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]

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            <div xml:id="echoid-div400" type="section" level="3" n="8">
              <p>
                <s xml:id="echoid-s2074" xml:space="preserve">
                  <pb o="174" rhead="IO. BAPT. BENED." n="186" file="0186" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0186"/>
                  <var>o.x.</var>
                et
                  <var>.B.</var>
                quoque in eodem loco amittere
                  <var>.c.s.</var>
                et
                  <var>.A.</var>
                in
                  <reg norm="aem" type="context">aẽ</reg>
                  <unsure/>
                re partem
                  <var>.i.o.</var>
                et
                  <var>.B.</var>
                partem.
                  <lb/>
                  <var>.t.s</var>
                . </s>
                <s xml:id="echoid-s2075" xml:space="preserve">Nunc quia corpus aqueum, cui correſpondet
                  <var>.e.o.</var>
                æquale eſt ipſi
                  <var>.A.</var>
                & corpus
                  <lb/>
                aqueum, cui correſpondet
                  <var>.c.s.</var>
                æquale eſt i pſi
                  <var>.B.</var>
                vt eſt ab Archimede
                  <reg norm="probatum" type="context">probatũ</reg>
                : </s>
                <s xml:id="echoid-s2076" xml:space="preserve">com
                  <lb/>
                muni quadam ſcientiæ ratione, ſequitur eandem proportionem futuram
                  <var>.o.x.</var>
                ad
                  <var>.e.o.</var>
                  <lb/>
                quæ eſt
                  <var>.u.s.</var>
                ad
                  <var>.c.s.</var>
                ob
                  <reg norm="eaſdemque" type="simple">eaſdemq́;</reg>
                rationes idem erit de
                  <var>.x.o.</var>
                ad
                  <var>.i.o.</var>
                ut
                  <var>.u.s.</var>
                ad
                  <var>.t.s.</var>
                &
                  <reg norm="idem" type="context">idẽ</reg>
                  <lb/>
                etiam erit de
                  <var>.o.x.</var>
                ad
                  <var>.s.u.</var>
                vt de
                  <var>.e.o.</var>
                ad
                  <var>.c.s.</var>
                vt etiam de
                  <var>.o.i.</var>
                ad
                  <var>.s.t</var>
                . </s>
                <s xml:id="echoid-s2077" xml:space="preserve">Vnde ex .19. lib.
                  <lb/>
                quintí erit de
                  <var>.x.i.</var>
                ad
                  <var>.u.t.</var>
                quemadmodum de
                  <var>.x.o.</var>
                ad
                  <var>.u.s.</var>
                idem dico de
                  <var>.x.e.</var>
                ad
                  <var>.u.c</var>
                . </s>
                <s xml:id="echoid-s2078" xml:space="preserve">Ex
                  <lb/>
                11. igitur dicti lib. erit. de
                  <var>.x.i.</var>
                ad
                  <var>.u.t.</var>
                quemadmodum de
                  <var>.x.e.</var>
                ad
                  <var>.u.c.</var>
                ex quibus
                  <reg norm="quidem" type="context">quidẽ</reg>
                  <lb/>
                proportionibus, ſi ſubtra
                  <lb/>
                  <figure xlink:label="fig-0186-01" xlink:href="fig-0186-01a" number="250">
                    <image file="0186-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0186-01"/>
                  </figure>
                hantur proportiones @reſi
                  <lb/>
                  <reg norm="ſtentiarum" type="context">ſtẽtiarum</reg>
                extrinſecus
                  <reg norm="ad- uenentium" type="context">ad-
                    <lb/>
                  uenẽtium</reg>
                , proportiones
                  <lb/>
                quæ remanebunt, exter-
                  <lb/>
                tio communi axiomate
                  <lb/>
                ab Eucli. in principio pri­
                  <lb/>
                mi lib. poſito, ad inuicem
                  <lb/>
                erunt æquales, ſecundum quas eorundem corporum ſunt velocitates.</s>
              </p>
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            <div xml:id="echoid-div402" type="section" level="3" n="9">
              <head xml:id="echoid-head259" style="it" xml:space="preserve">Anrectè Aristoteles diſeruerit de proportionibus mo-
                <lb/>
              tuum in uacuo.</head>
              <head xml:id="echoid-head260" xml:space="preserve">CAP. IX.</head>
              <p>
                <s xml:id="echoid-s2079" xml:space="preserve">CVm verò Ariſtoteles circa finem cap .8. lib. 4. phyſicorum ſubiungit quod ea-
                  <lb/>
                dem proportione dicta corpora mouerentur in vacuo, vt in pleno, id pace
                  <reg norm="eius" type="simple">eiꝰ</reg>
                  <lb/>
                  <reg norm="dictum" type="context">dictũ</reg>
                ſit planè
                  <reg norm="erroneum" type="context">erroneũ</reg>
                eſt. </s>
                <s xml:id="echoid-s2080" xml:space="preserve">quia in pleno dictis corporibus ſubtrahitur proportio reſi
                  <lb/>
                ſtentiarum extrinſecarum à proportione ponderum, vt velocitatum proportio re-
                  <lb/>
                maneat, quę nulla eſſet, ſi dictarum reſiſtentiarum proportio, ponderum propor-
                  <lb/>
                tioni æqualis eſſet, & hanc ob cauſam diuerſam velocitatum proportionem in va-
                  <lb/>
                cuo haberent ab ea, quæ eſt in pleno.</s>
              </p>
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            <div xml:id="echoid-div403" type="section" level="3" n="10">
              <head xml:id="echoid-head261" style="it" xml:space="preserve">Quòd in uacuo corpor a eiuſdem materiæ æquali uelocita-
                <lb/>
              te mouerentur.</head>
              <head xml:id="echoid-head262" xml:space="preserve">CAP.X.</head>
              <p>
                <s xml:id="echoid-s2081" xml:space="preserve">QVòd ſupradicta corpora in vacuo naturaliter pari velocitate mouerentur,
                  <lb/>
                hac ratione aſſero.</s>
              </p>
              <p>
                <s xml:id="echoid-s2082" xml:space="preserve">Sint enim duo corpora
                  <var>.o.</var>
                et
                  <var>.g.</var>
                omogenea, et
                  <var>.g.</var>
                ſit dimidia pars ipſius
                  <var>.o.</var>
                ſint alia
                  <lb/>
                quoque duo corpora
                  <var>.a.</var>
                et
                  <var>.e.</var>
                omogenea primis, quorum quodlibet æquale ſit ipſi
                  <var>.g.</var>
                  <lb/>
                & imaginatione compręhendamus ambo poſita in extremitatibus alicuius lineæ, cu
                  <lb/>
                ius medium ſit
                  <var>.i.</var>
                clarum erit, tantum pondus habiturum, punctum
                  <var>.i.</var>
                quantum
                  <reg norm="centrum" type="context">centrũ</reg>
                  <lb/>
                ipſius
                  <var>.o.</var>
                quod
                  <var>.i.</var>
                virtute corporis
                  <var>.a.</var>
                et
                  <var>.e.</var>
                in vacuo,
                  <lb/>
                  <figure xlink:label="fig-0186-02" xlink:href="fig-0186-02a" number="251">
                    <image file="0186-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0186-02"/>
                  </figure>
                eadem velocitate moueretur, quacentrum ipſius .
                  <lb/>
                o: </s>
                <s xml:id="echoid-s2083" xml:space="preserve">cum autem difiuncta eſſent dicta corpora
                  <var>.a.</var>
                et
                  <var>.e.</var>
                  <lb/>
                à dicta linea, non ideo aliquo modo ſuam velocita­ </s>
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