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-div340" type="chapter" level="2" n="3">
            <div xml:id="echoid-div377" type="section" level="3" n="19">
              <pb o="162" rhead="IO. BAPT. BENED." n="174" file="0174" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0174"/>
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            <div xml:id="echoid-div379" type="section" level="3" n="20">
              <head xml:id="echoid-head232" style="it" xml:space="preserve">De uer a r atione .17. queſtionis.</head>
              <head xml:id="echoid-head233" xml:space="preserve">CAP. XX.</head>
              <p>
                <s xml:id="echoid-s1933" xml:space="preserve">DEcimaſeptima quæſtio ab Ariſtotele haud benè percepta fuit, quia is non ac-
                  <lb/>
                commodat partes vectis ſuis locis. </s>
                <s xml:id="echoid-s1934" xml:space="preserve">Quamobrem imaginemur duos vectes
                  <var>.
                    <lb/>
                  a.o.n.</var>
                et
                  <var>.o.e.u.</var>
                quorum centra, quæ hypomochlia appellantur ſint
                  <var>.o.</var>
                & pondera,
                  <lb/>
                quæ ſunt attollenda ſint
                  <var>.a.</var>
                et
                  <var>.e.</var>
                inter ſe æqualia, & diſtantię ſint
                  <var>.a.o.</var>
                et
                  <var>.e.o.</var>
                ſibi
                  <reg norm="inuicem" type="context">inuicẽ</reg>
                  <lb/>
                æquales, ſed
                  <var>.o.n.</var>
                æqualis ſit ipſi
                  <var>.o.u</var>
                : clarum erit,
                  <reg norm="quod" type="simple">ꝙ</reg>
                ad eleuandum
                  <var>.a.</var>
                oportebit depri
                  <lb/>
                mere
                  <var>.n.</var>
                & ad eleuandum
                  <var>.e.</var>
                oportebit attollere
                  <var>.u</var>
                . </s>
                <s xml:id="echoid-s1935" xml:space="preserve">Et quia omnia ſupponuntur æ qua
                  <lb/>
                  <handwritten xlink:label="hd-0174-01" xlink:href="hd-0174-01a" number="16"/>
                lia, clarum quoque erit, commu-
                  <lb/>
                ni ſcientia, tantam virtutem in
                  <lb/>
                  <figure xlink:label="fig-0174-01" xlink:href="fig-0174-01a" number="236">
                    <image file="0174-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0174-01"/>
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                n. quanta ſufficiet ad
                  <reg norm="attollendum" type="context">attollendũ</reg>
                  <lb/>
                a. in
                  <var>.u.</var>
                  <reg norm="quoque" type="simple">quoq;</reg>
                ſuffecturam ad ele-
                  <lb/>
                uandum
                  <var>.e.</var>
                quia
                  <reg norm="cum" type="context">cũ</reg>
                æqualibus an
                  <lb/>
                gulis ijs, quibus duæ virtutes
                  <var>.a.</var>
                  <lb/>
                et
                  <var>.n.</var>
                annituntur
                  <var>.o.</var>
                centro, ita
                  <var>.e.</var>
                  <lb/>
                et
                  <var>.u.</var>
                è contrario ſuo centro
                  <var>.o.</var>
                an
                  <lb/>
                nituntur. </s>
                <s xml:id="echoid-s1936" xml:space="preserve">& omnes rationes pro
                  <lb/>
                vecte
                  <var>.a.o.n.</var>
                quarto
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                huius tracta-
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                  <figure xlink:label="fig-0174-02" xlink:href="fig-0174-02a" number="237">
                    <image file="0174-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0174-02"/>
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                tus capitibus citatæ, vecti
                  <var>.o.e.u.</var>
                vt ſatis ſu
                  <lb/>
                  <reg norm="perque" type="simple">perq́;</reg>
                dixi in dicto capit .5. conuenire poſ-
                  <lb/>
                ſunt.</s>
              </p>
              <p>
                <s xml:id="echoid-s1937" xml:space="preserve">Nunc ſit aliqua pars ligni cindenda ſe-
                  <lb/>
                cundum venulas ſuas
                  <var>.d.e.f.g.</var>
                & ſit cuneus
                  <lb/>
                  <var>a.b.c.</var>
                qui vi mallei
                  <var>.P.</var>
                vſque ad
                  <var>.t.x.</var>
                pene-
                  <lb/>
                trarit. </s>
                <s xml:id="echoid-s1938" xml:space="preserve">Hinc clarum erit, quòd apertura
                  <lb/>
                  <var>i.m.r.</var>
                ligni, poſt quam infigitur cuneus ſe
                  <lb/>
                cundum venas, longíor erit parte
                  <var>.x.b.t.</var>
                cu
                  <lb/>
                nei, quæ ingreſſa eſt. </s>
                <s xml:id="echoid-s1939" xml:space="preserve">Oportet nunc ima-
                  <lb/>
                ginari duos vectes ſimiles ſupradictæ
                  <var>.u.e.
                    <lb/>
                  o.</var>
                in hunc modum, vt puncta
                  <var>i.r.</var>
                lìni ſint
                  <lb/>
                loco
                  <var>.u.</var>
                extremi
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                vectis, et
                  <var>.t.x.</var>
                loco vir
                  <lb/>
                tutis applicatæ ipſi
                  <var>.u.</var>
                & reſiſtentia circa
                  <lb/>
                punctum
                  <var>.m.</var>
                loco ponderis
                  <var>.e.</var>
                vectis
                  <var>.o.e.u.</var>
                  <lb/>
                dicti, & pars
                  <var>.K.</var>
                quaſi immediata poſt
                  <var>.m.</var>
                  <lb/>
                verſus extremitatem
                  <var>.f.e.</var>
                ligni, ſit loco hy-
                  <lb/>
                pomochlij
                  <var>.o</var>
                . </s>
                <s xml:id="echoid-s1940" xml:space="preserve">Hinc fiet vt quanto longio
                  <lb/>
                res erunt lineæ
                  <var>.i.m.K.</var>
                et
                  <var>.r.m.K.</var>
                tantò quo
                  <lb/>
                que facilius virtutes
                  <var>.t.x.</var>
                impellent
                  <var>.i.r</var>
                .</s>
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