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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DE MECHAN.
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            <div xml:id="echoid-div363" type="section" level="3" n="12">
              <pb o="155" rhead="DE MECHAN." n="167" file="0167" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0167"/>
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            <div xml:id="echoid-div366" type="section" level="3" n="13">
              <head xml:id="echoid-head218" style="it" xml:space="preserve">Quòd Ariſtotelisratio in 6. quæſtione poſit a non ſit admittenda.</head>
              <head xml:id="echoid-head219" xml:space="preserve">CAP. XIII.</head>
              <p>
                <s xml:id="echoid-s1843" xml:space="preserve">VOlens Ariſtoteles rationem proponere, vnde fiat, vt nauis velocius moueatur
                  <lb/>
                cum antennam altiorem quàm cum depræſſiorem habet, id ad vectis ratio-
                  <lb/>
                nem refert, quod verum
                  <reg norm="non" type="context">nõ</reg>
                eſt. </s>
                <s xml:id="echoid-s1844" xml:space="preserve">Huiuſmodi enim ratione nauis tardius potius, quàm
                  <lb/>
                velocius ferri deberet, quia quantò altius eſt velum, vi venti impulſum,
                  <reg norm="tantò" type="context">tãtò</reg>
                magis
                  <lb/>
                proram ipſius nauis in aquam demergit. </s>
                <s xml:id="echoid-s1845" xml:space="preserve">Sed huiuſmodi effectus à maiori potius
                  <lb/>
                quantitate venti quam recipit, quàm ab alia aliqua cauſa oritur, quia ventus liberius
                  <lb/>
                  <reg norm="vehementiusque" type="simple">vehementiusq́;</reg>
                in altiore parte, quàm in depræſſione vagatur & perflat.</s>
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            <div xml:id="echoid-div367" type="section" level="3" n="14">
              <head xml:id="echoid-head220" style="it" xml:space="preserve">Quòdrationes ab Ariſtotele de octaua quæstione confictæ
                <lb/>
              ſufficient es non ſint.</head>
              <head xml:id="echoid-head221" xml:space="preserve">CAP. XIIII.</head>
              <p>
                <s xml:id="echoid-s1846" xml:space="preserve">RAtiones etiam ab Ariſtotele propoſitæ pro indaganda octauæ quæſtionis ve-
                  <lb/>
                ritate, in qua quærit vnde fiat, vt corpora rotundæ figuræ, ad
                  <reg norm="voluendum" type="context">voluendũ</reg>
                ſint
                  <lb/>
                faciliora reliquis, quarum reuolutionum corporum tres ſpecies aſſignat,
                  <reg norm="quarum" type="context">quarũ</reg>
                vna
                  <lb/>
                eſt, vt rotarum
                  <reg norm="curruum" type="context">curruũ</reg>
                ; </s>
                <s xml:id="echoid-s1847" xml:space="preserve">altera vt rotarum puteorum, aut trochlearum, quibus hauri-
                  <lb/>
                tur aqua; </s>
                <s xml:id="echoid-s1848" xml:space="preserve">& tertia, vt paruorum vaſorum a figulis fabricatorum,
                  <reg norm="ſufficientes" type="context">ſufficiẽtes</reg>
                  <reg norm="non" type="context">nõ</reg>
                ſunt.</s>
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              <p>
                <s xml:id="echoid-s1849" xml:space="preserve">Incipiens autem à prima dico dubium non eſſe, quin tangente corpore aliquo ro
                  <lb/>
                tundo aliquod planum mediante ſolo quodam puncto contingat, quemadmodum
                  <lb/>
                probat Theodoſius in .3. lib. primi & Vitellio in .71. lib. primi, &
                  <reg norm="ducendo" type="context">ducẽdo</reg>
                per
                  <reg norm="centrum" type="context">centrũ</reg>
                  <lb/>
                ſphæræ lineam vſque ad punctum contactus, ipſa erit perpendicularis plano contin-
                  <lb/>
                genti ſphęram dictam, vt probat
                  <reg norm="idem" type="context">idẽ</reg>
                Thęodoſius in .4. lib. primi
                  <reg norm="Alhazem" type="context">Alhazẽ</reg>
                in .25. quar-
                  <lb/>
                ti, & Vitellio in .7. primi. </s>
                <s xml:id="echoid-s1850" xml:space="preserve">Verum etiam eſt omnem inclinationem ponderoſam huiuſ
                  <lb/>
                modi corporis homogęnei totam hanc lineam æqualiter omni ex parte circundare;
                  <lb/>
                </s>
                <s xml:id="echoid-s1851" xml:space="preserve">cuius quidem rei exemplum in carta deſcribere poſſumus mediante figura circulari
                  <lb/>
                hîc ſubſcripta
                  <var>.a.n.e.u.</var>
                contigua lineæ rectæ
                  <var>.b.d.</var>
                in puncto
                  <var>.a.</var>
                vnde
                  <var>.e.o.a.</var>
                perpendicu
                  <lb/>
                laris erit ipſi
                  <var>.b.d.</var>
                ex .17. lib. 3. Eucli. &
                  <reg norm="tantum" type="context">tantũ</reg>
                ponderis habebimus à parte
                  <var>.a.u.e.</var>
                quan
                  <lb/>
                tum ab ipſa
                  <var>.a.n.e</var>
                . </s>
                <s xml:id="echoid-s1852" xml:space="preserve">Nuncigitur ſi imaginabimur ductum eſſe centrum verſus
                  <var>.u.</var>
                per
                  <lb/>
                lineam
                  <var>.o.u.</var>
                parallelam ipſi
                  <var>.a.d.</var>
                clarum nobis
                  <lb/>
                erit,
                  <reg norm="quod" type="simple">ꝙ</reg>
                  <reg norm="abſque" type="simple">abſq;</reg>
                vlla difficultate aut reſiſtentia
                  <reg norm="idem" type="context">idẽ</reg>
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0167-01a" xlink:href="fig-0167-01"/>
                ducemus, quia huiuſmodi centrum ab inferiori
                  <lb/>
                parte ad ſuperiorem, nunquam mutabit ſitum
                  <lb/>
                reſpectu
                  <reg norm="diſtantiæ" type="context">diſtãtiæ</reg>
                ſeu interualli, quę inter ipſum
                  <lb/>
                lineamq́ue
                  <var>.a.d.</var>
                intercedit,
                  <reg norm="quod" type="simple">ꝙ</reg>
                quidem centrum
                  <lb/>
                in ſe colligittotum pondus figurę
                  <var>.a.n.e.u.</var>
                & be
                  <lb/>
                neficio lineæ
                  <var>.e.o.a.</var>
                illud ipſum puncto
                  <var>.a.</var>
                in li-
                  <lb/>
                nea
                  <var>.b.a.d.</var>
                committit, productum
                  <var>.a.</var>
                nil refert,
                  <lb/>
                vt magis, aut minus verſus ipſum
                  <var>.d.</var>
                aut verſus
                  <lb/>
                b.
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                ; </s>
                <s xml:id="echoid-s1853" xml:space="preserve">ita vt
                  <reg norm="cum" type="context">cũ</reg>
                non oporteat vt huius figuræ
                  <lb/>
                  <reg norm="pondus" type="context">põdus</reg>
                , vna vice, magis eleuetur, quàm alia, ſed
                  <lb/>
                ſemper ęqualiter ſuper lineam
                  <var>.b.a.d.</var>
                quieſcat.</s>
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