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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                dio minus denſo, quàm ipſum ſit, (quia in medio ſe denſiore ſi poner etur, non graue
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                <s xml:id="echoid-s2029" xml:space="preserve">& poſito deinde eodem cor
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                <s xml:id="echoid-s2030" xml:space="preserve">Dico proportionem velocitatis eiuſdem corporis per
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                minus denſum, ad velocitatem eiuſdem per medium magis denſum futuram vt
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                eſſe, vt
                  <var>.u.i.</var>
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                  <var>.e.i.</var>
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                <s xml:id="echoid-s2031" xml:space="preserve">Quæne
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                nc diximus,
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                planè ſimilia ſuntijs, quæ ſupra ſcripſimus, quia idem eſt dicere, proportionem velo
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                citatum, duorum corporum hetereogeneorum, ſed ſimilium figura, & magnitudine
                  <lb/>
                æ qualium, in vno ſolo medio, æqualem eſſe
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                proportioni ponderum ipſorum, vt ſi dicam?</s>
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                  <unsure/>
                  <lb/>
                proportionem velocitatum vnius ſolum cor-
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                poris per diuerſa media eandem eſſe cum ea.
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                quæ eſt
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              <head xml:id="echoid-head247" style="it" xml:space="preserve">Poſſe uelocitatem alicuius corporis proportionem contrariam
                <lb/>
              in diuerſis medijs habere cum denſitate eorum.</head>
              <head xml:id="echoid-head248" xml:space="preserve">CAP. III.</head>
              <p>
                <s xml:id="echoid-s2033" xml:space="preserve">POſſibile eſt in rerum natura corpus aliquod huiuſmodi denſitate præditum re-
                  <lb/>
                periri, vt velocitas eius motus naturalis per aerem, velocitati per aquamita pro
                  <lb/>
                portionata exiſtat, vt eſt
                  <reg norm="denſitas" type="context">dẽſitas</reg>
                aquæ denſitati aeris. </s>
                <s xml:id="echoid-s2034" xml:space="preserve">Denſitas aquæ notetur (exem-
                  <lb/>
                pli gratia) per
                  <var>.u.i.</var>
                & ea, quæaeris eſt per
                  <var>.e.i.</var>
                & pondus alicuius corporis in aere per
                  <lb/>
                  <var>e.a.</var>
                & pondus eiuſdem corporis in aqua per
                  <var>.u.a.</var>
                ita tamen, quod eadem proportio
                  <lb/>
                ſit
                  <var>.e.a.</var>
                ad
                  <var>.u.a.</var>
                vt
                  <var>.u.i.</var>
                ad
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                vnde per vltimam ſuppoſitionem
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                capitis, pro
                  <lb/>
                portio velocitatis prædicti corporis per aerem,
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                  <var>e.a.</var>
                ad
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              <head xml:id="echoid-head249" style="it" xml:space="preserve">Oſcitanter ab Ariſtotele nonnibil prolatum cap 8.
                <lb/>
              lib. 4 Phyſicorum.</head>
              <head xml:id="echoid-head250" xml:space="preserve">CAP. IIII.</head>
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                <s xml:id="echoid-s2035" xml:space="preserve">EX ſupradictis patet in vniuerſum non eſſe verum quod Ariſto .8. cap .4. lib. phy­
                  <lb/>
                ſicorum ſcribit, velocitates ſcilicet motuum alicuius corporis per diuerſa me-
                  <lb/>
                dia, proportionatas eſſe denſitatibus eorundem mediorum. </s>
                <s xml:id="echoid-s2036" xml:space="preserve">Quocirca, ſit propor-
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                tio
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                vt
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                aquę ad
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                  <reg norm="denſitatem" type="context">dẽſitatem</reg>
                .et
                  <var>.e.a.</var>
                ad
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                vt ponderis alicuius
                  <lb/>
                corporis in aere ad pondus eiuſdem in aqua, ita tamen vt maior aut minor propor-
                  <lb/>
                tio ſit
                  <var>.e.a.</var>
                ad
                  <var>.u.a.</var>
                quam
                  <var>.u.i.</var>
                ad
                  <var>.e.i.</var>
                vnde exiſtente proportione velocitatis per
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