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]

Page concordance

< >
Scan Original
161 149
162 150
163 151
164 152
165 153
166 154
167 155
168 156
169 157
170 158
171 159
172 160
173 161
174 162
175 163
176 164
177 165
178 166
179 167
180 168
181 169
182 170
183 171
184 172
185 173
186 174
187 175
188 176
189 177
190 178
< >
page |< < (177) of 445 > >|
    <echo version="1.0">
      <text type="book" xml:lang="la">
        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div387" type="chapter" level="2" n="4">
            <div xml:id="echoid-div409" type="section" level="3" n="13">
              <p>
                <s xml:id="echoid-s2099" xml:space="preserve">
                  <pb o="177" rhead="DISPVTATIONES." n="189" file="0189" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0189"/>
                quam
                  <var>.u.</var>
                ad
                  <var>.m.e.</var>
                & ex .27. maior erit proportio
                  <var>.c.i.</var>
                ad
                  <var>.u.e.</var>
                quam
                  <var>.z.i.</var>
                ad
                  <var>.e.m.</var>
                ideſt
                  <var>.s.</var>
                g
                  <lb/>
                ad
                  <var>.r.x.</var>
                quod Ariſtoteli in mentem non venerat. </s>
                <s xml:id="echoid-s2100" xml:space="preserve">Alijs quoque modis idem proba-
                  <lb/>
                ri poteſt, vt ſi diceret aliquis, maiorem proportionem eſſe
                  <var>.e.m.</var>
                ad
                  <var>.m.u.</var>
                quam
                  <var>.i.z.</var>
                ad
                  <lb/>
                  <var>z.c.</var>
                (quia
                  <var>.e.m.</var>
                ad
                  <var>.m.u.</var>
                eadem eſt ratio vt ad
                  <var>.z.c.</var>
                ex .7. quinti, ſed proportio
                  <var>.e.m.</var>
                ad
                  <var>.
                    <lb/>
                  z.c.</var>
                maior eſt quam
                  <var>.i.z.</var>
                ad
                  <var>.z.c.</var>
                ex .8. eiuſdem, ergo ea, quæ eſt
                  <var>.e.m.</var>
                ad
                  <var>.m.u.</var>
                ex .12. ma
                  <lb/>
                for erit, quam
                  <var>.i.z.</var>
                ad
                  <var>.z.c.</var>
                ) vnde componendo, ea quæ eſt
                  <var>.e.u.</var>
                ad
                  <var>.m.u.</var>
                maior erit illa,
                  <lb/>
                quæ eſt
                  <var>.i.c.</var>
                ad
                  <var>.z.c.</var>
                &
                  <reg norm="permutando" type="context">permutãdo</reg>
                , quam ea, quæ eſt
                  <var>.e.u.</var>
                ad
                  <var>.i.c.</var>
                ea, quæ eſt
                  <var>.m.u.</var>
                ad
                  <var>.z.c.</var>
                  <lb/>
                & ex .33. quinti, ea, quæ eſt
                  <var>.e.m.</var>
                ad
                  <var>.i.z.</var>
                maior erit ea, quæ eſt
                  <var>.e.u.</var>
                ad
                  <var>.i.c</var>
                .</s>
              </p>
              <figure position="here" number="255">
                <image file="0189-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0189-01"/>
              </figure>
            </div>
            <div xml:id="echoid-div410" type="section" level="3" n="14">
              <head xml:id="echoid-head269" style="it" xml:space="preserve">Quid ſequatur ex ſupradistis.</head>
              <head xml:id="echoid-head270" xml:space="preserve">CAP. XIIII.</head>
              <p>
                <s xml:id="echoid-s2101" xml:space="preserve">EX præcedenti capite manifeſtè depræhenditur, in vniuerſum Ariſtotelis opi-
                  <lb/>
                nionem veram non eſſe in prima parte vltimi capitis. lib. 7. phyſicorum; </s>
                <s xml:id="echoid-s2102" xml:space="preserve">quia
                  <lb/>
                in eo loco ſupponens ipſe corpus
                  <var>.B.</var>
                pręcedentis capitis eſſe dimidiam partem ipſius
                  <lb/>
                D. quantum ad aream corpoream ſpectat (ſunt tamen pondere ad inuicem æqualia)
                  <lb/>
                ait
                  <var>.B.</var>
                futurum duplo velocius ipſo
                  <var>.D</var>
                . </s>
                <s xml:id="echoid-s2103" xml:space="preserve">Ego verò præcedenti capite accepi
                  <var>.e.u.</var>
                pro
                  <lb/>
                velocitate reſidua corporis
                  <var>.B.</var>
                (ſubtracta ea tamen parte, quam ei reſiſtentia adimit,
                  <lb/>
                quæ erat
                  <var>.e.a.</var>
                ) et
                  <var>.i.c.</var>
                pro ea, quæ eſt corporis
                  <var>.D.</var>
                et
                  <var>.r.x.</var>
                pro ea, quæ eſt corporis
                  <var>.V.</var>
                et
                  <var>.
                    <lb/>
                  s.g.</var>
                pro ea, quæ eſt corporis
                  <var>.M</var>
                . </s>
                <s xml:id="echoid-s2104" xml:space="preserve">Dicat nunc Ariſtoteles, quę nam harum duarum pro
                  <lb/>
                portionum dupla erit? </s>
                <s xml:id="echoid-s2105" xml:space="preserve">quia ſi earum aliqua talis erit, alia nullo modo eſſe poterit,
                  <lb/>
                vt iam oſtendi, etiamſi duo corpora
                  <var>.V.</var>
                et
                  <var>.M.</var>
                eaſdem conditiones habeant, quas
                  <var>.B.</var>
                  <lb/>
                et
                  <var>.D</var>
                . </s>
                <s xml:id="echoid-s2106" xml:space="preserve">Ratio autem, quæ Ariſtotelem induxerit ad illud credendum, nulla alia eſſe
                  <lb/>
                potuit, quàm quod putarit reſiſtentias proportionatas eſſe magnitudinibus corpo-
                  <lb/>
                reis, ideſt quemadmodum
                  <var>.B.</var>
                erat corporaliter dimidia pars ipſius
                  <var>.D.</var>
                ſic etiam habe
                  <lb/>
                ret medietatem eius reſiſtentiæ, quam habuiſſet corpus
                  <var>.D</var>
                . </s>
                <s xml:id="echoid-s2107" xml:space="preserve">Quod etſi verum eſſet,
                  <lb/>
                non tamen ſequeretur neceſſariò in quibuſlibet corporibus futuram velocitatum
                  <lb/>
                proportionem eandem, quæ reſiſtentiarum eſt, vt ſuperiore capite oſtendimus.</s>
              </p>
            </div>
            <div xml:id="echoid-div411" type="section" level="3" n="15">
              <head xml:id="echoid-head271" style="it" xml:space="preserve">Numrestè ſenſerit Philoſophus reſistentias proportionales
                <lb/>
              eße cum corporibus mobilibus.</head>
              <head xml:id="echoid-head272" xml:space="preserve">CAP. XV.</head>
              <p>
                <s xml:id="echoid-s2108" xml:space="preserve">QVòd Ariſtoteles crediderit reſiſtentias proportionatas eſſe corporibus, erra-
                  <lb/>
                uit. </s>
                <s xml:id="echoid-s2109" xml:space="preserve">Si ſuperficies ijſdem proportionatæ eſſent, dubium non eſt, quin
                  <lb/>
                reſiſtentiæ quoque ipſæ, ijſdem proportionatæ exiſterent, ſupponendo eas ſimiles
                  <lb/>
                ſitu, dum eadem corpora mouerentur. </s>
                <s xml:id="echoid-s2110" xml:space="preserve">Sed eadem proportio non eſt inter ſuperfi- </s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum