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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[3.13.] Quòd Ariſtotelisratio in 6. quæſtione poſit a non ſit admittenda. CAP. XIII.
Page: 167 (155)
[3.14.] Quòdrationes ab Ariſtotele de octaua quæstione confictæ ſufficient es non ſint. CAP. XIIII.
Page: 167 (155)
[3.15.] Quod Aristotelis ratio none queſtionis admittendanon ſit. CAP. XV.
Page: 171 (159)
[3.16.] Quod Aristotelis rationes de decima queſtione ſint reijciende. CAP. XVI.
Page: 171 (159)
[3.17.] De uer a cauſa .12. questionis mechanice. CAP. XVII.
Page: 172 (160)
[3.18.] De decimatertia questione. CAP. XVIII.
Page: 173 (161)
[3.19.] De decimaquart a queſtione. CAP. XIX.
Page: 173 (161)
[3.20.] De uer a r atione .17. queſtionis. CAP. XX.
Page: 174 (162)
[3.21.] De uera & intrinſeca cauſa trocble arum. CAP. XXI.
Page: 175 (163)
[3.22.] Depropria cauſa .24. quæſtionis. CAP. XXII.
Page: 177 (165)
[3.23.] De uer a cauſa .30. quæstionis. CAP. XXIIII.
Page: 179 (167)
[3.24.] Deratione .35. & ultimæ quæstionis. CAP. XXV.
Page: 179 (167)
[4.] DISPVTATIONES DE QVIBVSDAM PLACITIS ARISTOTELIS.
Page: 180 (168)
[4.1.] Qualiter & ubi Ariſtoteles de uelocitate motuum natura-lium localium aliter tractauerit quam nos ſentiamus. CAP.I.
Page: 180 (168)
[4.2.] Quædam ſupponenda ut conſtet cur circa uelocit atem motuum natur alium localium ab Ariſtotelis placitis recedamus. CAP. II.
Page: 181 (169)
[4.3.] Poſſe uelocitatem alicuius corporis proportionem contrariam in diuerſis medijs habere cum denſitate eorum. CAP. III.
Page: 182 (170)
[4.4.] Oſcitanter ab Ariſtotele nonnibil prolatum cap 8. lib. 4 Phyſicorum. CAP. IIII.
Page: 182 (170)
[4.5.] Exempla dictorum. CAP.V.
Page: 183 (171)
[4.6.] Quod proportiones ponderum eiuſdem corporis in diuerſis medijs pro portiones eorum mediorum denſit atum non ſeruant. Unde ne-ceßariò inæquales proportiones uelocitatum producuntur. CAP. VI.
Page: 184 (172)
[4.7.] Corpora grauia aut leuia eiuſdem figur æ et materiæ ſed inæqualis magnitudinis, in ſuis motibus natur alibus uelocit atis, in eo dem medio, proportionem longè diuerſam ſeruatura eße quam Aristoteliuiſum fuerit. CAP. VII.
Page: 184 (172)
[4.8.] Quod duo corpor a in æqualia eiuſdem materia in diuerſis medijs eandem uelocitatis proportionem retinebunt. CAP. VIII.
Page: 185 (173)
[4.9.] Anrectè Aristoteles diſeruerit de proportionibus mo-tuum in uacuo. CAP. IX.
Page: 186 (174)
[4.10.] Quòd in uacuo corpor a eiuſdem materiæ æquali uelocita-te mouerentur. CAP.X.
Page: 186 (174)
[4.11.] Corpora licet inæqualia eiuſdem materiæ & figuræ, ſireſiſten-tias habuerint ponderibus proportionales æqualiter mouebuntur. CAP. XI.
Page: 187 (175)
[4.12.] Maior hic demonſir atur eſſe proportio ponder is corpor is den ſioris ad pondus minus denſi in medijs dẽſioribus, quam ſit eorundem corporum in medio minus denſo, nec corporum ponder a ſeruare proportionem denſitatis mediorum. CAP. XII.
Page: 187 (175)
[4.13.] Longe aliter ueritatem ſe habere quam Aristoteles doceat in fine libri ſeptimi phyſicorum. CAP. XIII.
Page: 188 (176)
[4.14.] Quid ſequatur ex ſupradistis. CAP. XIIII.
Page: 189 (177)
[4.15.] Numrestè ſenſerit Philoſophus reſistentias proportionales eße cum corporibus mobilibus. CAP. XV.
Page: 189 (177)
[4.16.] Fdipſum aliter demonſtr atur. CAP. XVI.
Page: 190 (178)
[4.17.] De alio Aristo. lapſu. CAP. XVII.
Page: 190 (178)
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            <div xml:id="echoid-div146" type="math:theorem" level="3" n="74">
              <p>
                <s xml:id="echoid-s642" xml:space="preserve">
                  <pb o="49" rhead="THEOREM. ARIT." n="61" file="0061" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0061"/>
                Secundus tertiusq́ue terminus reperiuntur, eſt
                  <lb/>
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                    <image file="0061-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0061-01"/>
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                enim ſecundus
                  <var>.e.i.</var>
                tertius
                  <var>.i.o.</var>
                et
                  <var>.e.a.</var>
                quando-
                  <lb/>
                quidem ex præſuppoſito
                  <var>.e.i.</var>
                æqualis eſt
                  <var>.s.q.</var>
                et
                  <lb/>
                  <var>i.o.</var>
                æqualis
                  <var>.r.c.</var>
                et
                  <var>.a.e.</var>
                cum ſit æqualis
                  <var>.g.t.</var>
                cui
                  <lb/>
                pariter æqualis eſt
                  <var>.r.u.</var>
                ex quo
                  <var>.a.e.</var>
                æqualis
                  <lb/>
                eſt
                  <var>.u.r</var>
                . </s>
                <s xml:id="echoid-s643" xml:space="preserve">Itaque illud ſequitur
                  <var>.a.o.</var>
                ipſi
                  <var>.q.p.</var>
                  <lb/>
                æqualem eſſe.</s>
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            <div xml:id="echoid-div148" type="math:theorem" level="3" n="75">
              <head xml:id="echoid-head91" xml:space="preserve">THEOREMA
                <num value="75">LXXV</num>
              .</head>
              <p>
                <s xml:id="echoid-s644" xml:space="preserve">CVR ſumma duorum terminorum extremorum imparium arithmeticæ pro-
                  <lb/>
                portionalitatis ſemper duplo medij termini æqualis eſt.</s>
              </p>
              <p>
                <s xml:id="echoid-s645" xml:space="preserve">Exempli gratia, ſunt hitres termini proportionalitatis arithmeticæ .20. 15. 10
                  <lb/>
                ſumma duorum extremorum erit .30. quæ duplum eſt medij termini .15.</s>
              </p>
              <p>
                <s xml:id="echoid-s646" xml:space="preserve">Quod vt ſpeculemur, tres termini, tribus lineis
                  <var>.b.d</var>
                :
                  <var>n.u.</var>
                et
                  <var>.q.p.</var>
                  <reg norm="ſignificentur" type="context">ſignificẽtur</reg>
                . </s>
                <s xml:id="echoid-s647" xml:space="preserve">Di-
                  <lb/>
                co nunc quòd ſumma
                  <var>.b.d.</var>
                cum
                  <var>.q.p.</var>
                nempe
                  <var>.
                    <lb/>
                  h.d.</var>
                ſemper duplo
                  <var>.n.u.</var>
                ſcilicet
                  <var>.g.u.</var>
                æqualis
                  <lb/>
                  <figure xlink:label="fig-0061-02" xlink:href="fig-0061-02a" number="84">
                    <image file="0061-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0061-02"/>
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                erit. </s>
                <s xml:id="echoid-s648" xml:space="preserve">Tum differentia
                  <var>.b.d.</var>
                ad
                  <var>.n.u.</var>
                ſit
                  <var>.c.d.</var>
                quæ
                  <lb/>
                æqualis erit
                  <var>.e.u.</var>
                differentiæ inter
                  <var>n.u.</var>
                et
                  <var>.q.p.</var>
                  <lb/>
                patet enim in linea
                  <var>.h.d</var>
                :
                  <var>b.c.</var>
                æqualem eſſe
                  <var>.n.
                    <lb/>
                  u.</var>
                ſed
                  <var>.n.u.</var>
                ex
                  <var>.n.e.</var>
                componitur æquali
                  <var>.q.p.</var>
                et
                  <lb/>
                ex
                  <var>.e.u.</var>
                æquali
                  <var>.c.d.</var>
                cum
                  <reg norm="itaque" type="simple">itaq;</reg>
                in
                  <var>.h.d.</var>
                partem
                  <var>.
                    <lb/>
                  h.b.</var>
                reperiamus æqualem
                  <var>.n.e.</var>
                gratia
                  <var>.q.p.</var>
                &
                  <lb/>
                partem
                  <var>.c.d.</var>
                æquale
                  <var>m.e.u.</var>
                manifeſtum erit
                  <lb/>
                  <var>h.d.</var>
                æqualem eſſe
                  <var>.g.u</var>
                .</s>
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              <head xml:id="echoid-head92" style="it" xml:space="preserve">BINA PROBLEMAT A EX DVOBVS PRAEDICTIS
                <lb/>
              THEOREMATIBVS DEPENDENTIA.</head>
              <p>
                <s xml:id="echoid-s649" xml:space="preserve">EX duobus prædictis theorematibus duo problemata oriuntur,
                  <reg norm="quorum" type="context">quorũ</reg>
                primum
                  <lb/>
                eſt. </s>
                <s xml:id="echoid-s650" xml:space="preserve">Datis tribus quantitatibus cognitis, ſi quis quartam inuenire voluerit,
                  <lb/>
                quæ eiuſmodi ſit reſpectu tertiæ, qualis eſt ſecunda reſpectu primæ, ſecunda cum
                  <lb/>
                tertia in ſummam colligenda erit, ex qua detracta prima, ſupererit quarta.</s>
              </p>
              <p>
                <s xml:id="echoid-s651" xml:space="preserve">Exempli gratia, cognitis tribus quantitatibus .20. 17. 9. ſi quartam inuenire vo
                  <lb/>
                luerimus eiuſmodi proportionem cum tertia arithmeticè ſeruantem, quam ſecunda
                  <lb/>
                cum prima, ſecundam cum tertia in ſummam colligemus,
                  <reg norm="dabiturque" type="simple">dabiturq́;</reg>
                ſumma .26. ex
                  <lb/>
                qua detracta prima quantitate, quarta relinquetur nempe .6. quod ex .74. theore-
                  <lb/>
                mate dependet.</s>
              </p>
              <p>
                <s xml:id="echoid-s652" xml:space="preserve">Idipſum tamen proueniret ſi quis ex tertio termino differentiam primi atque ſe-
                  <lb/>
                cundi detraheret; </s>
                <s xml:id="echoid-s653" xml:space="preserve">hæc tamen via non tam vniuerſalis eſtqu àm illa. </s>
                <s xml:id="echoid-s654" xml:space="preserve">N ſi quartus ter
                  <lb/>
                minus incognitus tertio maior eſſe deberet, dictam differentiam cum tertio termi-
                  <lb/>
                mino in ſummam colligere oporteret.</s>
              </p>
              <p>
                <s xml:id="echoid-s655" xml:space="preserve">Alterum problema eſt, quòd inuentis duobus terminis, ſi tertius requiratur, ſe-
                  <lb/>
                cundus duplicandus erit, ex qua ſumma detracto primo, ſtatim tertius proferetur,
                  <lb/>
                quod problema ex præcedenti theoremate dependet.</s>
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