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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[4.18.] Quomodo dignoſcatur proportio uelocitatis duorum ſimilium corporum omogeniorum inaqualium. CAP. XVIII.
Page: 191 (179)
[4.19.] Quam ſit inanis ab Ariſtotele ſuſcepta demonſtratio quod uacuum non detur. CAP. XIX.
Page: 191 (179)
[4.20.] Non ſatis dilucidè Ariſtotelem de loco ratiocinatum fuiße. CAP. XX.
Page: 192 (180)
[4.21.] Vtrum bene Aristoteles ſenſerit de infinito. CAP. XXI.
Page: 193 (181)
[4.22.] Exagitatur ab Ariſtotele adductatemporis definitio. CAP. XXII.
Page: 194 (182)
[4.23.] Motum rectum eſſe continuum, uel dißentiente Ariſtotele. CAP. XXIII.
Page: 195 (183)
[4.24.] Idem uir grauisſimus an bene ſenſerit de motibus corporum uiolentis & natur alibus. CAP. XXIIII.
Page: 196 (184)
[4.25.] Motum rectum & natur alem non eſſe primo & per ſe quicquid Ariſtoteli uiſum ſit. CAP. XXV.
Page: 196 (184)
[4.26.] Omne corpus eſſe in loco proprio graue, ut Aristoteli placuit, non eft admittendum. CAP. XXVI.
Page: 197 (185)
[4.27.] Haud admittendam opinionem Principis Peripateticorum de circulo, & ſpbæra. CAP. XXVII.
Page: 197 (185)
[4.28.] Occultam fuiße grauisſimo Stagirit & canſam ſcintilla-tionis ſtellarum. CAP. XXVIII.
Page: 198 (186)
[4.29.] Daricontinuum infinitum motum ſuper rectam at que finitam lineam. CAP. XXIX.
Page: 198 (186)
[4.30.] Non eſſe ſolis calorem à motu localι ipſius corporis ſolaris, ut Ariſtoteli placuit. CAP. XXX.
Page: 199 (187)
[4.31.] Vnde caloris ſolis prode at incrementum & state, et byeme decrementum. CAP. XXXI.
Page: 200 (188)
[4.32.] Nullum corpus ſenſus expers à ſono offendi, præterquam Aristoteles crediderit. CAP. XXXII.
Page: 201 (189)
[4.33.] Pytagoreorum opinionem de ſonitu corporum cælestium non fuiſſe ab Aristotele ſublatam. CAP. XXXIII.
Page: 202 (190)
[4.34.] Deraro et denſo nonnulla, minus diligenter à Peripateticis perpenſa. CAP. XXXIIII.
Page: 203 (191)
[4.35.] Motum rectum curuo poſſe comparari etiam diſentiente Ariſtotele. CAP. XXXV.
Page: 206 (194)
[4.36.] Minus ſufficienter exploſam fuiſſe ab Ariſtotele opinionem cre-dentium plures mundos exiſtere. CAP. XXXVI.
Page: 207 (195)
[4.37.] Anrectè loquutus ſit Phyloſopbus de extenſione luminis per uacuum. CAP. XXXVII.
Page: 208 (196)
[4.38.] An rectè phyloſophiœ penus Ariſtoteles ſenſerit de loco im-pellendo à pyramide. CAP. XXXVIII.
Page: 208 (196)
[4.39.] Examinatur quam ualida ſit ratio Aristotelis de inalterabilitate Cœli. CAP. XXXIX.
Page: 209 (197)
[5.] IN QVINTVM EVCLIDIS LIBRVM
Page: 210 (198)
[Item 5.1.]
Page: 210 (198)
[5.1.1.] Horum autem primum est.
Page: 210 (198)
[5.1.2.] SECVNDVM.
Page: 210 (198)
[5.1.3.] TERTIVM. Quę est εuclidis ſeptima propoſitio.
Page: 210 (198)
[5.1.4.] QVARTVM. εuclidis uerò nona propoſitio.
Page: 211 (199)
[5.1.5.] QVINTVM. Euclidis uerò octaua propoſitio.
Page: 211 (199)
[5.1.6.] SEXTVM. εuclidis uerò decima propoſitio.
Page: 211 (199)
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                ad velocitatem per aquam vt
                  <var>.e.a.</var>
                ad
                  <var>.a.u.</var>
                non erit ergo vt
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                ad
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                <s xml:id="echoid-s2037" xml:space="preserve">Ob hanc igitur
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                cauſam nimis diſſentaneum eſt rationi, opi-
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                nari proportionem velocitatis omnium cor
                  <lb/>
                porum grauium per aerem vnam
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                eſſe cum velocitate eorundem per aquam,
                  <lb/>
                quemadmodum Ariſtoteles ſenſit.</s>
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            <div xml:id="echoid-div394" type="section" level="3" n="5">
              <head xml:id="echoid-head251" style="it" xml:space="preserve">Exempla dictorum.</head>
              <head xml:id="echoid-head252" xml:space="preserve">CAP.V.</head>
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                <s xml:id="echoid-s2038" xml:space="preserve">POnamus, exempli gratia, aquam eſſe in denſitate dupla ad aerem, & aliquod
                  <lb/>
                graue corpus in aqua duplum ad denſitatem ipſius aquæ, vnde dictum corpus in
                  <lb/>
                denſitate ad aerem quadruplum erit; </s>
                <s xml:id="echoid-s2039" xml:space="preserve">quam ob cauſam, mediam ſui ponderis tota-
                  <lb/>
                lis partem in aqua, & in aere quartam partem, ex .7. lib. de inſidentibus aquæ ab Ar-
                  <lb/>
                chimede conſcripto, amitteret. </s>
                <s xml:id="echoid-s2040" xml:space="preserve">Moueretur igitur in aqua virtute illius mediæ partis
                  <lb/>
                  <reg norm="ponderis" type="context">põderis</reg>
                ſui, in aere
                  <reg norm="autem" type="wordlist">aũt</reg>
                uirtute
                  <reg norm="trium" type="context">triũ</reg>
                  <reg norm="quartarum" type="context">quartarũ</reg>
                ; </s>
                <s xml:id="echoid-s2041" xml:space="preserve">vnde proportio facultatis
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                dicti
                  <lb/>
                corporis in aere ad facultatem mouentem eiuſde m in aqua ſeſquialtera erit. </s>
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                  <reg norm="hocque" type="simple">hocq́;</reg>
                  <lb/>
                corpus appelletur
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                <s xml:id="echoid-s2043" xml:space="preserve">Sit aliud quoque corpus, quod
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                nominetur, ſimile figura, &
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                magnitudine corporea corpori
                  <var>.A.</var>
                ſed
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                , in proportione ſeſquialtera ad
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                ,
                  <lb/>
                & denſius erit aere in proportione tripla. </s>
                <s xml:id="echoid-s2044" xml:space="preserve">quamobrem corpus
                  <var>.A.</var>
                grauius erit cor-
                  <lb/>
                pore
                  <var>.B.</var>
                in aere in proportione ſeſquialtera, vnde etiam velocius erit ipſo
                  <var>.B.</var>
                in aere
                  <lb/>
                in eadem proportione, ſed corpus
                  <var>.B.</var>
                in aere, duplo maius pondus habebit,
                  <reg norm="quam" type="context">quã</reg>
                in
                  <lb/>
                aqua, cum in aere remaneant ei duæ ponderis tertiæ partes, & in aqua vna tantum,
                  <lb/>
                ita vt Ariſtoteli concedam corpus
                  <var>.B.</var>
                in aere, quam in aqua velocius futurum in ea-
                  <lb/>
                dem proportione, in qua, aqua eſt
                  <reg norm="denſior" type="context">dẽſior</reg>
                aere, ex Euclidis vndecima propoſitione
                  <lb/>
                lib. quinti. </s>
                <s xml:id="echoid-s2045" xml:space="preserve">Sed præter hæc omnia, ſi corpus
                  <var>.A.</var>
                eſſet etiam velocius in aere,
                  <reg norm="quam" type="context">quã</reg>
                in
                  <lb/>
                aqua, in eadem proportione, ſequeretur ex .16. dicti lib. quinti proportionem velo-
                  <lb/>
                citatis
                  <var>.A.</var>
                in aqua ad
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                ipſius
                  <var>.B.</var>
                in aqua etiam ſeſquialteram eſſe. </s>
                <s xml:id="echoid-s2046" xml:space="preserve">Sed cum
                  <lb/>
                corpus
                  <var>.A.</var>
                in denſitate ad aquam
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                ſit, & corpus
                  <var>.B.</var>
                  <reg norm="ſeſquialterum" type="context">ſeſquialterũ</reg>
                ad ipſam
                  <reg norm="aquam" type="context">aquã</reg>
                ,
                  <lb/>
                ſequetur
                  <reg norm="proportionem" type="context">proportionẽ</reg>
                ponderis ipſius
                  <var>.A.</var>
                ad
                  <reg norm="pondus" type="context">põdus</reg>
                ipſius
                  <var>.B.</var>
                in aqua eſſe in propor-
                  <lb/>
                tione dupla; </s>
                <s xml:id="echoid-s2047" xml:space="preserve">Vnde ex primo ſuppoſito capitis ſecundi proportio velocitatis
                  <var>.A.</var>
                ad
                  <lb/>
                velocitatem
                  <var>.B.</var>
                in aqua dupla erit, non ſeſquialtera. </s>
                <s xml:id="echoid-s2048" xml:space="preserve">Si ergo proportio velocitatis
                  <var>.
                    <lb/>
                  A.</var>
                ad eam quæ eſt
                  <var>.B.</var>
                in aqua dupla eſt, & ea, quæeſt
                  <var>.B.</var>
                in aere, ad eam, quæ eſt ipſius
                  <lb/>
                per aquam eſt etiam dupla (vnde ea quę eſt
                  <var>.A.</var>
                per aquam ęqualis erit ei, quæ eſt
                  <var>.B.</var>
                  <lb/>
                peraerem, ex .9. lib. quinti) & cum ea, quæ eſt
                  <var>.A.</var>
                ſit ei, quæ eſt
                  <var>.B.</var>
                per aerem ſeſqui-
                  <lb/>
                altera, erit ergo ea, quæ eſt
                  <var>.A.</var>
                per aerem, ei, quæ eſt ſuimet ipſius per aquam ſeſqui
                  <lb/>
                altera, non autem dupla, ex .7. eiuſdem libr. quinti. </s>
                <s xml:id="echoid-s2049" xml:space="preserve">Hiſce rationibus accedimus ad
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                confirmandam veritatem vltimi ſuppoſiti cap .2. proportionem videlicet velocita
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                tis
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                naturalis in diuerſis medijs
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                corporis
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                in ipſis medijs eſſe ean
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                dem cum ea, quæeſt inter pondera
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                dicti corporis in dictis medijs. de ijs
                  <lb/>
                tamen medijs intelligendo, quæ un-
                  <lb/>
                ctuoſa, aut pinguia non ſunt, ut ſunt
                  <lb/>
                oleum, lac, aut huiuſmodialia, quæà
                  <lb/>
                qualibet minima qualitate frigoris
                  <lb/>
                aut caloris alterantur, & impermea-
                  <lb/>
                biles fiunt.</s>
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