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
241 229
242 230
243 231
244 232
245 233
246 234
247 235
248 236
249 237
250 238
251 239
252 240
253 241
254 242
255 243
256 244
257 245
258 246
259 247
260 248
261 249
262 250
263 251
264 252
265 253
266 254
267 255
268 256
269 259
270 258
< >
page |< < (172) 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-div394" type="section" level="3" n="5">
              <pb o="172" rhead="IO. BAPT. BENED." n="184" file="0184" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0184"/>
            </div>
            <div xml:id="echoid-div396" type="section" level="3" n="6">
              <head xml:id="echoid-head253" style="it" xml:space="preserve">Quod proportiones ponderum eiuſdem corporis in diuerſis medijs pro
                <lb/>
              portiones eorum mediorum denſit atum non ſeruant. Unde ne-
                <lb/>
              ceßariò inæquales proportiones uelocitatum
                <lb/>
              producuntur.</head>
              <head xml:id="echoid-head254" xml:space="preserve">CAP. VI.</head>
              <p>
                <s xml:id="echoid-s2050" xml:space="preserve">OMne corpus graue variat proportionem ponderis per diuerſa media, vnde
                  <lb/>
                proportiones velocitatum inæquales exiſtunt. </s>
                <s xml:id="echoid-s2051" xml:space="preserve">Vt exempli gratia, ſi fue-
                  <lb/>
                rit corpus
                  <var>.A.</var>
                cuius pondus totale ſit
                  <var>.o.a.</var>
                quod in aqua diminutum ſit ratione partis
                  <var>.
                    <lb/>
                  e.o.</var>
                ita vt ei ſolum relinquatur pondus
                  <var>.a.e.</var>
                & in aeie adempta ſit ei pars
                  <var>.i.o.</var>
                vnde ſo
                  <lb/>
                lum remaneat pondus
                  <var>.a.i</var>
                . </s>
                <s xml:id="echoid-s2052" xml:space="preserve">Supponamus aliud
                  <reg norm="quoque" type="simple">quoq;</reg>
                medium in eadem proportio-
                  <lb/>
                ne minus denſum, quàm aer, quemadmodum aer minus denſus eſt, aqua, in quo, cor
                  <lb/>
                pus
                  <var>.A.</var>
                ammittat partem
                  <var>.t.o.</var>
                ponderis ſui, vnde ex .7. lib. de inſidentibus aquæ Ar-
                  <lb/>
                chimedis, eadem proportio erit
                  <var>.e.o.</var>
                ad
                  <var>.i.o.</var>
                quæ eſt
                  <var>.i.o.</var>
                ad
                  <var>.t.o</var>
                . </s>
                <s xml:id="echoid-s2053" xml:space="preserve">Supponamus
                  <reg norm="quoque" type="simple">quoq;</reg>
                  <lb/>
                eandem proportionem eſſe
                  <var>.a.i.</var>
                ad
                  <var>.a.e.</var>
                eſt
                  <var>.e.o.</var>
                ad
                  <var>.i.o.</var>
                </s>
                <s xml:id="echoid-s2054" xml:space="preserve">tunc dico non futuram ean-
                  <lb/>
                dem proportionem
                  <var>.t.a.</var>
                ad
                  <var>.a.i.</var>
                quæ eſt
                  <var>.i.o.</var>
                ad
                  <var>.t.o</var>
                . </s>
                <s xml:id="echoid-s2055" xml:space="preserve">Cum ſit ergo proportio
                  <var>.a.i.</var>
                  <lb/>
                ad
                  <var>.a.e.</var>
                ut
                  <var>.e.o.</var>
                ad
                  <var>.i.o.</var>
                erit diſiunctim
                  <var>.e.i.</var>
                ad
                  <var>.e.a.</var>
                vt
                  <var>.e.i.</var>
                ad
                  <var>.i.o</var>
                . </s>
                <s xml:id="echoid-s2056" xml:space="preserve">Quare ex .9. libr. quin­
                  <lb/>
                ti erit
                  <var>.a.e.</var>
                æqualis
                  <var>.i.o.</var>
                ſed cum ita ſehabeat
                  <var>.e.o.</var>
                ad
                  <var>.i.o.</var>
                vt
                  <var>.i.o.</var>
                ad
                  <var>.t.o.</var>
                ita quoque
                  <lb/>
                ſe habebit, ex vndecima quinti
                  <var>.a.i.</var>
                ad
                  <var>.e.a.</var>
                ut
                  <var>.i.o.</var>
                ad
                  <var>.t.o</var>
                . </s>
                <s xml:id="echoid-s2057" xml:space="preserve">Cum autem (vt vidimus).
                  <var>a.e.</var>
                  <lb/>
                ęqualis ſit ipſi
                  <var>.i.o.</var>
                non poterit eſſe proportio
                  <var>.t.a.</var>
                ad
                  <var>.i.a.</var>
                vt eſt
                  <var>.o.i.</var>
                ad
                  <var>.t.o.</var>
                quia ſi
                  <lb/>
                hoc eſſet, eſſet etiam diſiunctim proportio
                  <var>.i.t.</var>
                ad
                  <var>.i.a.</var>
                vt eſt
                  <var>.i.t.</var>
                ad
                  <var>.t.o.</var>
                & ex ſupradicta
                  <lb/>
                9. lib. quinti
                  <var>.a.i.</var>
                æqualis eſſet
                  <var>.t.o</var>
                . </s>
                <s xml:id="echoid-s2058" xml:space="preserve">Maximum autem inconueniens eſſet
                  <var>.t.o.</var>
                minorem
                  <lb/>
                  <var>o.i.</var>
                ideſt minorem
                  <var>.a.e.</var>
                æqualem eſſe
                  <var>.a.i.</var>
                quæ maior eſt
                  <var>.a.e</var>
                . </s>
                <s xml:id="echoid-s2059" xml:space="preserve">Oſtenſiuè tamen idem
                  <lb/>
                hoc modo probari poteſt, vt exiſtente
                  <var>.i.o.</var>
                ęquali ipſi
                  <var>.a.e.</var>
                per conſequens
                  <reg norm="quoque" type="simple">quoq;</reg>
                erit
                  <lb/>
                minor ipſa
                  <var>.a.i.</var>
                cum
                  <var>.a.e.</var>
                pars ſit ipſius
                  <var>a.i</var>
                . </s>
                <s xml:id="echoid-s2060" xml:space="preserve">
                  <reg norm="Pereandem" type="context">Pereãdem</reg>
                tamen rationem
                  <var>.o.t.</var>
                minoreſt
                  <var>.
                    <lb/>
                  o.i</var>
                . </s>
                <s xml:id="echoid-s2061" xml:space="preserve">Tanto magis igitur minor erit
                  <var>.t.o.</var>
                ipſa
                  <var>.i.a</var>
                . </s>
                <s xml:id="echoid-s2062" xml:space="preserve">Vnde ex .8. libri quinti maiorem pro
                  <lb/>
                portionem habebit
                  <var>.i.t.</var>
                  <lb/>
                ad
                  <var>.t.o.</var>
                quam ad
                  <var>.i.a.</var>
                &
                  <lb/>
                ex .28.
                  <reg norm="eiuſdem" type="context">eiuſdẽ</reg>
                lib
                  <var>.i.o.</var>
                ad
                  <lb/>
                  <var>t.o.</var>
                  <reg norm="maiorem" type="context">maiorẽ</reg>
                proportio-
                  <lb/>
                  <figure xlink:label="fig-0184-01" xlink:href="fig-0184-01a" number="247">
                    <image file="0184-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0184-01"/>
                  </figure>
                  <reg norm="nem" type="context">nẽ</reg>
                habebit, quàm.t.a.
                  <lb/>
                ad
                  <var>.i.a.</var>
                ex .12. igitur di-
                  <lb/>
                cti quinti maiorem pro
                  <lb/>
                portionem habebit
                  <var>.i.a.</var>
                ad
                  <var>.e.a.</var>
                quàm.t.a. ad
                  <var>.i.a.</var>
                ita ergo ſe habebunt ipſorum velo-
                  <lb/>
                citates.</s>
              </p>
            </div>
            <div xml:id="echoid-div398" type="section" level="3" n="7">
              <head xml:id="echoid-head255" style="it" xml:space="preserve">Corpora grauia aut leuia eiuſdem figur æ et materiæ ſed inæqualis
                <lb/>
              magnitudinis, in ſuis motibus natur alibus uelocit atis, in eo
                <lb/>
              dem medio, proportionem longè diuerſam ſeruatura
                <lb/>
              eße quam Aristoteliuiſum fuerit.</head>
              <head xml:id="echoid-head256" xml:space="preserve">CAP. VII.</head>
              <p>
                <s xml:id="echoid-s2063" xml:space="preserve">ESt mihi nunc probandum
                  <reg norm="quod" type="simple">ꝙ</reg>
                in uno
                  <reg norm="eodemque" type="simple">eodemq́;</reg>
                mcdio duo corpora inæqualia, ſed
                  <lb/>
                ſimili figura & materia, mouebuntur naturali motu, diuerſa tamen ratione ab </s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>