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-div71" type="math:theorem" level="3" n="32">
              <p>
                <s xml:id="echoid-s299" xml:space="preserve">
                  <pb o="21" rhead="THEOREM. ARIT." n="33" file="0033" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0033"/>
                retur .20. ſcilicet et .4. certè .24. perſingulas partes diuiſo, daretur vnum proue-
                  <lb/>
                niens ſex integra, & alterum vnum & quinta pars, quorum ſumma eſſet ſeptem in-
                  <lb/>
                tegra cum quinta parte, tum altera parte per alteram diuiſa, daretur vnum proue-
                  <lb/>
                niens quinque integrorum & alterum vnius quinti tantum, quorum ſumma eſſet
                  <lb/>
                quinque integra, & vna quinta pars, minor prima reliquorum duorum prouenien-
                  <lb/>
                tium per binarium.</s>
              </p>
              <p>
                <s xml:id="echoid-s300" xml:space="preserve">Cuius conſiderationis cauſa, propoſitus numerus linea
                  <var>.q.p.</var>
                ſignificetur, eius duę
                  <lb/>
                partes lineis
                  <var>.q.x.</var>
                et
                  <var>.x.p.</var>
                  <reg norm="tum" type="context">tũ</reg>
                  <var>.q.f.</var>
                ſit proueniens ex diuiſione totius
                  <var>.q.p.</var>
                per
                  <var>.x.p.</var>
                et
                  <var>.
                    <lb/>
                  q.i.</var>
                ſit proueniens ex diuiſione eiuſdem
                  <var>.q.p.</var>
                per
                  <var>.q.x.</var>
                adhæc
                  <var>.h.m.</var>
                ſit proueniens,
                  <lb/>
                ex diuiſione
                  <var>.q.x.</var>
                per
                  <var>x.p.</var>
                et
                  <var>.h.k.</var>
                proue-
                  <lb/>
                niensex diuiſione
                  <var>.p.x.</var>
                per
                  <var>.q.x.</var>
                patet igi-
                  <lb/>
                  <figure xlink:label="fig-0033-01" xlink:href="fig-0033-01a" number="44">
                    <image file="0033-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0033-01"/>
                  </figure>
                tur ex .22. theoremate huiuslibri proue-
                  <lb/>
                niés.h.m. minus eſſe proueniente
                  <var>.q.f.</var>
                per
                  <lb/>
                vnitaté, & proueniens
                  <var>.h.k.</var>
                minus proue-
                  <lb/>
                niente
                  <var>.q.i.</var>
                per alteram vnitatem. </s>
                <s xml:id="echoid-s301" xml:space="preserve">Itaque
                  <var>.
                    <lb/>
                  f.q.i.</var>
                maior erit
                  <var>.m.h.k.</var>
                per numerum binarium, quoderat propoſitum.</s>
              </p>
            </div>
            <div xml:id="echoid-div73" type="math:theorem" level="3" n="33">
              <head xml:id="echoid-head49" xml:space="preserve">THEOREMA.
                <num value="33">XXXIII</num>
              .</head>
              <p>
                <s xml:id="echoid-s302" xml:space="preserve">
                  <emph style="sc">QVilibet</emph>
                numerus, medius eſt
                  <lb/>
                proportionalis inter numerum
                  <lb/>
                  <figure xlink:label="fig-0033-02" xlink:href="fig-0033-02a" number="45">
                    <image file="0033-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0033-02"/>
                  </figure>
                ſui quadrati & vnitatem.</s>
              </p>
              <p>
                <s xml:id="echoid-s303" xml:space="preserve">Detur enim numerus propoſitus,
                  <lb/>
                qui linea
                  <var>.a.u.</var>
                ſignificetur, cuiusqua-
                  <lb/>
                dratum ſit
                  <var>.u.n.</var>
                vnitas linearis ſit
                  <var>.i.a.</var>
                  <lb/>
                et ſuperficialis
                  <var>.o.</var>
                patebit ex .18. ſexti
                  <lb/>
                aut 11. octaui proportionem
                  <var>.u.n.</var>
                ad
                  <var>.
                    <lb/>
                  o.</var>
                futuram duplam proportioni
                  <var>.u.a.</var>
                  <lb/>
                ad
                  <var>.i.a.</var>
                ſed
                  <var>.i.a.</var>
                e
                  <unsure/>
                t.o. eadem (ſpecie)
                  <lb/>
                res
                  <reg norm="sunt" type="context">sũt</reg>
                , tanta ſcilicet
                  <var>.a.i.</var>
                quanta
                  <var>.o.</var>
                vni
                  <lb/>
                  <figure xlink:label="fig-0033-03" xlink:href="fig-0033-03a" number="46">
                    <image file="0033-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0033-03"/>
                  </figure>
                tas eſt, Itaque proportio numeri
                  <var>.u.n.</var>
                  <lb/>
                ad
                  <var>.u.a.</var>
                æqualis erit proportioni
                  <var>.u.a.</var>
                  <lb/>
                ad
                  <var>.i.a</var>
                . </s>
                <s xml:id="echoid-s304" xml:space="preserve">Quare numerus
                  <var>.u.a.</var>
                inter nu-
                  <lb/>
                merum
                  <var>.u.n.</var>
                & vnitatem, medius erit
                  <lb/>
                proportionalis.</s>
              </p>
            </div>
            <div xml:id="echoid-div76" type="math:theorem" level="3" n="34">
              <head xml:id="echoid-head50" xml:space="preserve">THEOREMA
                <num value="34">XXXIIII</num>
              .</head>
              <p>
                <s xml:id="echoid-s305" xml:space="preserve">
                  <emph style="sc">HOc</emph>
                ipſum quod diximus & alia ratione ſpeculari licebit.</s>
              </p>
              <p>
                <s xml:id="echoid-s306" xml:space="preserve">Propoſitus numerus, nunc etiam per
                  <var>.a.u.</var>
                ſignificetur, eius quadratum per
                  <var>.
                    <lb/>
                  u.n.</var>
                vnitas linearis per
                  <var>.a.i.</var>
                  <reg norm="productumque" type="simple">productumq́;</reg>
                  <var>.a.u.</var>
                in
                  <var>.a.i.</var>
                terminetur,
                  <reg norm="ſitque" type="simple">ſitq́;</reg>
                  <var>.n.i</var>
                . </s>
                <s xml:id="echoid-s307" xml:space="preserve">quare
                  <lb/>
                  <var>n.i.</var>
                conſtabit numero íuperficiali æquali numero lineari
                  <var>.a.u.</var>
                & ex prima fexti aut .
                  <lb/>
                18. vel .19. ſeptimi, eadem erit proportio
                  <var>.u.n.</var>
                ad
                  <var>.i.n.</var>
                quæ eſt
                  <var>.a.u.</var>
                ad
                  <var>.a.i.</var>
                ſed nu-
                  <lb/>
                merus
                  <var>.a.u.</var>
                cum numero
                  <var>.n.i.</var>
                idem ſpecie eſt. </s>
                <s xml:id="echoid-s308" xml:space="preserve">Itaque medius eſt proportiona-
                  <lb/>
                lis inter
                  <var>.u.n.</var>
                & vnitatem.</s>
              </p>
            </div>
          </div>
        </div>
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