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-div354" type="section" level="3" n="8">
              <p>
                <s xml:id="echoid-s1797" xml:space="preserve">
                  <pb o="151" rhead="DE MECHAN." n="163" file="0163" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0163"/>
                et
                  <var>.E.M.</var>
                lineis productis vſque ad centrum regionis elementaris, vnde dictus angu-
                  <lb/>
                lus
                  <var>.M.E.G.</var>
                maior eſt alio, ex .16 lib. primi Eucli. </s>
                <s xml:id="echoid-s1798" xml:space="preserve">Qua ratione fit, vt hanc ob cauſam
                  <lb/>
                E. grauius ſit ipſo
                  <var>.D.</var>
                cum minus dependeat à centro
                  <var>.A.</var>
                vt primo cap. huius tractatus
                  <lb/>
                iam dixi. </s>
                <s xml:id="echoid-s1799" xml:space="preserve">Alia quoque eſtratio, qua dictum
                  <var>.E.</var>
                grauius fit ipſo
                  <var>.D.</var>
                quę quidem eſt
                  <lb/>
                maior diſtantia à centro
                  <var>.A.</var>
                libræ, per ſimiles rationes capit .4. huius tractatus ci-
                  <lb/>
                tatas.</s>
              </p>
              <p>
                <s xml:id="echoid-s1800" xml:space="preserve">Decimaquinta
                  <reg norm="quoque" type="simple">quoq;</reg>
                nil penitus valet, quę eſt .11. quęſtio Iordani, cuius Autho-
                  <lb/>
                ris opuſculum opera Traiani Bibliopolę Venetijs è tenebris in lucem emerſit.</s>
              </p>
            </div>
            <div xml:id="echoid-div356" type="section" level="3" n="9">
              <head xml:id="echoid-head210" style="it" xml:space="preserve">Quòdſummaratione ſtateræper æqualia interualla
                <lb/>
              ſint diuiſæ.</head>
              <head xml:id="echoid-head211" xml:space="preserve">CAP. IX.</head>
              <p>
                <s xml:id="echoid-s1801" xml:space="preserve">MAgna cum ratione
                  <reg norm="diuiduntur" type="context">diuidũtur</reg>
                ſtateræ per interualla ęqualia, in libras, aut in
                  <lb/>
                vncias, aut quoquo alio modo. </s>
                <s xml:id="echoid-s1802" xml:space="preserve">Nam ſit ſtatera exempli gratia
                  <var>.a.b.</var>
                  <lb/>
                & punctum,
                  <reg norm="quod" type="simple">ꝙ</reg>
                eam ſuſtinet ſit
                  <var>.c.</var>
                & vas illud,
                  <reg norm="quod" type="simple">ꝙ</reg>
                continetid, quod ponderari debet
                  <lb/>
                f. </s>
                <s xml:id="echoid-s1803" xml:space="preserve">Imaginemur nunc quod pondus brachij
                  <var>.c.b.</var>
                ab una parte, & pondus brachij
                  <var>.c.a.</var>
                  <reg norm="cum" type="context">cũ</reg>
                  <lb/>
                eo,
                  <reg norm="quod" type="simple">ꝙ</reg>
                eſt dicti vaſis
                  <var>.f.</var>
                ab altera parte, ſint cauſę, quibus ſtatera
                  <var>.a.b.c.</var>
                ſtet orizonta-
                  <lb/>
                lis. cui ſic orizontali manenti imaginemur ad punctum
                  <var>.a.</var>
                adiunctum eſſe pondus,
                  <lb/>
                veluti vnius librę. & ad punctum
                  <var>.d.</var>
                tam diſtanti à
                  <var>.c.</var>
                ut eſt
                  <var>.a.</var>
                ab ipſo
                  <var>.c.</var>
                aliud quoque
                  <lb/>
                pondus vnius libræ
                  <reg norm="additum" type="context">additũ</reg>
                eſſe, vnde
                  <reg norm="coni" type="context">cõi</reg>
                  <reg norm="quadam" type="context">quadã</reg>
                ſcientia ſtatera, non mouebitur ſitu.
                  <lb/>
                </s>
                <s xml:id="echoid-s1804" xml:space="preserve">
                  <reg norm="quia" type="simple">ꝗa</reg>
                exiſtentibus duobus hiſce ponderibus æqualibus, altero in
                  <var>.d.</var>
                & altero in
                  <var>.a.</var>
                remo
                  <lb/>
                ta cum eſſent
                  <var>.d.b.</var>
                et
                  <var>.f.</var>
                abſque dubio
                  <var>.a.d.</var>
                non mutaret ſitum, ſed
                  <var>.d.b.</var>
                et, f. in ſitu, in
                  <lb/>
                quo reperiuntur, à centro paribus viribus prędita ſunt. </s>
                <s xml:id="echoid-s1805" xml:space="preserve">Addendo igitur
                  <var>.d.b.</var>
                ipſi
                  <var>.d.</var>
                  <lb/>
                et
                  <var>.f.</var>
                ipſi .a: ſumma earum, æqualibus quoque viribus conſtabunt. ex communi ſen-
                  <lb/>
                tentia, quæ habet ſi ęqualibus addas ęqualia, tota quoque fient ęqualia. </s>
                <s xml:id="echoid-s1806" xml:space="preserve">Si verò
                  <lb/>
                ponderi ipſius
                  <var>.a.</var>
                aliud adderetur eidem ęquale, haberemus in
                  <var>.a.</var>
                duplum pon-
                  <lb/>
                dus ei
                  <reg norm="quod" type="simple">ꝙ</reg>
                eſt ipſius
                  <var>.d.</var>
                ſed volentes vt ſolum cum pondere ipſius
                  <var>.d.</var>
                ſtatera ſtet orizon
                  <lb/>
                talis, ſi dictum pondus ipſius
                  <var>.d.</var>
                longè diſtabit à centro
                  <var>.c.</var>
                per duplum ipſius
                  <var>.c.a.</var>
                ideſt
                  <lb/>
                ipſius
                  <var>.c.d.</var>
                id
                  <reg norm="quod" type="simple">ꝙ</reg>
                volumus aſſeque-
                  <lb/>
                mur, beneficio ſupradictarum ra
                  <lb/>
                  <figure xlink:label="fig-0163-01" xlink:href="fig-0163-01a" number="221">
                    <image file="0163-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0163-01"/>
                  </figure>
                tionum, adiuti opera ſextę lib. pri­
                  <lb/>
                mi de
                  <reg norm="ponderibus" type="context">põderibus</reg>
                Archimedis. </s>
                <s xml:id="echoid-s1807" xml:space="preserve">Et
                  <lb/>
                ſi quis aliud
                  <reg norm="quoque" type="simple">quoq;</reg>
                pondus adiun
                  <lb/>
                geret ipſi
                  <var>.a.</var>
                æquale illi priori, ad
                  <lb/>
                  <reg norm="efficiendum" type="context">efficiẽdum</reg>
                , vt ſtatera ſemper ori
                  <lb/>
                zontalis maneret, oporteret, vt
                  <reg norm="pondus" type="context">põdus</reg>
                ipſius
                  <var>.d.</var>
                ab
                  <var>.c.</var>
                longè diſtaret, ita vt huiuſmodi
                  <lb/>
                diſtantia tripla eſſet primæ, & ſic per quoſdam quaſi gradus interualla redderentur
                  <lb/>
                æqualia.</s>
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