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
191 179
192 180
193 181
194 182
195 183
196 184
197 185
198 186
199 187
200 188
201 189
202 190
203 191
204 192
205 193
206 194
207 195
208 196
209 197
210 198
211 199
212 200
213 201
214 202
215 203
216 204
217 205
218 206
219 207
220 208
< >
page |< < (176) 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-div407" type="section" level="3" n="12">
              <p>
                <s xml:id="echoid-s2088" xml:space="preserve">
                  <pb o="176" rhead="IO. BAPT. BENED." n="188" file="0188" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0188"/>
                ſed proportio
                  <var>.p.f.</var>
                ad
                  <var>.q.i.</var>
                maior eſſet ea, quæ eſt
                  <var>.c.f.</var>
                ad
                  <var>.q.i.</var>
                ex. octaua lib. quinti, vn-
                  <lb/>
                de ex .12. eiuſdem lib. maior eſſet
                  <var>.p.f.</var>
                ad
                  <var>.q.i.</var>
                quàm.o.f. ad
                  <var>.n.i.</var>
                ex .33. igitur eiuſdem,
                  <lb/>
                maior erit proportio
                  <var>.p.o.</var>
                ad
                  <var>.q.n.</var>
                quàm.p.f. ad
                  <var>.q.i</var>
                . </s>
                <s xml:id="echoid-s2089" xml:space="preserve">Sic quoque ſe habebunt ad inui
                  <lb/>
                cem velocitates, quod eſt propoſitum. </s>
                <s xml:id="echoid-s2090" xml:space="preserve">Cum autem proportio
                  <var>.p.o.</var>
                ad
                  <var>.q.n.</var>
                maior ſit,
                  <lb/>
                quàm.p.f. ad
                  <var>.q.i.</var>
                permurando igitur maior erit proportio
                  <var>.p.o.</var>
                ad
                  <var>.p.f.</var>
                quam
                  <var>.q.n.</var>
                ad
                  <var>.
                    <lb/>
                  q.i.</var>
                aut euerſim maior erit proportio
                  <var>.q.i.</var>
                ad
                  <var>.q.n.</var>
                quàm.p.f. ad
                  <var>.p.o.</var>
                vnde ſi proportio
                  <lb/>
                  <var>p.f.</var>
                ad
                  <var>.p.o.</var>
                eſſet ac ea, quæ eſt
                  <var>.o.g.</var>
                ad
                  <var>.f.g.</var>
                non eſſet
                  <var>.q.i.</var>
                ad
                  <var>.q.n.</var>
                ut eſt
                  <var>.o.g.</var>
                ad
                  <var>.f.g.</var>
                aut
                  <lb/>
                vt
                  <var>.n.k.</var>
                ad
                  <var>.i.k.</var>
                quodidem
                  <lb/>
                eſt, de quibus quidem re-
                  <lb/>
                  <figure xlink:label="fig-0188-01" xlink:href="fig-0188-01a" number="254">
                    <image file="0188-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0188-01"/>
                  </figure>
                bus, exemplis propoſitis
                  <lb/>
                quinto capite
                  <reg norm="mentionem" type="context">mẽtionem</reg>
                  <lb/>
                feci.</s>
              </p>
              <p>
                <s xml:id="echoid-s2091" xml:space="preserve">Velocitatibus autem ſe-
                  <lb/>
                quentibus pondera, ſequi
                  <lb/>
                tur proportionem veloci-
                  <lb/>
                citatum duorum corporum hetereogeneorum eandem non eſſe per diuerſa media,
                  <lb/>
                contra id, quod ſequeretur ſi Ariſtotelis opinionem .8. cap. lib. 4. phyſicorum re-
                  <lb/>
                ciperemus.</s>
              </p>
            </div>
            <div xml:id="echoid-div409" type="section" level="3" n="13">
              <head xml:id="echoid-head267" style="it" xml:space="preserve">Longe aliter ueritatem ſe habere quam Aristoteles
                <lb/>
              doceat in fine libri ſeptimi phyſicorum.</head>
              <head xml:id="echoid-head268" xml:space="preserve">CAP. XIII.</head>
              <p>
                <s xml:id="echoid-s2092" xml:space="preserve">NOn tam facile eſt aſſignare proportionem velocitatum duorum corporum na
                  <lb/>
                turalium, quam Ariſtoteles vltimo cap. lib. 7. phyſicorum putauit.</s>
              </p>
              <p>
                <s xml:id="echoid-s2093" xml:space="preserve">Quamobrem ſint duo corpora
                  <var>.B.</var>
                et
                  <var>.D.</var>
                materia
                  <reg norm="magnitudineque" type="simple">magnitudineq́;</reg>
                diuerſa, pondere
                  <lb/>
                tamen, & figura ſimilia, & proportio reſiſtentiarum, quas recipiunt à medio
                  <reg norm="dum" type="context">dũ</reg>
                mo-
                  <lb/>
                uentur, ſit. ut
                  <var>.o.i.</var>
                ad
                  <var>.a.e.</var>
                denotentur deinde velocitates totales abſque vlla reſiſten-
                  <lb/>
                tia ab
                  <var>.a.u.</var>
                et
                  <var>.o.c.</var>
                quæ æquales erunt ad inuicem per communem ſcientiam ex ſup-
                  <lb/>
                poſito, ſint alia deinde duo corpora
                  <var>.V.</var>
                et
                  <var>.M.</var>
                eodem modo ſe habentia ut prima
                  <var>.B.</var>
                  <lb/>
                et
                  <var>.D.</var>
                in eodem medio, ſed ex diuerſa materia ab ea, quæ eſt illorum duorum corpo
                  <lb/>
                rum, magnitudine tamen & figura ijſdem ſimilia: </s>
                <s xml:id="echoid-s2094" xml:space="preserve">ſignificentur quoque eo-
                  <lb/>
                rundem reſiſtentiæ per
                  <var>.t.s.</var>
                et
                  <var>.n.r.</var>
                & eorundem velocitates à nulla ex reſiſtentijs di-
                  <lb/>
                minutæ, per
                  <var>.n.x.</var>
                et
                  <var>.t.g.</var>
                vnde
                  <var>.n.r.</var>
                æqualis erit
                  <var>.a.e.</var>
                et
                  <var>.t.s.</var>
                ipſi
                  <var>.o.i.</var>
                et
                  <var>.n.x.</var>
                ipſi
                  <var>.t.g</var>
                :
                  <var>n.x.</var>
                ta-
                  <lb/>
                men et
                  <var>.t.g.</var>
                non erunt ęqualia
                  <var>.a.u.</var>
                et
                  <var>.o.c</var>
                . </s>
                <s xml:id="echoid-s2095" xml:space="preserve">Sed exempli gratia, ponamus ea eſſe mi-
                  <lb/>
                nora. </s>
                <s xml:id="echoid-s2096" xml:space="preserve">Supponamus nunc
                  <var>.e.u.</var>
                velocitatem eſſe quæ remanet ipſi
                  <var>.B.</var>
                cum applicata
                  <lb/>
                erit reſiſtentia
                  <var>.a.e.</var>
                dicto corpori
                  <var>.B.</var>
                quæ diminutam facit totam
                  <var>.a.u.</var>
                per
                  <var>.a.e.</var>
                  <reg norm="ſitque" type="simple">ſitq́;</reg>
                  <var>.i.c.</var>
                  <lb/>
                ea, quę remanet ipſi
                  <var>.o.c.</var>
                corporis
                  <var>.D.</var>
                et
                  <var>.r.x.</var>
                ea, quæ remanet
                  <var>.n.x.</var>
                corporis
                  <var>.V.</var>
                et
                  <var>.s.g.</var>
                  <lb/>
                ea, quæ eſt ex
                  <var>.t.g.</var>
                corporis
                  <var>.M</var>
                . </s>
                <s xml:id="echoid-s2097" xml:space="preserve">Vnde communi omnium
                  <reg norm="conſenſu" type="context">cõſenſu</reg>
                aſſequemur
                  <var>.e.u.</var>
                ma
                  <lb/>
                iorem futuram
                  <var>.r.x.</var>
                et
                  <var>.i.c.</var>
                ipſa
                  <var>.s.g</var>
                . </s>
                <s xml:id="echoid-s2098" xml:space="preserve">Scindatur deinde
                  <var>.a.m.</var>
                ad ęqualitatem
                  <var>.n.x.</var>
                et
                  <var>.o.z.</var>
                  <lb/>
                ipſius
                  <var>.t.g.</var>
                vnde
                  <var>.a.m.</var>
                ad
                  <var>.o.z.</var>
                et
                  <var>.m.u.</var>
                ad
                  <var>.z.c.</var>
                æquales habebimus, ut quoque
                  <var>.e.m.</var>
                ad
                  <var>.r.
                    <lb/>
                  x.</var>
                et
                  <var>.i.z.</var>
                ad
                  <var>.s.g.</var>
                quamobrem
                  <var>.e.m.</var>
                maior erit ipſa
                  <var>.z.i.</var>
                maior igitur erit proportio
                  <var>.z.c.</var>
                  <lb/>
                ad
                  <var>.z.i.</var>
                quàm.m.u. ad
                  <var>.m.e.</var>
                (quia
                  <var>.z.c.</var>
                ad
                  <var>.z.i.</var>
                ita ſe habet vt
                  <var>.m.u.</var>
                ad
                  <var>.i.z.</var>
                ex .7. lib. quin-
                  <lb/>
                ti, ſed
                  <var>.m.u.</var>
                ad
                  <var>.i.z.</var>
                maior eſt quam ad
                  <var>.m.e.</var>
                ex .8. dicti lib. vnde ex .12. eiuſdem
                  <var>.z.c.</var>
                ad
                  <lb/>
                ad
                  <var>.z.i.</var>
                maior erit, quàm.m.u. ad
                  <var>.m.e</var>
                . </s>
                <s xml:id="echoid-s2099" xml:space="preserve">Ergo ex .28. maior proportio erit
                  <var>.c.i.</var>
                ad
                  <var>.z.i.</var>
                </s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>