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]

Page concordance

< >
Scan Original
131 119
132 120
133 121
134 122
135 123
136 124
137 125
138 126
139 127
140 128
141 129
142 130
143 131
144 132
145 133
146 134
147 135
148 136
149 137
150 138
151 139
152 140
153 141
154 142
155 143
156 144
157 145
158 146
159 147
160 148
< >
page |< < (143) of 445 > >|
DE MECHAN.
    <echo version="1.0">
      <text type="book" xml:lang="la">
        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div340" type="chapter" level="2" n="3">
            <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>
              <div xml:id="echoid-div342" type="float" level="4" n="1">
                <figure xlink:label="fig-0154-01" xlink:href="fig-0154-01a">
                  <image file="0154-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0154-01"/>
                </figure>
                <handwritten xlink:label="hd-0154-01" xlink:href="hd-0154-01a"/>
              </div>
            </div>
            <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/>
                  <anchor type="handwritten" xlink:label="hd-0155-01a" xlink:href="hd-0155-01"/>
                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/>
                  <anchor type="handwritten" xlink:label="hd-0155-02a" xlink:href="hd-0155-02"/>
                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>
              </p>
              <div xml:id="echoid-div344" type="float" level="4" n="1">
                <handwritten xlink:label="hd-0155-01" xlink:href="hd-0155-01a"/>
                <handwritten xlink:label="hd-0155-02" xlink:href="hd-0155-02a"/>
              </div>
              <figure position="here">
                <image file="0155-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0155-01"/>
              </figure>
            </div>
          </div>
        </div>
      </text>
    </echo>