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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IO. BAPT. BENED.
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          <div xml:id="echoid-div340" type="chapter" level="2" n="3">
            <div xml:id="echoid-div348" type="section" level="3" n="5">
              <p>
                <s xml:id="echoid-s1749" xml:space="preserve">
                  <pb o="146" rhead="IO. BAPT. BENED." n="158" file="0158" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0158"/>
                huius effectus conuerſo, ideſt, vt quemadmodum nunc ſupponuntur
                  <var>.o.</var>
                et
                  <var>.u.</var>
                eſſe duo
                  <lb/>
                centra quibus
                  <reg norm="ſuſtinetur" type="simple">ſuſtinet̃</reg>
                pondus
                  <var>.e.</var>
                ipſius
                  <var>.n.</var>
                imaginemur
                  <var>.n.</var>
                eſſe quoddam centrum à
                  <lb/>
                quo pendeant duo pondera
                  <var>.o.</var>
                et
                  <var>.u.</var>
                ſic inuicem proportionata, ut ſunt
                  <var>.u.i.</var>
                et
                  <var>.i.o.</var>
                  <lb/>
                certe horum ponderum cauſa ſtatera
                  <var>.o.s.</var>
                quam vectem appellabamus à nulla parte
                  <lb/>
                inclinabitur. </s>
                <s xml:id="echoid-s1750" xml:space="preserve">Redeuntes nunc ad propoſitum, dicemus
                  <reg norm="quod" type="simple">ꝙ</reg>
                annitente pondere ipſius
                  <var>.
                    <lb/>
                  n.</var>
                minus ad
                  <var>.u.</var>
                quam ad
                  <var>.o.</var>
                ideſt ad
                  <var>.t.</var>
                minori vi opus erit in
                  <var>.u.</var>
                quàm in
                  <var>.t.</var>
                ad attollen-
                  <lb/>
                dum pondus ipſius
                  <var>.n.</var>
                & ſic per conſequens quantò longius erit punctum
                  <var>.u.</var>
                ab
                  <var>.t.</var>
                tan
                  <lb/>
                tò minori quoque vi egebit, & conſequenter quando vis, aut reſiſtentia in
                  <var>.u.</var>
                ita pro
                  <lb/>
                portionata erit illi, quæ eſt ipſius
                  <var>.o.</var>
                vt eſt
                  <var>.o.i.</var>
                ad
                  <var>.i.u.</var>
                vectis non mouebitur. </s>
                <s xml:id="echoid-s1751" xml:space="preserve">Sed quan
                  <lb/>
                do erit proportio maior, reſiſtentiæ ipſius
                  <var>.u.</var>
                ad eam, quæ eſt ipſius
                  <var>.o.</var>
                ea, quæ eſt
                  <var>.o.
                    <lb/>
                  i.</var>
                ad
                  <var>.i.u.</var>
                </s>
                <s xml:id="echoid-s1752" xml:space="preserve">tunc vectis à par-
                  <lb/>
                teipſius
                  <var>.u.s.</var>
                eleuabitur, ſi
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0158-01a" xlink:href="fig-0158-01"/>
                vero proportio minor eſſet
                  <lb/>
                quàm.o.i. ad
                  <var>.i.u.</var>
                </s>
                <s xml:id="echoid-s1753" xml:space="preserve">tunc ve-
                  <lb/>
                ctis ab eadem parte depri-
                  <lb/>
                metur.</s>
              </p>
              <div xml:id="echoid-div348" type="float" level="4" n="1">
                <figure xlink:label="fig-0157-01" xlink:href="fig-0157-01a">
                  <image file="0157-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0157-01"/>
                </figure>
                <figure xlink:label="fig-0158-01" xlink:href="fig-0158-01a">
                  <image file="0158-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0158-01"/>
                </figure>
              </div>
            </div>
            <div xml:id="echoid-div350" type="section" level="3" n="6">
              <head xml:id="echoid-head205" style="it" xml:space="preserve">De ratione cuiuſdam uis adauctæ.</head>
              <head xml:id="echoid-head206" xml:space="preserve">CAP. VI.</head>
              <p>
                <s xml:id="echoid-s1754" xml:space="preserve">QVibuſdam in locis vtuntur
                  <reg norm="quidam" type="context">quidã</reg>
                  <reg norm="quodam" type="context">quodã</reg>
                  <reg norm="inſtrumento" type="context">inſtrumẽto</reg>
                piſtorio ad
                  <reg norm="ſubigendam" type="context context">ſubigẽdã</reg>
                pa-
                  <lb/>
                ſtam, vnius tantum hominis ui adhibita, quæ quidem machina cum mihi di-
                  <lb/>
                gna contemplatione eſſe videatur, eius aliquam rationem proponere volui, pro cu-
                  <lb/>
                ius deſcriptione imaginemur planum, in quo ſedet ille, qui voluit paſtam, & in quo
                  <lb/>
                ipſa paſta eſt repoſita
                  <var>.T.S.D.</var>
                & triangulum
                  <var>.T.A.S.</var>
                immobile perpendiculare-
                  <lb/>
                q́ue ſuperficiei dicti plani, angulo autem
                  <var>.A.</var>
                coniunctum lignum
                  <var>.A.E.</var>
                vt ſemidiame
                  <lb/>
                trum mobilem, & æqualem perpendiculari ipſius trianguli, </s>
                <s xml:id="echoid-s1755" xml:space="preserve">unde
                  <var>.A.</var>
                loco centri erit
                  <lb/>
                et
                  <var>.D.O.</var>
                ſit ſemidiameter, qui paſtam contundit, & ab eius extremo
                  <var>.O.</var>
                (quod
                  <var>.O.</var>
                  <lb/>
                quando
                  <var>.D.O.</var>
                orizontalis eſt, in baſi dicti trianguli reperitur) veniat lignum
                  <var>.O.V.</var>
                  <lb/>
                quod cum
                  <var>.A.V.</var>
                ſit æquale perpendiculari imaginatæ ab angulo
                  <var>.A.</var>
                baſi
                  <var>.T.S.</var>
                  <reg norm="deno- datum" type="context">deno-
                    <lb/>
                  datũ</reg>
                  <reg norm="tantum" type="wordlist/context">tñ</reg>
                utvulgo
                  <reg norm="dicitur" type="simple">dicit̃</reg>
                ſeu flexile in
                  <var>.O.</var>
                & in
                  <var>.V.</var>
                vt elleuare
                  <reg norm="atque" type="simple">atq;</reg>
                deprimere ſemidiame
                  <lb/>
                trum
                  <var>.D.O.</var>
                poſſit, et
                  <var>.V.O.</var>
                ſit æqualis
                  <var>.A.V.</var>
                et
                  <var>.V.</var>
                medium ſit inter
                  <var>.A.</var>
                et
                  <var>.E.</var>
                vnde
                  <var>.A.V.</var>
                  <lb/>
                cum
                  <var>.O.V.</var>
                æquales erunt
                  <var>.A.E.</var>
                ſunt deinde duo ligna
                  <reg norm="perpendicularia" type="context">perpẽdicularia</reg>
                ab
                  <var>.A.</var>
                ad baſim
                  <lb/>
                fixa, & immobilia inter ſe adeò diſtantia, vt inter ipſa
                  <reg norm="pertranſeant" type="context context">pertrãſeãt</reg>
                  <var>.O.V.</var>
                et
                  <var>.D.O.</var>
                ſupra
                  <lb/>
                & infra, ne deuiet ſemidiametrum
                  <var>.D.O</var>
                . </s>
                <s xml:id="echoid-s1756" xml:space="preserve">In extremitate deinde ipſius
                  <var>.E.</var>
                ſit lignum
                  <lb/>
                quoddam tenue, vt digitus polex, ad angulos rectos cum
                  <var>.A.E.</var>
                quod ab aliquo, qui
                  <lb/>
                antedictam machinam ſtet, manibus teneatur, qui quidem homo idipſum lignum,
                  <lb/>
                ideſt ſemidiametrum
                  <var>.A.E.</var>
                à ſuperficie trianguli dicti, ad ſe trahendo, & deinde ver
                  <lb/>
                ſus eundem triangulum impellendo, vim quandam maximam mediante ſemidia
                  <lb/>
                metro
                  <var>.D.O.</var>
                ſuper paſtam excitat.</s>
              </p>
              <p>
                <s xml:id="echoid-s1757" xml:space="preserve">Pro cuius rei contemplatione volo vt ſecundam hanc ſubſcriptam figuram
                  <var>.b.a.
                    <lb/>
                  u.x.</var>
                imaginemur, in qua
                  <var>.u.</var>
                exprimat
                  <var>.A.</var>
                primæ figuræ, &
                  <var>.a.</var>
                denotet
                  <var>.O.</var>
                &
                  <var>.o.V.</var>
                &
                  <var>.x.
                    <lb/>
                  E.</var>
                imaginemur etiam
                  <var>.u.a.</var>
                baſem trianguli
                  <var>.a.u.o.</var>
                cui
                  <var>.o.t.</var>
                perpendicularis dictæ baſi
                  <var>.
                    <lb/>
                  u.a.</var>
                addatur. </s>
                <s xml:id="echoid-s1758" xml:space="preserve">
                  <reg norm="Hucuſque" type="simple">Hucuſq;</reg>
                igitur
                  <var>.u.o.</var>
                æqualis erit
                  <var>.o.x.</var>
                & ipſi
                  <var>.o.a.</var>
                imaginemur etiam
                  <var>.a.o.</var>
                  <lb/>
                vſque ad
                  <var>.b.</var>
                ita productam vt
                  <var>.o.b.</var>
                æqualis ſit
                  <var>.o.a.</var>
                ponamus etiam pondus in
                  <var>.a.</var>
                impel- </s>
              </p>
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