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-div379" type="section" level="3" n="20">
              <pb o="163" rhead="DE MECHAN." n="175" file="0175" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0175"/>
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            <div xml:id="echoid-div381" type="section" level="3" n="21">
              <head xml:id="echoid-head234" style="it" xml:space="preserve">De uera & intrinſeca cauſa trocble arum.</head>
              <head xml:id="echoid-head235" xml:space="preserve">CAP. XXI.</head>
              <p>
                <s xml:id="echoid-s1941" xml:space="preserve">PRo intelligenda vera, & intrinſeca ratione, vnde fiat ut multitudo rotularum in
                  <lb/>
                trochleis cauſa ſit, ut exigua vis ſurſum moueat, aut attollat
                  <reg norm="pondera" type="context">põdera</reg>
                magna. </s>
                <s xml:id="echoid-s1942" xml:space="preserve">Ima
                  <lb/>
                ginemur duas hîc ſubſcriptas trochlæas explicatas tranſuerſaliter in hunc modum,
                  <lb/>
                ideſt ſit
                  <reg norm="paruum" type="context">paruũ</reg>
                  <reg norm="tignum" type="context">tignũ</reg>
                  <var>.a.b.</var>
                fixum &
                  <reg norm="parallelum" type="context">parallelũ</reg>
                orizonti. cui ſint rotulæ appenſe ab infe
                  <lb/>
                riori parte ad ſuperiorem
                  <reg norm="huicque" type="simple">huicq́;</reg>
                è regione
                  <reg norm="oppoſitus" type="simple">oppoſitꝰ</reg>
                ſit aliud
                  <reg norm="tignum" type="context">tignũ</reg>
                  <var>.c.d.</var>
                quod moueri
                  <lb/>
                poſſit ab imo ad ſumum, ſuper quod totidem ſint rotulæ aut radij,
                  <reg norm="cum" type="context">cũ</reg>
                annexa poſtea
                  <lb/>
                fuerit funis puncto
                  <var>.b.</var>
                fixo, eam faciendo pertranſire per rotulas tam à parte ſupe-
                  <lb/>
                riore, quam ab inferiore; </s>
                <s xml:id="echoid-s1943" xml:space="preserve">& appenſum deinde cum erit paruo illi tigno
                  <var>.c.d.</var>
                mobili
                  <lb/>
                pondus
                  <var>.E.</var>
                ducendo poſtmodum extremum
                  <var>.f.</var>
                funis tranſeuntis per rotulas, idem pla
                  <lb/>
                nè fiet quod à trochlęis ſimul unitis fieri ſolet. </s>
                <s xml:id="echoid-s1944" xml:space="preserve">Cuius quidem effectus ratio ſub no-
                  <lb/>
                ſtram cognitionem cadet facilius in huiuſmodi figura. </s>
                <s xml:id="echoid-s1945" xml:space="preserve">Imaginemur ſeparatim ſta-
                  <lb/>
                teram
                  <var>.g.h.</var>
                cuius
                  <reg norm="centrum" type="context">cẽtrum</reg>
                ſit
                  <var>.K.</var>
                ita ſitum, ut brachium
                  <var>.g.k.</var>
                ſit duplum ad brachium
                  <var>.K.
                    <lb/>
                  h.</var>
                ſupponendo igitur in puncto
                  <var>.g.</var>
                pondus, aut virtutem mouentem unius libræ, & in
                  <lb/>
                h. duarum librarum,
                  <reg norm="abſque" type="simple">abſq;</reg>
                dubio hæ duæ uirtutes in huiuſmodi diſtantijs à centro
                  <lb/>
                  <handwritten xlink:label="hd-0175-01" xlink:href="hd-0175-01a" number="17"/>
                ęquales
                  <reg norm="inuicem" type="context">inuicẽ</reg>
                  <reg norm="erunt" type="context">erũt</reg>
                , ob rationes prioribus capitibus iam allatas, & ſtatera orizontalis
                  <lb/>
                manebit. </s>
                <s xml:id="echoid-s1946" xml:space="preserve">Vnde clarum erit,
                  <reg norm="quod" type="simple">ꝙ</reg>
                quæuis etiam exigua virtus adiuncta ipſi
                  <var>.g.</var>
                mouebit
                  <lb/>
                ſtateram extra orizontalem ſitum. </s>
                <s xml:id="echoid-s1947" xml:space="preserve">Nunc ſi puncto
                  <var>.i.</var>
                ex æquo medio inter
                  <var>.g.</var>
                et
                  <var>.K.</var>
                  <lb/>
                applicata erit virtus ipſius
                  <var>.h.</var>
                non amplius conſiderato brachio
                  <var>.K.h.</var>
                inclinante uirtu-
                  <lb/>
                te ipſius
                  <var>.i.</var>
                eandem partem verſus, in quam inclinabat, quando erat in
                  <var>.h.</var>
                ſed uirtus ip
                  <lb/>
                ſius
                  <var>.g.</var>
                inclinet contrario modo,
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                ab eo, quo inclinabat prius; </s>
                <s xml:id="echoid-s1948" xml:space="preserve">clarum
                  <reg norm="quoque" type="simple">quoq;</reg>
                  <lb/>
                erit, communi conceptu, & ob ea, quæ cap .5. huius tractatus ſunt dicta
                  <var>.g.h.</var>
                ſemper
                  <lb/>
                in eodem ſitu abſque motu manſuram,
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                ſtateram appellabimus mobilem, &
                  <lb/>
                primam. </s>
                <s xml:id="echoid-s1949" xml:space="preserve">Imaginemur nunc à puncto
                  <var>.e.</var>
                fixo deſcendere funem
                  <var>.e.K.</var>
                quæ fulciat pun
                  <lb/>
                ctum
                  <var>.K.</var>
                extremum diametri
                  <var>.g.K.</var>
                quam intelligo pro diametro vnius ex rotulis infe
                  <lb/>
                rioribus trochleæ; </s>
                <s xml:id="echoid-s1950" xml:space="preserve">& ſit
                  <var>.n.l.m.</var>
                diameter vnius ex rotulis ſuperioribus alterius parui
                  <lb/>
                tigni defixi à parte inclinationis ipſius
                  <var>.g.</var>
                & parallela diametro
                  <var>.g.K.</var>
                cuius diametri
                  <lb/>
                centrum fixum ſit
                  <var>.l.</var>
                & ſit coniunctum
                  <var>.g.</var>
                punctum, à fune cum puncto
                  <var>.m.</var>
                quæ
                  <reg norm="tam" type="context">tã</reg>
                per-
                  <lb/>
                pendicularis ſit primo diametro
                  <var>.g.i.K.</var>
                quàm ſecundo
                  <var>.n.m.</var>
                ideſt ita vt anguli
                  <var>.n.m.g.</var>
                  <lb/>
                  <figure xlink:label="fig-0175-01" xlink:href="fig-0175-01a" number="238">
                    <image file="0175-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0175-01"/>
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                </s>
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