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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page |< < (149) of 445 > >|
DE MECHAN.
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            <div xml:id="echoid-div352" type="section" level="3" n="7">
              <p>
                <s xml:id="echoid-s1783" xml:space="preserve">
                  <pb o="149" rhead="DE MECHAN." n="161" file="0161" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0161"/>
                proportio
                  <reg norm="ponderis" type="context">põderis</reg>
                  <var>.a.</var>
                ad pon
                  <lb/>
                dusipſius
                  <var>.b.</var>
                eadem ſit cum
                  <lb/>
                ea quę eſt
                  <var>.o.t.</var>
                ad
                  <var>.o.e.</var>
                ſub co
                  <lb/>
                  <reg norm="gnitionem" type="context">gnitionẽ</reg>
                noſtram cadere po
                  <lb/>
                teſt, primum cognoſcendo
                  <lb/>
                angulos obliquitatis librę,
                  <lb/>
                ideſt angulos
                  <var>.b.o.u.</var>
                et
                  <var>.a.o.
                    <lb/>
                  u.</var>
                quia oportet ſemper ſup-
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0161-01a" xlink:href="fig-0161-01"/>
                ponere ſitum aliquem no-
                  <lb/>
                tum. </s>
                <s xml:id="echoid-s1784" xml:space="preserve">Si nobis deinde co-
                  <lb/>
                gnita erit proportio ipſius
                  <var>.
                    <lb/>
                  o.u.</var>
                ad
                  <var>.o.b.</var>
                et. ad
                  <var>.o.a.</var>
                aſſe-
                  <lb/>
                quemur cognitionem angu
                  <lb/>
                li
                  <var>.b.</var>
                et
                  <var>.o.a.u.</var>
                & per conſe-
                  <lb/>
                quens ipſius
                  <var>.o.a.t.</var>
                eius reſi-
                  <lb/>
                dui, vnde poſtea beneficio
                  <lb/>
                angulorum
                  <var>.e.</var>
                et
                  <var>.t.</var>
                rectorum
                  <lb/>
                & laterum
                  <var>.o.b.</var>
                et
                  <var>.o.a.</var>
                cogni
                  <lb/>
                torum in cognitionem
                  <var>.o.t.</var>
                  <lb/>
                et
                  <var>.o.e.</var>
                facile deueniemus.</s>
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                  <image file="0161-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0161-01"/>
                </figure>
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            <div xml:id="echoid-div354" type="section" level="3" n="8">
              <head xml:id="echoid-head209" xml:space="preserve">CAP. VIII.</head>
              <p>
                <s xml:id="echoid-s1785" xml:space="preserve">QVod autem idem Tartalea in .6. propoſitione, & Iordanus in ſecunda parte.
                  <lb/>
                </s>
                <s xml:id="echoid-s1786" xml:space="preserve">ſecundæ propoſitionis ſcribunt, maximum quoque errorem inſe continet.
                  <lb/>
                </s>
                <s xml:id="echoid-s1787" xml:space="preserve">Dicunt enim
                  <reg norm="angulum" type="context">angulũ</reg>
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                  <var>h.a.f.</var>
                differentem ab
                  <lb/>
                angulo
                  <var>.d.b.f.</var>
                alia ra-
                  <lb/>
                tione non eſſe quàm
                  <lb/>
                per angulum conta-
                  <lb/>
                ctus
                  <reg norm="duorum" type="context">duorũ</reg>
                  <reg norm="circulorum" type="context">circulorũ</reg>
                ,
                  <lb/>
                vt in ſua figura ſcribit
                  <lb/>
                Tartalea; </s>
                <s xml:id="echoid-s1788" xml:space="preserve">id quod fal-
                  <lb/>
                ſiſſimum eſt. </s>
                <s xml:id="echoid-s1789" xml:space="preserve">
                  <reg norm="Quam" type="context">Quã</reg>
                ob
                  <lb/>
                cauſam in ſubſcripta
                  <lb/>
                figura ſit libra
                  <var>.B.A.</var>
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0161-02a" xlink:href="fig-0161-02"/>
                & eius centrum. </s>
                <s xml:id="echoid-s1790" xml:space="preserve">C et
                  <var>.
                    <lb/>
                  u.</var>
                  <reg norm="centrum" type="context">centrũ</reg>
                regionis ele
                  <lb/>
                mentaris, et
                  <var>.A.u.</var>
                et
                  <var>.B.
                    <lb/>
                  u.</var>
                lineæ
                  <reg norm="inclinationum" type="context">inclinationũ</reg>
                .
                  <lb/>
                </s>
                <s xml:id="echoid-s1791" xml:space="preserve">Imaginemur deinde
                  <lb/>
                lineam
                  <var>.B.K.</var>
                  <reg norm="parallelam" type="context">parallelã</reg>
                  <lb/>
                ipſi
                  <var>.A.u.</var>
                quæ gyrum
                  <var>.
                    <lb/>
                  B.F.A.</var>
                in puncto
                  <var>.K.</var>
                  <lb/>
                communi ſcientiæ
                  <reg norm="prae­ cepto" type="simple">prę­
                    <lb/>
                  cepto</reg>
                ſcindet, & habe
                  <lb/>
                bimus angulum
                  <var>.K.B.
                    <lb/>
                  Z.</var>
                æqualem angulo
                  <var>.
                    <lb/>
                  H.A.F.</var>
                ideſt
                  <var>.u.A.F.</var>
                  <lb/>
                (quia
                  <var>.H.u.</var>
                et
                  <var>.D.</var>
                  <reg norm="unum" type="context">unũ</reg>
                  <lb/>
                ſunt) cum ex .29. libr.
                  <lb/>
                primi Euclidis angu- </s>
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