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]

Table of Notes

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          <div xml:id="echoid-div340" type="chapter" level="2" n="3">
            <div xml:id="echoid-div340" type="section" level="3" n="1">
              <p>
                <s xml:id="echoid-s1705" xml:space="preserve">
                  <pb o="142" rhead="IO. BAPT. BENED." n="154" file="0154" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0154"/>
                quetur dictum pondus grauius futurum pro parte
                  <var>.F.C.</var>
                quam pro ea, quæ eſt
                  <var>.A.F.</var>
                &
                  <lb/>
                minus ſupra centrum
                  <var>.B.</var>
                pro dicta parte
                  <var>.F.C.</var>
                quam pro parte
                  <var>.A.F.</var>
                quieturum; </s>
                <s xml:id="echoid-s1706" xml:space="preserve">&
                  <lb/>
                dictum brachium quanto magis orizontale erit à ſitu
                  <var>.B.F.</var>
                tantò minus-ſupra dictum
                  <lb/>
                centrum
                  <var>.B.</var>
                quieſcet, & hac ratione grauius quoque erit, & quanto magis vicinum
                  <lb/>
                erit ipſi
                  <var>.A.</var>
                à dicto
                  <var>.F.</var>
                tantò magis ſuper centrum
                  <var>.B.</var>
                quoque quieſcet, vnde
                  <reg norm="tantò" type="context">tãtò</reg>
                quo-
                  <lb/>
                que leuius exiſtet. </s>
                <s xml:id="echoid-s1707" xml:space="preserve">Idem dico de omni ſitu brachij per girum inferiorem
                  <var>.C.Q.</var>
                vbi
                  <lb/>
                pondus pendebit à centro
                  <var>.B.</var>
                dictum centrum attrahendo, quemadmodum ſuperius
                  <lb/>
                illud impellebat. </s>
                <s xml:id="echoid-s1708" xml:space="preserve">Hæc verò omnia cap. ſequenti melius percipientur.</s>
              </p>
            </div>
            <div xml:id="echoid-div342" type="section" level="3" n="2">
              <head xml:id="echoid-head197" style="it" xml:space="preserve">De proportione ponderis extremitatis brachij libr &
                <lb/>
              in diuerſo ſitu ab orizontali.</head>
              <head xml:id="echoid-head198" xml:space="preserve">CAP. II.</head>
              <p>
                <s xml:id="echoid-s1709" xml:space="preserve">
                  <emph style="sc">PRoportio</emph>
                ponderis in
                  <var>.C.</var>
                ad idem pondus in F. erit quemadmodum totius
                  <lb/>
                brachij
                  <var>.B.C.</var>
                ad partem
                  <var>.B.u.</var>
                poſitam inter centrum & lineam
                  <var>.F.u.M.</var>
                inclinatio-
                  <lb/>
                nis, quam pondus ab extremitate
                  <var>.F.</var>
                liberum verſus mundi
                  <reg norm="centrum" type="context">centrũ</reg>
                conficeret. </s>
                <s xml:id="echoid-s1710" xml:space="preserve">Quod
                  <lb/>
                vt facilius intelligamus imaginemur
                  <reg norm="alterum" type="context">alterũ</reg>
                brachium libræ
                  <var>.B.D.</var>
                & in extremo
                  <var>.D.</var>
                  <lb/>
                locatum aliquod pondus minus pondere
                  <var>.C.</var>
                vt
                  <var>.B.u.</var>
                pars
                  <var>.B.C.m.</var>
                nor eſt
                  <var>.B.D.</var>
                cla-
                  <lb/>
                rè cognoſcetur ex .6. lib. primi de ponderibus Archimedis, quòd ſi in puncto
                  <var>.u.</var>
                col-
                  <lb/>
                locatum erit pondus ipſius
                  <var>.C.</var>
                libra nihil penitus à ſitu orizontali dimouebitur. </s>
                <s xml:id="echoid-s1711" xml:space="preserve">Sed
                  <lb/>
                perinde eſt quòd pondus
                  <var>.F.</var>
                æquale
                  <var>.C.</var>
                ſit in extremo
                  <var>.F.</var>
                in ſitu brachij
                  <var>.B.F.</var>
                  <reg norm="quam" type="context">quã</reg>
                vt ſit
                  <lb/>
                in puncto
                  <var>.u.</var>
                in ſitu ipſius
                  <var>.B.u.</var>
                orizontali. </s>
                <s xml:id="echoid-s1712" xml:space="preserve">Ad cuius rei euidentiam imaginemur
                  <reg norm="filum" type="context">filũ</reg>
                  <var>.
                    <lb/>
                  F.u.</var>
                perpendiculare, & in cuius extremo
                  <var>.u.</var>
                pendere pondus, quod erat in
                  <var>.F.</var>
                vnde cla
                  <lb/>
                rum erit quòd eundem effectum gignet, ac ſi fuiſſet in
                  <var>.F.</var>
                quod, vt iam diximus re-
                  <lb/>
                manens affixum puncto
                  <var>.u.</var>
                brachij
                  <var>.B.u.</var>
                tantò minus graue eſt ſitu ipſius
                  <var>.C.</var>
                quantò
                  <var>.u.
                    <lb/>
                  B.</var>
                minus eſt ipſo
                  <var>.B.C</var>
                . </s>
                <s xml:id="echoid-s1713" xml:space="preserve">Idem aſſero ſi brachium eſſet in ſitu
                  <var>.e.B.</var>
                quod facilè cogno-
                  <lb/>
                ſcere poterimus, ſi imaginemur filum appenſum ipſi
                  <var>.u.</var>
                brachij
                  <var>.B.C.</var>
                & vſque ad
                  <var>.e.</var>
                  <lb/>
                  <reg norm="perpendicularem" type="context">perpendicularẽ</reg>
                , in quo extremo
                  <reg norm="appensum" type="context">appensũ</reg>
                eſſet pondus æquale ponderi
                  <var>.C.</var>
                &
                  <reg norm="liberum" type="context">liberũ</reg>
                  <lb/>
                ab
                  <var>.e.</var>
                brachij
                  <var>.B.e.</var>
                vnde libra orizontalis manebit. </s>
                <s xml:id="echoid-s1714" xml:space="preserve">Sed ſi brachium
                  <var>.B.e.</var>
                conſolida-
                  <lb/>
                tum fuiſſet in tali ſitu cum orizontali
                  <var>.B.D.</var>
                  <lb/>
                  <figure xlink:label="fig-0154-01" xlink:href="fig-0154-01a" number="210">
                    <image file="0154-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0154-01"/>
                  </figure>
                &
                  <reg norm="appenſo" type="context">appẽſo</reg>
                  <reg norm="pondere" type="context">põdere</reg>
                  <var>.C.</var>
                in
                  <var>.e.</var>
                libero à filo, nec
                  <lb/>
                  <reg norm="aſcenderet" type="context">aſcẽderet</reg>
                ,
                  <reg norm="neque" type="simple">neq;</reg>
                deſcenderet. </s>
                <s xml:id="echoid-s1715" xml:space="preserve">quia tantum
                  <lb/>
                eſt quod ipſum ſit appenſum filo,
                  <reg norm="quod" type="simple">ꝙ</reg>
                pendet
                  <lb/>
                ab
                  <var>.u.</var>
                quantum quòd ab ipſo liberum
                  <reg norm="appem" type="context">appẽ</reg>
                  <lb/>
                nſum fuiſſet
                  <var>.e.</var>
                brachij
                  <var>.B.e.</var>
                & hoc procede
                  <lb/>
                ret ab eo quòd partim pendereta centro
                  <var>.
                    <lb/>
                  B.</var>
                & ſi
                  <reg norm="brachium" type="context">brachiũ</reg>
                eſſet in ſitu
                  <var>.B.Q.</var>
                totum
                  <reg norm="pon" type="context">põ</reg>
                  <lb/>
                dus centro
                  <var>.B.</var>
                remaneret appenſum,
                  <reg norm="quem- admodum" type="context">quem-
                    <lb/>
                  admodũ</reg>
                in ſitu
                  <var>.B.A.</var>
                  <reg norm="totum" type="context">totũ</reg>
                dicto centro an-
                  <lb/>
                niteretur. </s>
                <s xml:id="echoid-s1716" xml:space="preserve">vnde fit vt hoc modo pondus
                  <lb/>
                magis aut minus ſit graue, quò magis
                  <lb/>
                aut minus à centro pendet, aut eidem niti-
                  <lb/>
                tur: </s>
                <s xml:id="echoid-s1717" xml:space="preserve">
                  <reg norm="atque" type="simple">atq;</reg>
                hæc eſt cauſa proxima, & per ſe,
                  <lb/>
                  <handwritten xlink:label="hd-0154-01" xlink:href="hd-0154-01a" number="2"/>
                qua fit vt vnum
                  <reg norm="idemque" type="simple">idemq;</reg>
                pondus in vno eo-
                  <lb/>
                  <reg norm="demque" type="simple">demq́;</reg>
                medio magis aut minus graue exi- </s>
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