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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                <head xml:id="echoid-head336" xml:space="preserve">NONVM.</head>
                <head xml:id="echoid-head337" style="it" xml:space="preserve">Euclidis uero tertiadecima propoſitio.</head>
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                    <emph style="sc">Qvotiescvnqve</emph>
                  aliqua proportio plurium proportionum inuicem æqua-
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                  lium, tertia aliqua proportione, maior aut minor fuerit, quælibet prædictarum æqua
                    <lb/>
                  lium inter ſe, tertia illa proportione maior aut minor pariter erit.</s>
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                <head xml:id="echoid-head338" xml:space="preserve">DECIMVM.</head>
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                    <emph style="sc">Qvotiescvnqve</emph>
                  fuerint ex vna parte plurestermini (ſiue coniuncti ſiue di-
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                  ſiuncti ſint) æquales ſinguli vni tertio termino; </s>
                  <s xml:id="echoid-s2426" xml:space="preserve">ex altera verò parte totidem fuerint
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                  alteri tertio termino æquales, proportio aggregati priorum terminorum ad
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                  ter-
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                  tium, æqualis erit proportioni aggregati reliquorum terminorum ad ſuum tertium,
                    <lb/>
                  & è conuerſo, ita ſe habebit primus tertius terminus ad ſuos multos terminos, ſicut
                    <lb/>
                  ſe habet ſecundus tertius terminus ad ſuos ſimul ſumptos.</s>
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                <head xml:id="echoid-head339" xml:space="preserve">VNDECIMVM.</head>
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                  <s xml:id="echoid-s2427" xml:space="preserve">Aggregatum ex partibus proportiona litatis continuæ, quod inter maximum, &
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                  minimum terminum omnium terminorum proportionalium compræhenditur, ſem
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                  per multiplex eſt ad ſingulas partiales proportiones, ex quibus ipſum componitur.</s>
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                <head xml:id="echoid-head340" xml:space="preserve">DVODECIMVM.</head>
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                  <s xml:id="echoid-s2428" xml:space="preserve">Quæuis proportio quocunque modo diuiſa fuerit, ex iis partibus componitur, in
                    <lb/>
                  quas diuiditur.</s>
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                  <s xml:id="echoid-s2429" xml:space="preserve">Cum enim bæ præpoſitiones ſint ita conſpicuæ ipſi intellectui, ut
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                  dubio inter obie
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                  ct a ipſius intellectus connumerari poſſint, nullus ſanæ mentis eas negabit.</s>
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                <head xml:id="echoid-head341" xml:space="preserve">THEOR.I. II. ET III.</head>
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                  <s xml:id="echoid-s2430" xml:space="preserve">PRimum, ſecundum, & tertium theorema quinti Euclidis ab ipſo ſatis exactè de
                    <lb/>
                  monſtratur, ſtudioſus itaque autorem conſulat.</s>
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                <head xml:id="echoid-head342" xml:space="preserve">THEOREM. IIII.</head>
                <p>
                  <s xml:id="echoid-s2431" xml:space="preserve">QVartum vero Theorema Eu-
                    <lb/>
                    <figure xlink:label="fig-0212-01" xlink:href="fig-0212-01a" number="262">
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                  clidis ego ſic
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                  .
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                  <s xml:id="echoid-s2432" xml:space="preserve">ſit, verbi gratia, proportio
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                  quæ eſt
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                  ad
                    <var>.d.</var>
                  ſumptis multiplici-
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                  bus
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                  et
                    <var>.f.</var>
                  ad
                    <var>.a.</var>
                  et
                    <var>.c.</var>
                  æqualiter, item
                    <lb/>
                  multiplicibus
                    <var>.g.</var>
                  et
                    <var>.h.</var>
                  ad
                    <var>.b.</var>
                  et
                    <var>.d.</var>
                  dico
                    <lb/>
                  proportionem
                    <var>.e.</var>
                  ad
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                  eſſe eandem
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                  quæ eſt
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                  ad
                    <var>.h</var>
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                  <s xml:id="echoid-s2433" xml:space="preserve">Habemus enim ex .10
                    <lb/>
                  poſtulato præmiſſo, eandem futuram
                    <lb/>
                  proportionem
                    <var>.e.</var>
                  ad
                    <var>.a.</var>
                  quæ eſt
                    <var>.f.</var>
                  ad
                    <var>.c.</var>
                    <lb/>
                  & ita
                    <var>.b.</var>
                  ad
                    <var>.g.</var>
                  quæ eſt
                    <var>.d.</var>
                  ad
                    <var>.h.</var>
                  ex præ-
                    <lb/>
                  ſuppoſito verò
                    <reg norm="cum" type="context">cũ</reg>
                  ſic ſe habeat
                    <var>.a.</var>
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                    <lb/>
                  b. ſicut
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                    <var>.d.</var>
                  erit ex primo poſtula-
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                  <s xml:id="echoid-s2434" xml:space="preserve">Nam proportio
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                    <var>.g.</var>
                  compo
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                  nitur ex eis quæ ſunt
                    <var>.e.</var>
                  ad .a: et
                    <var>.a.</var>
                  ad
                    <var>. </var>
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