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-div367" type="section" level="3" n="14">
              <p>
                <s xml:id="echoid-s1863" xml:space="preserve">
                  <pb o="157" rhead="DE MECHAN." n="169" file="0169" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0169"/>
                  <var>b.a.d.</var>
                non æquediſtaret, ſed ſurſum traheret ſuper
                  <var>.u.</var>
                aut ſubter, aliquid de ſua vi vir
                  <lb/>
                  <reg norm="tuteque" type="simple">tuteq́;</reg>
                amitteret, & tantò plus, quantò inclinata magis eſſet verſus
                  <var>.a.o.e.</var>
                & tandem
                  <lb/>
                cum eſſet vnita cum
                  <var>.a.o.e.</var>
                aut ad ſuperius, aut ad inferius quantalibet ui, etiam ſi in-
                  <lb/>
                finita, figuram extra ſitum primæ lineæ
                  <var>.a.o.e.</var>
                non moueret, ſed ſi ſurſum traheret ſe
                  <lb/>
                iungeret eam à linea
                  <var>.b.a.d.</var>
                non ob id tamen efficeret, ut centrum
                  <var>.o.</var>
                exiret extra pri
                  <lb/>
                mam lineam
                  <var>.a.o.e</var>
                .</s>
              </p>
              <p>
                <s xml:id="echoid-s1864" xml:space="preserve">Secunda verò ſpecies, tribus reuolutionum modis, abſque axis mutatione conſta
                  <lb/>
                re poteſt, ideſt modo, quo reuoluuntur trochleæ mediante fune, & quo reuoluuntur
                  <lb/>
                aliquæ rotæ, in quibus aliquod animal incedit; </s>
                <s xml:id="echoid-s1865" xml:space="preserve">& quo reuoluuntur illæ, quæ in homi
                  <lb/>
                nis manu circunuoluuntur medio alicuius manubrij inflexi. </s>
                <s xml:id="echoid-s1866" xml:space="preserve">Hi omnes modi cum
                  <lb/>
                circulari figura magis,
                  <reg norm="quam" type="context">quã</reg>
                cum alia quauis, faciliores euadunt. </s>
                <s xml:id="echoid-s1867" xml:space="preserve">Et primò ſi priorem
                  <lb/>
                modum conſiderabimus, vt mediante fune quælibet figura, quæ circularis non ſit,
                  <lb/>
                voluatur, ſupponamus exemplo debere reuolui pentagonum æquiangulum
                  <var>.a.e.i.o.
                    <lb/>
                  u.</var>
                circa centrum
                  <var>.c.</var>
                mediante fune
                  <var>.q.u.a.e.i.p.</var>
                neceſſariò occurrent (in hac figura an-
                  <lb/>
                gulorum,
                  <reg norm="laterumque" type="simple">laterumq́;</reg>
                diſparium) plures inæqualitates, quæ reuolutionem eiuſdem fi-
                  <lb/>
                guræ irregularem efficient; </s>
                <s xml:id="echoid-s1868" xml:space="preserve">quarum vna erit, quod duæ partes funis, ideſt
                  <var>.u.q.</var>
                et
                  <var>.i.p.</var>
                  <lb/>
                non erunt in vna
                  <reg norm="eademque" type="simple">eademq́;</reg>
                inter ſe diſtantia ſemper, quod facile intellectu erit, ſi ima
                  <lb/>
                ginabimur ductas eſſe lineas
                  <var>.a.i</var>
                :
                  <var>u.i</var>
                : et
                  <var>.i.c.t.</var>
                ſi funis duo pondera habebit alterum
                  <lb/>
                altero maius, ſuis extremis appenſa, vnde debeat figura virtute ponderis maioris cir
                  <lb/>
                cunuolui: </s>
                <s xml:id="echoid-s1869" xml:space="preserve">dictæ duæ partes
                  <var>.u.q.</var>
                et
                  <var>.i.p.</var>
                eiuſdem funis,
                  <reg norm="mundi" type="context">mũdi</reg>
                centrum, dum firmæ ma
                  <lb/>
                nebunt, reſpicient; </s>
                <s xml:id="echoid-s1870" xml:space="preserve">ſed permittentes pondera libera; </s>
                <s xml:id="echoid-s1871" xml:space="preserve">maius, efficiens vt circunuolua-
                  <lb/>
                tur figura; </s>
                <s xml:id="echoid-s1872" xml:space="preserve">efficiet, vt aliquando vnum exlateribus, eiuſdem figuræ mundi
                  <reg norm="quoque" type="simple">quoq;</reg>
                cen
                  <lb/>
                trum reſpiciet, vt in
                  <lb/>
                  <figure xlink:label="fig-0169-01" xlink:href="fig-0169-01a" number="229">
                    <image file="0169-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0169-01"/>
                  </figure>
                figura
                  <var>.A.</var>
                  <reg norm="ſicque" type="simple">ſicq́;</reg>
                etiam
                  <lb/>
                linea
                  <var>.i.c.t.</var>
                (pro
                  <reg norm="exem- plo" type="context">exẽ-
                    <lb/>
                  plo</reg>
                ) erit menſura di-
                  <lb/>
                ſtantiæ funium inter
                  <lb/>
                ipſas, & deinde
                  <reg norm="circum" type="context">circũ</reg>
                  <lb/>
                uoluendo etiam di-
                  <lb/>
                ſtabuntinter ſe per li
                  <lb/>
                  <reg norm="neam" type="context">neã</reg>
                  <var>.i.a.</var>
                aut
                  <var>.i.u.</var>
                vt in
                  <lb/>
                figura
                  <var>.B.</var>
                  <reg norm="innotuit" type="context">ĩnotuit</reg>
                  <reg norm="exem" type="context">exẽ</reg>
                  <lb/>
                plo, & ſic etiam ali-
                  <lb/>
                quando erunt magis
                  <lb/>
                  <reg norm="diſtantes" type="context">diſtãtes</reg>
                , quàm linea
                  <lb/>
                  <var>t.i.</var>
                & minus quàm.i.
                  <lb/>
                a: </s>
                <s xml:id="echoid-s1873" xml:space="preserve">nunquam tamen minus quam
                  <var>.t.i.</var>
                neque magis
                  <reg norm="quam" type="context">quã</reg>
                  <lb/>
                  <var>i.a.</var>
                aut
                  <var>.i.u.</var>
                quæ ſunt æquales; </s>
                <s xml:id="echoid-s1874" xml:space="preserve">Quæ quidem varietas,
                  <lb/>
                  <figure xlink:label="fig-0169-02" xlink:href="fig-0169-02a" number="230">
                    <image file="0169-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0169-02"/>
                  </figure>
                in hanc, & in illam partem impellet partes penden-
                  <lb/>
                tes funis, vnde æqualiter non trahent. </s>
                <s xml:id="echoid-s1875" xml:space="preserve">Idem dico, ſi
                  <lb/>
                extrema
                  <var>.q.</var>
                et
                  <var>.p.</var>
                eſſent quoque ſemper in vna
                  <reg norm="eademque" type="context simple">eadẽq́;</reg>
                  <lb/>
                diſtantia; </s>
                <s xml:id="echoid-s1876" xml:space="preserve">neque à corpore
                  <reg norm="ponderoſo" type="context">põderoſo</reg>
                eſſent attracta,
                  <lb/>
                quia aliæ partes ipſius
                  <var>.u.q.</var>
                et
                  <var>.i.p.</var>
                ex ſupradictis ratio-
                  <lb/>
                nibus vnam
                  <reg norm="eademque" type="simple">eademq́;</reg>
                diſtantiam
                  <reg norm="non" type="context">nõ</reg>
                ſemper
                  <reg norm="ſeruarent" type="context">ſeruarẽt</reg>
                .
                  <lb/>
                </s>
                <s xml:id="echoid-s1877" xml:space="preserve">vnde fieret vt cum diuerſis angulis tam
                  <var>.i.p.</var>
                  <reg norm="quam" type="context">quã</reg>
                  <var>.u.q.</var>
                  <lb/>
                  <reg norm="traherent" type="context">traherẽt</reg>
                ſemidiametros
                  <var>.c.i</var>
                :
                  <var>c.e</var>
                :
                  <var>c.a</var>
                :
                  <var>c.u.</var>
                et
                  <var>.c.o.</var>
                quia
                  <reg norm="non" type="context">nõ</reg>
                  <lb/>
                ſemper traherent ope ſeu virtute anguli æqualis ipſi
                  <var>.
                    <lb/>
                  c.i.p</var>
                . </s>
                <s xml:id="echoid-s1878" xml:space="preserve">Hæc autem inę qualitas communis eſt omnibus </s>
              </p>
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