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-div374" type="section" level="3" n="17">
              <p>
                <s xml:id="echoid-s1923" xml:space="preserve">
                  <pb o="161" rhead="DE MECHAN." n="173" file="0173" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0173"/>
                maneat, ſed citò fiat curua, cum dictum corpus
                  <var>.a.</var>
                duabus virtutibus moueatur, qua-
                  <lb/>
                rum vna eſt, violentia impræſſa, & alia natura, contra opinionem Tartaleæ, qui ne-
                  <lb/>
                gat corpus aliquod motibus violen
                  <lb/>
                  <figure xlink:label="fig-0173-01" xlink:href="fig-0173-01a" number="234">
                    <image file="0173-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0173-01"/>
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                to & naturali ſimul & ſemel moueri
                  <lb/>
                poſſe. </s>
                <s xml:id="echoid-s1924" xml:space="preserve">
                  <reg norm="Neque" type="simple">Neq;</reg>
                eſt
                  <reg norm="ſilentio" type="context">ſilẽtio</reg>
                  <reg norm="prætereundus" type="context">prætereũdus</reg>
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                hac in re
                  <reg norm="quidam" type="simple context">ꝗdã</reg>
                notatu
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                effectus,
                  <lb/>
                qui eiuſmodi eſt,
                  <reg norm="quod" type="simple">ꝙ</reg>
                quanto magis
                  <lb/>
                creſcit impetus in corpore
                  <var>.a.</var>
                cauſa
                  <lb/>
                tus ab augumento velocitatis giri
                  <lb/>
                ipſius
                  <var>.e.</var>
                  <reg norm="tantò" type="context">tãtò</reg>
                magis oportet, vt ſen-
                  <lb/>
                tiat ſe trahi manus à dicto corpore
                  <lb/>
                a. mediante fune, quia quantò ma-
                  <lb/>
                ior impetus motus ipſi
                  <var>.a.</var>
                eſt impręſ
                  <lb/>
                ſus, tantò magis dictum corpus
                  <var>.a.</var>
                  <lb/>
                ad rectum iter peragendum incli-
                  <lb/>
                natur, vnde vt recta incedat, tantò
                  <lb/>
                maiore quoque vi trahit.</s>
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            <div xml:id="echoid-div376" type="section" level="3" n="18">
              <head xml:id="echoid-head228" style="it" xml:space="preserve">De decimatertia questione.</head>
              <head xml:id="echoid-head229" xml:space="preserve">CAP. XVIII.</head>
              <p>
                <s xml:id="echoid-s1925" xml:space="preserve">DEcimatertia quæſtio ad vectem omnino eſt referenda. </s>
                <s xml:id="echoid-s1926" xml:space="preserve">Imaginari debemus
                  <lb/>
                axem cylindrici iugi, hypomochlion eſſe. </s>
                <s xml:id="echoid-s1927" xml:space="preserve">Quod reſtat, illud ipſum totum de
                  <lb/>
                pendet à .4.
                  <reg norm="quintoque" type="simple">quintoq́;</reg>
                cap. huius tractatus. </s>
                <s xml:id="echoid-s1928" xml:space="preserve">Vna tamen differentia inter hanc machi-
                  <lb/>
                nam,
                  <reg norm="vectemque" type="simple">vectemq́;</reg>
                reperitur, quæ eſt,
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                iugum aliquam reſiſtentiam pro coniunctione
                  <lb/>
                calcata in loco, in quo voluitur, magis quàm hypomochlion vecti efficiat.</s>
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            <div xml:id="echoid-div377" type="section" level="3" n="19">
              <head xml:id="echoid-head230" style="it" xml:space="preserve">De decimaquart a queſtione.</head>
              <head xml:id="echoid-head231" xml:space="preserve">CAP. XIX.</head>
              <p>
                <s xml:id="echoid-s1929" xml:space="preserve">RAtiones etiam decimæquartæ quæſtionis dependent ab ijs, quæ ſunt vectis, vt
                  <lb/>
                exempli gratia ſit lignum
                  <var>.a.b.c.d.</var>
                frang endum in medio, annitendo genibus
                  <lb/>
                in punctum
                  <var>.o.</var>
                clariſſimè tunc videbimus,
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                tenentes marlus longè à medio, in locis
                  <lb/>
                a. et
                  <var>.c.</var>
                facilius
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                cum labore illum frangemus, quàm ſi eaſdem vicinas me-
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                dio eiuſdem ligni in locis
                  <var>.e.</var>
                et
                  <var>.i.</var>
                poneremus. </s>
                <s xml:id="echoid-s1930" xml:space="preserve">Cuius rei rationes
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                ſunt
                  <reg norm="cum" type="context">cũ</reg>
                ijs, quæ
                  <lb/>
                primis huius tractatus capitibus propoſitæ fuerunt. </s>
                <s xml:id="echoid-s1931" xml:space="preserve">Imaginemur lineas rectas ductas
                  <lb/>
                à puncto
                  <var>.o.</var>
                ad loca
                  <var>.a.e.i.</var>
                et
                  <var>.c.</var>
                hinc manifeſtè perſpiciemus eorum, quæ iam diximus
                  <lb/>
                ratione,
                  <reg norm="quod" type="simple">ꝙ</reg>
                loca
                  <var>.e.</var>
                et
                  <var>.i.</var>
                mediantibus duabus lineis
                  <var>.e.o.</var>
                et
                  <var>.i.o.</var>
                magis annitentur
                  <var>.o.</var>
                cen
                  <lb/>
                tro, quàm loco
                  <var>.a.</var>
                et
                  <var>.c.</var>
                  <reg norm="duarum" type="context">duarũ</reg>
                  <reg norm="linearum" type="context">linearũ</reg>
                  <var>.a.o.</var>
                et
                  <var>.c.o.</var>
                beneficio; </s>
                <s xml:id="echoid-s1932" xml:space="preserve">vnde vim
                  <reg norm="quoque" type="simple">quoq;</reg>
                maiorem
                  <lb/>
                  <reg norm="habebunt" type="context">habebũt</reg>
                  <lb/>
                  <figure xlink:label="fig-0173-02" xlink:href="fig-0173-02a" number="235">
                    <image file="0173-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0173-02"/>
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                in
                  <var>.a.</var>
                et
                  <var>.c.</var>
                  <lb/>
                quàm in
                  <lb/>
                e. et
                  <var>.i</var>
                .</s>
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