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. BAPT. BENED.
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              <head xml:id="echoid-head201" style="it" xml:space="preserve">Quemadmodum exſupradictis cauſis omnes staterarum &
                <lb/>
              uectium cauſæ dependeant.</head>
              <head xml:id="echoid-head202" xml:space="preserve">CAP. IIII.</head>
              <p>
                <s xml:id="echoid-s1728" xml:space="preserve">VIs brachij longioris alicuius ſtateræ, aut vectis, maior breuioris, ab ijs, quæ in ſu
                  <lb/>
                perioribus capitibus diximus, ideſt
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                nitatur
                  <reg norm="pendeatuem" type="context">pendeatuẽ</reg>
                magis aut minus à
                  <lb/>
                centro pondus in extremitate brachij maioris poſitum, oboritur. </s>
                <s xml:id="echoid-s1729" xml:space="preserve">Quamobrem illud
                  <lb/>
                à nobis primò eſt cognoſcendum, ſtateras, aut vectes, puras mathematicas li-
                  <lb/>
                neas non eſſe, ſed naturales, hincque exiſtere corpora cum materia coniuncta. </s>
                <s xml:id="echoid-s1730" xml:space="preserve">Nunc
                  <lb/>
                igitur imaginemur
                  <var>.n.s.</var>
                eam ſuperficiem eſſe, quæ ſecundum longitudinem axem ſta
                  <lb/>
                teræ ſcindit. </s>
                <s xml:id="echoid-s1731" xml:space="preserve">& ſupponamus ipſius centrum eſſe primum in
                  <var>.i.</var>
                & maius brachium eſſe
                  <lb/>
                  <var>.i.u</var>
                : minus autem
                  <var>.i.n.</var>
                & lineam verticalem
                  <var>.i.o.</var>
                quæ tanta ſit, quanta eſt ſpiſſitu-
                  <lb/>
                do, aut craſſities ipſius ſtateræ à ſuperiori latere ad inferius, ad faciliorem intelligen-
                  <lb/>
                tiam, ſupponendo
                  <var>.n.s.</var>
                  <reg norm="parallelogrammam" type="context">parallelogrãmam</reg>
                . </s>
                <s xml:id="echoid-s1732" xml:space="preserve">Poſitis igitur duobus ponderibus æquali-
                  <lb/>
                  <anchor type="handwritten" xlink:label="hd-0156-01a" xlink:href="hd-0156-01"/>
                bus in extremitatibus brachiorum, experientia innoteſcit,
                  <reg norm="quod" type="simple">ꝙ</reg>
                pondus ad
                  <var>.u.s.</var>
                appen-
                  <lb/>
                ſum, viol entiam faciet ponderi appenſo ad
                  <var>.n.x.</var>
                ſed nos volumus inueſtigare
                  <reg norm="causam" type="context">causã</reg>
                  <lb/>
                huius effectus, quæ à nemine vnquam literarum monumentis,
                  <reg norm="quod" type="simple">ꝙ</reg>
                ſciam, conſignata
                  <lb/>
                  <anchor type="handwritten" xlink:label="hd-0156-02a" xlink:href="hd-0156-02"/>
                fuit. </s>
                <s xml:id="echoid-s1733" xml:space="preserve">Iam diximus ſtateram, aut vectem materialem eſſe &
                  <var>.n.s.</var>
                eius ſuperficiem me-
                  <lb/>
                diam, ſupponendo
                  <var>.i.</var>
                eſſe centrum quo nititur dicta ſtatera aut vectis; </s>
                <s xml:id="echoid-s1734" xml:space="preserve">Cum hocer-
                  <lb/>
                go ita ſe habeat, ſint
                  <var>.u.s.</var>
                et
                  <var>.n.x.</var>
                lineæ inclinationum ponderum, & imaginemur,
                  <reg norm="quod" type="simple">ꝙ</reg>
                  <lb/>
                dicta pondera pendeant à punctis
                  <var>.u.</var>
                et
                  <var>.n.</var>
                vt reuera pendent, etiam ſi appenſa eſſent
                  <lb/>
                ſub
                  <var>.s.</var>
                et
                  <var>.x.</var>
                quia punctum
                  <var>.u.</var>
                & punctum
                  <var>.n.</var>
                ita coniuncta ſunt cum
                  <var>.s.</var>
                et
                  <var>.x.</var>
                ut qui
                  <reg norm="vnum" type="context">vnũ</reg>
                  <lb/>
                trahit alterum quoque trahat. </s>
                <s xml:id="echoid-s1735" xml:space="preserve">Imaginemur quoque duas lineas
                  <var>.i.u</var>
                :
                  <var>i.n.</var>
                et
                  <var>.i.e.</var>
                quę
                  <lb/>
                  <var>i.e.</var>
                faciat angulum
                  <var>.o.i.e.</var>
                æqualem angulo
                  <var>.o.i.n</var>
                . </s>
                <s xml:id="echoid-s1736" xml:space="preserve">Hinc clarè nobis patebit, ſi quis ipſi
                  <lb/>
                e. pondus ipſius
                  <var>.u.</var>
                (
                  <reg norm="quod" type="simple">ꝙ</reg>
                æquale eſt ponderi
                  <var>.n.</var>
                ) appenderet, id eandem planè vim habe
                  <lb/>
                ret, quam pondus ipſius
                  <var>.n.</var>
                habet, & ſtateram neque ſurſum, neque deorſum moue-
                  <lb/>
                ret, quia ambo pondera ad centrum
                  <var>.i.</var>
                mediantibus lineis
                  <var>.e.i.</var>
                et
                  <var>.n.i.</var>
                exęquo annite-
                  <lb/>
                rentur, ſed dicto pondere poſito in .u: linea
                  <var>.u.i.</var>
                per quam pondus centro annititur,
                  <lb/>
                magis orizontalis quam
                  <var>.e.i.</var>
                fit, & linea
                  <var>.u.s.</var>
                inclinationis longius diſtans à centro
                  <var>.i.</var>
                  <lb/>
                  <anchor type="handwritten" xlink:label="hd-0156-03a" xlink:href="hd-0156-03"/>
                quàm linea
                  <var>.e.t.</var>
                vnde huiuſmodi pondus magis quoque liberum à centro
                  <var>.i.</var>
                reſultat.
                  <lb/>
                </s>
                <s xml:id="echoid-s1737" xml:space="preserve">magisque ponderoſum, quam cum erat in
                  <var>.e.</var>
                ratione eorum, quæ primo & ſecundo
                  <lb/>
                capitibus diximus, & ob hanc cauſam ſuperat pondus poſitum in
                  <var>.n</var>
                . </s>
                <s xml:id="echoid-s1738" xml:space="preserve">Sed ſi centrum
                  <lb/>
                fuerit .in
                  <var>.o.</var>
                imaginabimur duas lineas
                  <var>.o.s.</var>
                et
                  <var>.o.x.</var>
                & ſupponemus quòd pondera po-
                  <lb/>
                ſita ſint in
                  <var>.s.</var>
                et
                  <var>.x.</var>
                vnde exiſtente magis orizontali linea
                  <var>.o.s.</var>
                quam erit
                  <var>.o.x.</var>
                & linea
                  <lb/>
                  <var>u.s.</var>
                inclinationis longius diſtante à centro
                  <var>.o.</var>
                quàm linea
                  <var>.e.t.</var>
                eius pondus erit
                  <reg norm="quoque" type="simple">quoq;</reg>
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                  <anchor type="figure" xlink:label="fig-0156-01a" xlink:href="fig-0156-01"/>
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