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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IO. BAPT. BENED.
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            <div xml:id="echoid-div432" type="section" level="3" n="32">
              <pb o="190" rhead="IO. BAPT. BENED." n="202" file="0202" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0202"/>
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            <div xml:id="echoid-div433" type="section" level="3" n="33">
              <head xml:id="echoid-head307" style="it" xml:space="preserve">Pytagoreorum opinionem de ſonitu corporum cælestium non
                <lb/>
              fuiſſe ab Aristotele ſublatam.</head>
              <head xml:id="echoid-head308" xml:space="preserve">CAP. XXXIII.</head>
              <p>
                <s xml:id="echoid-s2289" xml:space="preserve">SEnſerunt Pythagorici orbes cæleſtes dum circunuoluuntur, non autem corpora
                  <lb/>
                ſtellarum ſolum, æd ere ſonu. </s>
                <s xml:id="echoid-s2290" xml:space="preserve">Quibus dum Ariſtoteles contradicere cogitat,
                  <lb/>
                maximè fauet. </s>
                <s xml:id="echoid-s2291" xml:space="preserve">Eatamen opinio è phyloſophorum ſcholis eſt explodenda, quia aut
                  <lb/>
                orbes ſunt ſibi ipſis contigui, aut inuicem diſtantes: </s>
                <s xml:id="echoid-s2292" xml:space="preserve">ſi ab inuicem diſtant (quod
                  <lb/>
                nemo adhuc conceſſit, quia hac ratione vacuum introduceretur) clarum eſt, quod
                  <lb/>
                cum ſe minime tangant, ſonum edere nequeunt: </s>
                <s xml:id="echoid-s2293" xml:space="preserve">Si verò eorum vnus alteri ſit conti
                  <lb/>
                guus,
                  <reg norm="neque" type="simple">neq;</reg>
                etiam ab ipſis ſonus reſultare poterit, quia pro certo putandum eſt,
                  <reg norm="ipſorum" type="context">ipſorũ</reg>
                  <lb/>
                ſuperficies tam politas eſſe, ac lenas, vt nihil omnino aſperitatis, aut inæqualitatis
                  <lb/>
                contineant. </s>
                <s xml:id="echoid-s2294" xml:space="preserve">Vt exempli gratia, ſi aliquis duo ſpecula plana inuicem confricaret, nul
                  <lb/>
                lum planè ſonum audiret, ſed ſi hoc faceret cum duabus ſuperficiebus a ſperis,
                  <reg norm="ſonum" type="context">ſonũ</reg>
                  <lb/>
                perſentiret, & tanto maiorem; </s>
                <s xml:id="echoid-s2295" xml:space="preserve">quantò aſperiores eſſent dictæ ſuperficies, & qui vult
                  <lb/>
                vtarcus lirę, ex corda ſonum eliciat, colophonia dictum arcum illinet, vt aſperiorem
                  <lb/>
                reddat. </s>
                <s xml:id="echoid-s2296" xml:space="preserve">Neceſſarium quoque eſt vt tremat ſiue trepidet corpus, quod
                  <reg norm="ſonum" type="context">ſonũ</reg>
                edere
                  <lb/>
                debet; </s>
                <s xml:id="echoid-s2297" xml:space="preserve">Neque etiam abſque aere ſonus efficipotelt, quia aer ſonat ingrediendo
                  <lb/>
                velociter ad implendum locum, vt non remaneat vacuus. </s>
                <s xml:id="echoid-s2298" xml:space="preserve">Sed ſupponendo in æche
                  <lb/>
                rea regione neque aerem eſſe, neque corpus aliquod fluidum, clarè patebit orbes
                  <lb/>
                cœleſtes ex ſeſe nullum emittere ſonum. </s>
                <s xml:id="echoid-s2299" xml:space="preserve">Idem affirmo de fricatione ſuperficiei con
                  <lb/>
                cauæ infimi orbis lunaris cum conuexa materiæ à dicto orbe contentæ, ſuperioribus
                  <lb/>
                rationibus fultus, vt etiam experientia à corpore aliquo fluido, quod in alio velociſ
                  <lb/>
                ſimè moueretur deſumpta fretus, cuius corporis ſuperficies tamen lenis eſſet, à quo
                  <lb/>
                ſonus non gigneretur. </s>
                <s xml:id="echoid-s2300" xml:space="preserve">Et non minus dicere poſſum, corpus fluidum moueri in con-
                  <lb/>
                tinente loco immobili, quam dictum corpus continens illud eſſe, quod moueretur,
                  <lb/>
                & non fluidum corpus. </s>
                <s xml:id="echoid-s2301" xml:space="preserve">Cuius rei poſſumus etiam exemplum habere à quouis
                  <lb/>
                corpore perfectè rotundo, quod circa ſuum axem velociſſimè moueatur, nullum ſo-
                  <lb/>
                num efficiet, quia nullam aeris partem extra ſuum
                  <reg norm="locum" type="context">locũ</reg>
                impellit dum mouetur non
                  <lb/>
                ſecundum totum, ſed ſecundum ſuas partes, quarum quælibet abſque reſiſtentia im-
                  <lb/>
                mediatè ſubintrat locum alterius, abſque temporis interpoſitione. </s>
                <s xml:id="echoid-s2302" xml:space="preserve">nec huiuſmodi
                  <lb/>
                locum aliquo modo eadem materia dicti corporis, quod circunuoluitur: </s>
                <s xml:id="echoid-s2303" xml:space="preserve">deſtitutum
                  <lb/>
                dimittat. </s>
                <s xml:id="echoid-s2304" xml:space="preserve">Sed ſi Pythagorici de alia quadam harmoniæ ſpecie ab ea, quæ eſt ſono-
                  <lb/>
                rum, vt à diuerſis velocitatibus motuum, aut à diuerſis magnitudinibus aut diſtantiis,
                  <lb/>
                aut ſtellarum influxibus intellexiſſent, rectè ſenſiſſent exparte, non autem omnino,
                  <lb/>
                quia ea harmoniam efficere nequeunt, quæ ad
                  <reg norm="inuicem" type="context">inuicẽ</reg>
                ſecundum interualla harmoni-
                  <lb/>
                ca proportionata non ſunt, vt ſunt dupla, ſeſquial tera, ſeſquitertia, ſeſquiquarta, ſeſ-
                  <lb/>
                quiquinta, ſupertripartientia quintas,
                  <reg norm="ſuperbipartientia" type="context">ſuperbipartiẽtia</reg>
                tertias, & quę ab ijs
                  <reg norm="dependent" type="context">dependẽt</reg>
                  <lb/>
                ideſt coniuncta ſunt cum duplis; </s>
                <s xml:id="echoid-s2305" xml:space="preserve">de conſonantijs loquendo. de diſſonantiis idem di
                  <lb/>
                co, quæ harmonicis inſeruiunt modulationibus, vt
                  <reg norm="ſeſquioctauum" type="context">ſeſquioctauũ</reg>
                ,
                  <reg norm="ſeſquinonum" type="context">ſeſquinonũ</reg>
                , ſeſqui
                  <lb/>
                  <reg norm="quintundecimum" type="context context">quintũdecimũ</reg>
                ,
                  <reg norm="ſequiuigeſimunquartum" type="context context">ſequiuigeſimũquartũ</reg>
                ,
                  <reg norm="ſeſquioctuogeſimum" type="context">ſeſquioctuogeſimũ</reg>
                , & ſuperbipartiens vigeſi
                  <lb/>
                masquintas. </s>
                <s xml:id="echoid-s2306" xml:space="preserve">
                  <reg norm="Verum" type="context">Verũ</reg>
                quidem eſt nonnulla harmonica interualla in aſpectibus
                  <reg norm="comperta" type="context">cõperta</reg>
                  <lb/>
                fuiſſe, vt Prolomeus oſtendit, & alii quoque aſſerunt. </s>
                <s xml:id="echoid-s2307" xml:space="preserve">ineſt tamen huic rei nonnihil
                  <lb/>
                difficultatis. </s>
                <s xml:id="echoid-s2308" xml:space="preserve">vt exempli gratia, ſi ſubtrahamus diateſſaron extra diapaſon, remanet
                  <lb/>
                diapente, & ſi à diapente ſubtrahamus ſemiditonum, remanet ditonum (quæ duæ </s>
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