERTIVM. Quę est εuclidis ſeptima propoſitio.
[5.1.4.] QVARTVM. εuclidis uerò nona propoſitio.
[5.1.5.] QVINTVM. Euclidis uerò octaua propoſitio.
[5.1.6.] SEXTVM. εuclidis uerò decima propoſitio.
[5.1.7.] SEPTIMVM. Euclidis uerò undecima propoſitio.
[5.1.8.] OCTAVVM. εuclidis uerò duodecima propoſitio.
[5.1.9.] NONVM. Euclidis uero tertiadecima propoſitio.
[5.1.10.] DECIMVM.
[5.1.11.] VNDECIMVM.
[5.1.12.] DVODECIMVM.
[Item 5.2.]
[5.2.1.] THEOR.I. II. ET III.
[5.2.2.] THEOREM. IIII.
[5.2.3.] THEOR.V. ET VI.
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                    <num value="60">
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                    60.</num>
                  ) 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.</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
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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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                  cum ſuis radicibus
                    <var>.e.g.</var>
                  et
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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.</s>
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                <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>
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                    <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
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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. </s>
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                    <reg norm="Quando" type="wordlist">Qũo</reg>
                  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
                    <lb/>
                  praxi? </s>
                  <s xml:id="echoid-s3455" xml:space="preserve">vnde ſequetur
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                  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-
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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-
                    <lb/>
                  maſquintas appellatur, & cum cognouerit ſemiditonum conſonantem eſſe ſeſqui-
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                  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
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                  catur ſuperbipartienstertias; </s>
                  <s xml:id="echoid-s3458" xml:space="preserve">omnium ſimplicium conſonantiarum cognitioni, ex-
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                  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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