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
261 249
262 250
263 251
264 252
265 253
266 254
267 255
268 256
269 259
270 258
271 259
272 260
273 261
274 222
275 263
276 264
277 265
278 266
279 267
280 268
281 269
282 270
283 271
284 272
285 273
286 274
287 275
288 276
289 277
290 278
< >
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>