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-div372" type="section" level="3" n="16">
              <pb o="160" rhead="IO. BABPT. BENED." n="172" file="0172" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0172"/>
              <p>
                <s xml:id="echoid-s1909" xml:space="preserve">Sit exempli gratia libra
                  <var>.a.i.e.</var>
                quæ in vtraque extremitate vnciam vnam ſolum
                  <lb/>
                ponderis obtineat, & ſit libra
                  <var>.n.i.u.</var>
                æqualis priori, quæ pro ſingula extremitate
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                  <lb/>
                  <handwritten xlink:label="hd-0172-01" xlink:href="hd-0172-01a" number="15"/>
                ponderis libram habeat. </s>
                <s xml:id="echoid-s1910" xml:space="preserve">Ariſtoteles admiratur, quòd addendo ipſi
                  <var>.e.</var>
                mediam pon
                  <lb/>
                deris vnciam, brachium
                  <var>.i.e.</var>
                velocius cadat, quàm
                  <reg norm="adijciendo" type="context">adijciẽdo</reg>
                  <reg norm="ipsam" type="context">ipsã</reg>
                  <reg norm="mediam" type="context">mediã</reg>
                  <reg norm="vnciam" type="context">vnciã</reg>
                ipſi
                  <var>.u.</var>
                  <lb/>
                brachij
                  <var>.i.u</var>
                . </s>
                <s xml:id="echoid-s1911" xml:space="preserve">Quod à duabus cauſis proficiſcitur, quarum prior eſt, magna differentia
                  <lb/>
                proportionis vnius libræ ad medietatem vnius vnciæ, ad proportionem vnius vnciæ
                  <lb/>
                ad ipſam medietatem, quia ſi pondus adiectum extremo
                  <var>.u.</var>
                dimidiæ eſſet libræ , &
                  <lb/>
                cum eadem tarditate brachium moueret, optimo iure in admirationem poſſet Ari-
                  <lb/>
                ſtoteles duci. </s>
                <s xml:id="echoid-s1912" xml:space="preserve">Sed hoc fieri non poſſet, quia ipſum deprimeret cum eadem quaſi ve
                  <lb/>
                locitate, qua media vncia brachium
                  <var>.i.e</var>
                . </s>
                <s xml:id="echoid-s1913" xml:space="preserve">Dixi autem quaſi, quia nonnihil diſcrimi-
                  <lb/>
                nis intercederet, quod proficiſcitur à ſecunda ratione. </s>
                <s xml:id="echoid-s1914" xml:space="preserve">Et hæc, reſiſtentia eſt , quæ
                  <lb/>
                oritur à ſparto, quia quantò maius pondus continet libra, tantò magis præmit ſpar
                  <lb/>
                tum in loco, in quo ſuſtinetur; </s>
                <s xml:id="echoid-s1915" xml:space="preserve">vnde maior reſiſtentia in circunuolutione
                  <reg norm="eiuſdem" type="context">eiuſdẽ</reg>
                ſpar
                  <lb/>
                ti, in loco, in quo quieſcit, exoritur, quia ipſum eſt corpus materiale. </s>
                <s xml:id="echoid-s1916" xml:space="preserve">Si quis autem
                  <lb/>
                vellet, vt brachium
                  <var>.i.u.</var>
                eadem agilitate, qua
                  <var>.i.e.</var>
                deſcenderet, oporteret, vt propor-
                  <lb/>
                tio dimidiæ librę adiectæ ponderi ipſius
                  <var>.u.</var>
                  <lb/>
                  <figure xlink:label="fig-0172-01" xlink:href="fig-0172-01a" number="233">
                    <image file="0172-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0172-01"/>
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                quod eſt vnius libræ, vim ſuam haberet,
                  <lb/>
                quæ excederet reſiſtentiam ſui ſparti (me-
                  <lb/>
                dio brachiorum maiorum ijs qui ſunt
                  <var>.a.i.
                    <lb/>
                  e.</var>
                ) ita proportionatam, vt proportionata
                  <lb/>
                eſt vis dimidiæ vnciæ ipſi e. iunctæ, reſiſten
                  <lb/>
                tiæ ſui ſparti. </s>
                <s xml:id="echoid-s1917" xml:space="preserve">Huiuſmodi rationes cum ro-
                  <lb/>
                tis grauioribus
                  <reg norm="leuioribusque" type="simple">leuioribusq;</reg>
                , & ijs, quę à cor
                  <lb/>
                poribus quibuſlibet grauibus impelluntur, accommodatæ fuerint, titubantem intel
                  <lb/>
                lectum confirmabunt.</s>
              </p>
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            <div xml:id="echoid-div374" type="section" level="3" n="17">
              <head xml:id="echoid-head226" style="it" xml:space="preserve">De uer a cauſa .12. questionis mechanice.</head>
              <head xml:id="echoid-head227" xml:space="preserve">CAP. XVII.</head>
              <p>
                <s xml:id="echoid-s1918" xml:space="preserve">VEra ratio, cur multò longius corpus aliquod graue impellatur funda, quam
                  <lb/>
                manu, inde oritur, quòd circunuoluendo fundam, maior impræſſio impetus
                  <lb/>
                motus fit in corpore graui, quàm fieret manu, quod corpus liberatum deinde cum
                  <lb/>
                fuerit à funda, natura duce, iter
                  <reg norm="fuum" type="context">fuũ</reg>
                à puncto, à quo proſilijt, per lineam contiguam
                  <lb/>
                giro, quem poſtremò faciebat, ſuſcipit. </s>
                <s xml:id="echoid-s1919" xml:space="preserve">
                  <reg norm="Dubitandumque" type="simple">Dubitandumq́</reg>
                non eſt, quin dicta funda
                  <lb/>
                maior impetus motus dicto corpori imprimi poſſit,
                  <reg norm="cum" type="context">cũ</reg>
                ex multis circumactibus, ma-
                  <lb/>
                ior ſemper impetus dicto corpori accedat. </s>
                <s xml:id="echoid-s1920" xml:space="preserve">Manus autem eiuſdem corporis motus,
                  <lb/>
                dum illud ipſum circunuoluitur (pace Ariſtotelis dixerim) centrum non eſt, neque
                  <lb/>
                funis eſt ſemidiameter. </s>
                <s xml:id="echoid-s1921" xml:space="preserve">Immo manus quam maximè fieri poteſt in orbem cietur;
                  <lb/>
                </s>
                <s xml:id="echoid-s1922" xml:space="preserve">qui quidem motus in orbem, vt circumagatur etiam ipſum corpus, cogit, quod qui-
                  <lb/>
                dem corpus, naturali quadam inclinatione, exiguo quodam impetu iam incępto,
                  <lb/>
                vellet recta iter peragere, vt in ſubſcripta figura patet, in qua
                  <var>.e.</var>
                ſignificat manum
                  <var>.a.</var>
                  <lb/>
                corpus
                  <var>.a.b.</var>
                lineam rectam tangentem girum
                  <var>.a.a.a.a.</var>
                quando corpus liberum rema-
                  <lb/>
                net. </s>
                <s xml:id="echoid-s1923" xml:space="preserve">Verum quidem eſt, impręſſum illum impetum, continuò paulatim decreſcere
                  <lb/>
                vnde ſtatim inclinatio grauitatis eiuſdem corporis ſubingreditur, quæ ſeſe miſcens
                  <lb/>
                cum impręſſione facta per vim, non permittit, vt linea
                  <var>.a.b.</var>
                longo tempore recta per </s>
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