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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IO. BABPT. BENED.
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            <div xml:id="echoid-div350" type="section" level="3" n="6">
              <pb o="148" rhead="IO. BABPT. BENED." n="160" file="0160" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0160"/>
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            <div xml:id="echoid-div352" type="section" level="3" n="7">
              <head xml:id="echoid-head207" style="it" xml:space="preserve">De quibuſdam erroribus Nicolai Tartaleæ circa pondera
                <lb/>
              corporum & eorum motus, quorum aliqui deſumpti
                <lb/>
              fuerunt à fordano ſcriptore quodam antiquo.</head>
              <head xml:id="echoid-head208" xml:space="preserve">CAP. VII.</head>
              <p>
                <s xml:id="echoid-s1761" xml:space="preserve">CVm magis amici veritatis eſſe debeamus quàm cuiuſquam hominis, quemad-
                  <lb/>
                modum Ariſto. ſcribit, detegam hoc loco quoſdam errores Nicolai Tartaleę
                  <lb/>
                de ponderibus corporum, & velocitatibus motuum localium. </s>
                <s xml:id="echoid-s1762" xml:space="preserve">Et primum decipitur
                  <lb/>
                is in .8. lib. ſuarum diuerſarum inuentionum in ſecunda propoſitione, cum non ani-
                  <lb/>
                maduerterit quanti momenti ſint extrinſecæ reſiſtentiæ.</s>
              </p>
              <p>
                <s xml:id="echoid-s1763" xml:space="preserve">Subiectum quoque tertiæ propoſitionis eſt malè demonſtratum, quia idem pla-
                  <lb/>
                nè ex eius demonſtratione iam dicta corporibus hætereogeneis, aut figura diuerſis
                  <lb/>
                contingeret, quod ad velocitates attinet.</s>
              </p>
              <p>
                <s xml:id="echoid-s1764" xml:space="preserve">In quarta propoſitione, quod ad
                  <reg norm="diſputandum" type="context context">diſputãdũ</reg>
                proponit
                  <reg norm="non" type="context">nõ</reg>
                concludit melius. </s>
                <s xml:id="echoid-s1765" xml:space="preserve">
                  <reg norm="autem" type="context">autẽ</reg>
                id
                  <lb/>
                ab eo
                  <reg norm="ſequitur" type="simple">ſequit̃</reg>
                , quod Archimedes in .6. propoſitione lib. primi de
                  <reg norm="ponderibus" type="context">põderibus</reg>
                  <reg norm="probauit" type="simple">ꝓbauit</reg>
                .</s>
              </p>
              <handwritten/>
              <p>
                <s xml:id="echoid-s1766" xml:space="preserve">Sed in ſecunda parte quintę propoſitionis non uidet
                  <reg norm="quod" type="simple">ꝙ</reg>
                uigore ſitus eo modo, quo
                  <lb/>
                ipſe diſputat, nulla elicitur ponderis differentia. </s>
                <s xml:id="echoid-s1767" xml:space="preserve">quia ſi corpus
                  <var>.B.</var>
                deſcendere debet
                  <lb/>
                per arcum
                  <var>.i.l.</var>
                corpus
                  <var>.A.</var>
                aſcendere debet per arcum
                  <var>.u.s.</var>
                æqualem, & ſimilem. eadem
                  <lb/>
                quoque ratione ſituatum, vt eſt arcus
                  <var>.i.l.</var>
                vnde vt eſt facilè corpori
                  <var>.B.</var>
                deſcendere
                  <lb/>
                per arcum
                  <var>.i.l.</var>
                difficile ita erit corpori
                  <var>.A.</var>
                aſcendere per arcum
                  <var>.u.s</var>
                . </s>
                <s xml:id="echoid-s1768" xml:space="preserve">Hęc autem qnin
                  <lb/>
                ta propoſitio Tartaleæ eſt ſecuuda quæſtio à Iordano propoſita.</s>
              </p>
              <p>
                <s xml:id="echoid-s1769" xml:space="preserve">Quòd autem ad primum corollarium dictæ propoſitionis attinet, verum ille qui
                  <lb/>
                dem ſcribit, eius tamen effectus cauſa & à Iordano prius, & ab ipſo poſtea citata, na-
                  <lb/>
                tura ſua vera non eſt. </s>
                <s xml:id="echoid-s1770" xml:space="preserve">quia vera cauſa per ſe ab eo oritur,
                  <reg norm="quod" type="simple">ꝙ</reg>
                à centro libræ dependeat
                  <lb/>
                vt primo cap. huius tractatus oſtendi. </s>
                <s xml:id="echoid-s1771" xml:space="preserve">Secundum verò corollarium falſum eſſe, ijs ra
                  <lb/>
                tionibus quas nunc ſubiungam, patebit. </s>
                <s xml:id="echoid-s1772" xml:space="preserve">Imaginemur
                  <var>.u.</var>
                pro centro regionis ele-
                  <lb/>
                mentaris, & libram
                  <var>.b.o.a.</var>
                obliquam reſpectu ad
                  <var>.u.</var>
                & brachijs æqualibus
                  <reg norm="conſtantem" type="context">conſtãtem</reg>
                ,
                  <lb/>
                & pondera in
                  <var>.a.</var>
                et in
                  <var>.b.</var>
                etiam æqualia. </s>
                <s xml:id="echoid-s1773" xml:space="preserve">lineæ autem inclinationum ſint
                  <var>.a.u.</var>
                et
                  <var>.b.u.</var>
                  <lb/>
                imaginemur etiam lineam
                  <var>.o.u.</var>
                & à centro
                  <var>.o.</var>
                libræ duas
                  <var>.o.t.</var>
                et
                  <var>.o.e.</var>
                perpendiculares
                  <lb/>
                inclinationum lineis; </s>
                <s xml:id="echoid-s1774" xml:space="preserve">vnde pondus ipſius
                  <var>.a.</var>
                in huiuſmodi ſitu tam erit proportiona
                  <lb/>
                tum ponderi
                  <var>.b.</var>
                quam proportionata erit linea
                  <var>.o.t.</var>
                lineæ
                  <var>.o.e.</var>
                ex eo
                  <reg norm="quod" type="simple">ꝙ</reg>
                tertio cap. hu-
                  <lb/>
                iustractatus probaui, ſed linea
                  <var>.o.t.</var>
                maior eſt linea
                  <var>.o.e.</var>
                quod ſic probo. </s>
                <s xml:id="echoid-s1775" xml:space="preserve">Imaginemur
                  <lb/>
                triangulum
                  <var>.u.a.b.</var>
                circunſcriptum eſſe à circulo
                  <var>.u.a.n.b.</var>
                cuius
                  <var>.c.</var>
                ſit centrum,
                  <reg norm="quod" type="simple">ꝙ</reg>
                erit
                  <lb/>
                extra lineam
                  <var>.u.o.</var>
                cum ſupponatur
                  <var>.a.o.b.</var>
                obliquam eſſe reſpectu ad
                  <var>.u.o</var>
                . </s>
                <s xml:id="echoid-s1776" xml:space="preserve">Imagine-
                  <lb/>
                mur deinde à centro
                  <var>.c.</var>
                lineam
                  <var>.c.o.s.</var>
                vſque ad circunferentiam, quæ perpendicula-
                  <lb/>
                ris erit ipſi
                  <var>.a.b.</var>
                ex tertia lib. 3. Eucli. </s>
                <s xml:id="echoid-s1777" xml:space="preserve">ſi poſteà imaginemur duas lineas
                  <var>.c.a.</var>
                et
                  <var>.c.b.</var>
                ha
                  <lb/>
                bebimus ex .8. lib. primi, angulum
                  <var>.a.c.o.</var>
                æqualem angulo
                  <var>.b.c.o</var>
                . </s>
                <s xml:id="echoid-s1778" xml:space="preserve">Vnde ex .25. lib. 3.
                  <lb/>
                arcus
                  <var>.a.s.</var>
                æqualis erit arcui
                  <var>.b.s.</var>
                ſed ſi imaginabimur
                  <var>.u.o.</var>
                ad circunferentiam vſque
                  <lb/>
                productam, clarum erit
                  <reg norm="quod" type="simple">ꝙ</reg>
                arcum
                  <var>.s.b.</var>
                ſecaret in puncto
                  <var>.n.</var>
                vnde arcus
                  <var>.n.b.</var>
                minor erit
                  <lb/>
                arcu
                  <var>.n.a.</var>
                & ſic etiam angulus
                  <var>.n.u.b.</var>
                minor erit angulo
                  <var>.n.u.a.</var>
                ex
                  <ref id="ref-0024">ultima lib. 6.</ref>
                </s>
                <s xml:id="echoid-s1779" xml:space="preserve">Imagi-
                  <lb/>
                nemur nunc alium quendam circulum, cuius
                  <var>.o.u.</var>
                ſit diameter, cuius circunferentia
                  <lb/>
                per duo puncta
                  <var>.e.</var>
                et
                  <var>.t.</var>
                  <reg norm="prætergradiatur" type="simple">prætergradiat̃</reg>
                , cum in ipſis ſint angulirecti, quod quilibet ex
                  <lb/>
                ſeratio cinando colligere poteſt, ſi .30. lib. 3. in mentem reuocauerit. </s>
                <s xml:id="echoid-s1780" xml:space="preserve">Sed cum angu-
                  <lb/>
                lus
                  <var>.o.u.t.</var>
                ſit maior angulo
                  <var>.o.u.e.</var>
                arcus
                  <var>.o.t.</var>
                maior erit arcu
                  <var>.o.e.</var>
                ex vltima .6. vnde cor
                  <lb/>
                da
                  <var>.o.t.</var>
                maior erit corda ipſius
                  <var>.o.e.</var>
                ex conuerſo .27. lib. 3. quod eſt propoſitum. </s>
                <s xml:id="echoid-s1781" xml:space="preserve">Pon-
                  <lb/>
                  <anchor type="handwritten" xlink:label="hd-0160-01a" xlink:href="hd-0160-01"/>
                dusigitur ipſius
                  <var>.a.</var>
                in huiuſmodi ſitu, pondere ipſius
                  <var>.b.</var>
                grauius erit. </s>
                <s xml:id="echoid-s1782" xml:space="preserve">Quod è directo ijs
                  <lb/>
                repugnat quæ Tartalea in 2. parte quinræ propoſitionis ediſerit, & per conſequens
                  <lb/>
                2. corollarij falſitatem oſtendit, vt eam quoque, quæ in 6. propoſitione latet. </s>
                <s xml:id="echoid-s1783" xml:space="preserve">quia
                  <reg norm="cum" type="context">cũ</reg>
                </s>
              </p>
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