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-div342" type="section" level="3" n="2">
              <p>
                <s xml:id="echoid-s1717" xml:space="preserve">
                  <pb o="143" rhead="DE MECHAN." n="155" file="0155" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0155"/>
                ſtat. </s>
                <s xml:id="echoid-s1718" xml:space="preserve">Et quamuis appellem latus
                  <var>.B.C.</var>
                orizontale, ſupponens illud angulum rectum
                  <lb/>
                cum
                  <var>.C.O.</var>
                facere, vnde angulus
                  <var>.C.B.Q.</var>
                fit vt minor ſit recto, ob quantitatem vnius
                  <lb/>
                anguli ęqualis ei, quem duæ
                  <var>.C.O.</var>
                et
                  <var>.B.Q.</var>
                in centro regionis
                  <reg norm="elementaris" type="context">elemẽtaris</reg>
                  <reg norm="conſtituunt" type="context">conſtituũt</reg>
                ,
                  <lb/>
                hoc tamen nihil refert, cum dictus angulus inſenſibilis ſit magnitudinis. </s>
                <s xml:id="echoid-s1719" xml:space="preserve">Ab iſtis au-
                  <lb/>
                tem rationibus elicere poſſumus, quod ſi punctus
                  <var>.u.</var>
                erit ex æquo medius inter cen-
                  <lb/>
                trum
                  <var>.B.</var>
                & extremum
                  <var>.C.</var>
                pondus
                  <var>.F.</var>
                aut
                  <var>.M.</var>
                pendebit, aut nitetur pro medietate dicto
                  <lb/>
                centro
                  <var>.B.</var>
                & ſi dictum
                  <var>.u.</var>
                erit propius
                  <var>.B.</var>
                quam puncto
                  <var>.C.</var>
                pendebit ab ipſo, aut nitetur
                  <lb/>
                ipſi amplius
                  <reg norm="quam" type="context">quã</reg>
                exmedietate, & ſi magis verſus
                  <var>.C.</var>
                minus
                  <reg norm="quam" type="context">quã</reg>
                ex medietate
                  <reg norm="nitetur" type="simple">nitet̃</reg>
                .</s>
              </p>
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            <div xml:id="echoid-div344" type="section" level="3" n="3">
              <head xml:id="echoid-head199" style="it" xml:space="preserve">Quòd quantit as cuiuſlibet ponderis, aut uirtus mouens re-
                <lb/>
              ſpectu alterius quantitatis cognoſcatur beneficio
                <lb/>
              perpendicularium ductarum à centro
                <lb/>
              libr & ad line am inclinationis.</head>
              <head xml:id="echoid-head200" xml:space="preserve">CAP. III.</head>
              <p>
                <s xml:id="echoid-s1720" xml:space="preserve">EX ijs, quæ à nobis hucuſque ſunt dicta, facilè intelligi poteſt,
                  <reg norm="quod" type="simple">ꝙ</reg>
                quantitas
                  <var>.B.u.</var>
                  <lb/>
                quæ ferè perpendicularis eſt à centro
                  <var>.B.</var>
                ad lineam
                  <var>.F.u.</var>
                inclinationis, ea eſt,
                  <lb/>
                  <handwritten xlink:label="hd-0155-01" xlink:href="hd-0155-01a" number="3"/>
                quæ nos ducit in cognitionem quantitatis virtutis ipſius
                  <var>.F.</var>
                in huiuſmodi ſitu, conſti
                  <lb/>
                tuens videlicet linea
                  <var>.F.u.</var>
                cum brachio
                  <var>.F.B.</var>
                angulum acutum
                  <var>.B.F.u</var>
                . </s>
                <s xml:id="echoid-s1721" xml:space="preserve">Vt hoc tamen
                  <lb/>
                melius intelligamus, imaginemur libram
                  <var>.b.o.a.</var>
                fixam in centro
                  <var>.o.</var>
                ad. cuius etrema
                  <lb/>
                ſint appenſa duo pondera, aut duæ virtutes mouentes
                  <var>.e.</var>
                et
                  <var>.c.</var>
                ita tamen
                  <reg norm="quod" type="simple">ꝙ</reg>
                linea incli-
                  <lb/>
                nationis
                  <var>.e.</var>
                ideſt
                  <var>.b.e.</var>
                faciat angulum rectum cum
                  <var>.o.b.</var>
                in puncto
                  <var>.b.</var>
                linea verò inclina
                  <lb/>
                tionis
                  <var>.c.</var>
                ideſt
                  <var>.a.c.</var>
                faciat angulum acutum, aut obtuſum cum
                  <var>.o.a.</var>
                in puncto
                  <var>.a</var>
                . </s>
                <s xml:id="echoid-s1722" xml:space="preserve">Imagi-
                  <lb/>
                nemur ergo lineam
                  <var>.o.t.</var>
                perpendicularem lineæ
                  <var>.c.a.</var>
                inclinationis, vnde
                  <var>.o.t.</var>
                minor
                  <lb/>
                erit
                  <var>.o.a.</var>
                ex .18. primi Euclidis. ſecetur deinde imaginatione
                  <var>o.a.</var>
                in puncto
                  <var>.i.</var>
                ita ut
                  <lb/>
                  <var>o.i.</var>
                æqualis. </s>
                <s xml:id="echoid-s1723" xml:space="preserve">ſit
                  <var>.o.t.</var>
                & puncto
                  <var>.i.</var>
                appenſum ſit pondus æquale ipſi
                  <var>.c.</var>
                cuius inclinationis
                  <lb/>
                linea parallela ſit lineæ inclinationis ponderis
                  <var>.e.</var>
                ſupponendo tamen pondus aut vir
                  <lb/>
                tutem
                  <var>.c.</var>
                ea ratione maiorem eſſe ea, quæ eſt
                  <var>.e.</var>
                qua
                  <var>.b.o.</var>
                maior eſt
                  <var>.o.t.</var>
                abſque dubio
                  <lb/>
                ex .6. lib. primi Archi. de ponderibus
                  <var>.b.o.i.</var>
                non mouebitur ſitu, ſed ſi loco
                  <var>.o.i.</var>
                imagi
                  <lb/>
                nabimur
                  <var>.o.t.</var>
                conſolidatam cum
                  <var>.o.b.</var>
                & per lineam
                  <var>.t.c.</var>
                attractam virtute
                  <var>.c.</var>
                ſimiliter
                  <lb/>
                quoque continget ut
                  <var>b.o.</var>
                t; </s>
                <s xml:id="echoid-s1724" xml:space="preserve">communi quadam ſcientia, non moueatur ſi tu. </s>
                <s xml:id="echoid-s1725" xml:space="preserve">Eſt ergo
                  <lb/>
                  <handwritten xlink:label="hd-0155-02" xlink:href="hd-0155-02a" number="4"/>
                quod propoſuimus verum quantitatem alicuius ponderis reſpectu ad eam, quæ eſt
                  <lb/>
                alterius debere depræhendi à perpendicularibus, quæ à centro libræ ad lineas incli
                  <lb/>
                nationis exiliunt. </s>
                <s xml:id="echoid-s1726" xml:space="preserve">Hinc autem innoteſcit facillimè, quantum vigoris, & vis pondus,
                  <lb/>
                aut virtus
                  <var>.c.</var>
                ad angulum rectum cum
                  <var>.o.a.</var>
                minimè trahens, amitttat. </s>
                <s xml:id="echoid-s1727" xml:space="preserve">Hinc quoque co
                  <lb/>
                rollarium quoddam ſequetur, quò d quantò propinquius erit centrum
                  <var>.o.</var>
                libræ cen-
                  <lb/>
                tro regionis elementaris, tantò quo que minus erit graue.</s>
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