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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          <div xml:id="echoid-div387" type="chapter" level="2" n="4">
            <div xml:id="echoid-div411" type="section" level="3" n="15">
              <p>
                <s xml:id="echoid-s2110" xml:space="preserve">
                  <pb o="178" rhead="IO. BAPT. BENED." n="190" file="0190" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0190"/>
                cies, & quæ inter corpor a
                  <reg norm="reperitur" type="simple">reperit̃</reg>
                : </s>
                <s xml:id="echoid-s2111" xml:space="preserve">Ariſtoteles igitur in eo defecit. </s>
                <s xml:id="echoid-s2112" xml:space="preserve">Quòd
                  <reg norm="autem" type="context">autẽ</reg>
                inter
                  <lb/>
                ſuperficies non eadem ſit proportio, quæ inter corpora extat, ſi primo ad ſphęricas
                  <lb/>
                mentem verterimus, intelligemus proportionem eam, quæ inter duas ſphæras repe
                  <lb/>
                ritur triplam ſemper exiſtere ei, quæ eſt inter ipſarum diametros ex vltima .12. libr.
                  <lb/>
                Euclid. </s>
                <s xml:id="echoid-s2113" xml:space="preserve">Eſt autem proportio, quæ eſt inter ſuperficies ſphęricas ęqualis ei, quæ eſt
                  <lb/>
                ipſorum circulorum maiorum ex .16. lib. quinti, cum ex .31. primi de ſphæra & cy-
                  <lb/>
                lindro Archimedis, omnis ſphærica ſuperficies quadrupla, ſit maiori circulo ipſius
                  <lb/>
                ſphęræ, ſed proportio, quæ eſt inter dictos circulos, eſt dupla ei, quæ eſt inter
                  <reg norm="eorun- dem" type="context context">eorũ-
                    <lb/>
                  dẽ</reg>
                diametros ex .2. lib. 12. Euc. </s>
                <s xml:id="echoid-s2114" xml:space="preserve">ergo
                  <reg norm="proportio" type="simple">ꝓportio</reg>
                , quæ eſt inter corpora, ſeſquialtera erit
                  <lb/>
                ei, quæ eſt ſuperficierum, & non æqualis, ut Ariſtoteles putauit. </s>
                <s xml:id="echoid-s2115" xml:space="preserve">Idem de corporibus
                  <lb/>
                ſimilibus à ſuperficiebus planis terminatis dico, ratiocinando mediante .36. lib. 11.
                  <lb/>
                et .18. ſexti, vnde cognoſcemus proportionem corporum, proportioni laterum, tri-
                  <lb/>
                plam futuram, & ſuperficierum proportionem, laterum proportioni duplam. </s>
                <s xml:id="echoid-s2116" xml:space="preserve">Quare
                  <lb/>
                corporum proportio, ei, quæ ſuperficierum eſt, ſeſquialtera erit, ita ut ſi velocitates
                  <lb/>
                extitiſſent ad inuicem proportionatæ, vt ſuperficies, proportio velocitatis corporis
                  <var>.
                    <lb/>
                  B.</var>
                ei, quæ eſt corporis
                  <var>.C.</var>
                fuiſſet ſubſeſquialtera proportioni corporum, & non æqua
                  <lb/>
                lis eidem.</s>
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            <div xml:id="echoid-div412" type="section" level="3" n="16">
              <head xml:id="echoid-head273" style="it" xml:space="preserve">Fdipſum aliter demonſtr atur.</head>
              <head xml:id="echoid-head274" xml:space="preserve">CAP. XVI.</head>
              <p>
                <s xml:id="echoid-s2117" xml:space="preserve">ALio quoque modo probari poteſt non eſſe in vniuerſum verum id, quod Ari-
                  <lb/>
                ſtoteles in prima parte capitis vltimi lib. 7. phyſicorum ait, ſic ſcribens.</s>
              </p>
              <p>
                <s xml:id="echoid-s2118" xml:space="preserve">Si
                  <var>.A.</var>
                quidem ſit id quod mouet
                  <var>.B.</var>
                verò id quod mouetur, et
                  <var>.C.</var>
                ſit longitudo per
                  <lb/>
                quam, et
                  <var>.D.</var>
                tempus in quo eſt motum, in tempore nimirum ęquali, potentia æqua-
                  <lb/>
                lis
                  <var>.A.</var>
                dimidium ipſius
                  <var>.B.</var>
                per duplum mouebit ipſius
                  <var>.C.</var>
                per ipſum autem
                  <var>.C.</var>
                in dimi
                  <lb/>
                dio temporis
                  <var>.D.</var>
                ſic enim erit rationis ſimilitudo.</s>
              </p>
              <p>
                <s xml:id="echoid-s2119" xml:space="preserve">Sit ergo corpus
                  <var>.o.</var>
                ſeptimi capitis pondere æquali corpori
                  <var>.u.</var>
                eiuſdem capitis, ſed
                  <lb/>
                area corporea minusipſo
                  <var>.u.</var>
                pro medietate. </s>
                <s xml:id="echoid-s2120" xml:space="preserve">Simile tamen figura. </s>
                <s xml:id="echoid-s2121" xml:space="preserve">Imaginemur
                  <reg norm="nunc" type="context">nũc</reg>
                  <lb/>
                tertium aliud corpus omogeneum ipſi
                  <var>.u.</var>
                quod ſit
                  <var>.i.</var>
                magnitudine & figura ſimile ipſi
                  <lb/>
                o. vnde minor erit ipſo
                  <var>.u.</var>
                pro media parte, & hanc ob cauſam ipſum
                  <var>.u.</var>
                erit duplo ma
                  <lb/>
                gis graue, quàm ipſum
                  <var>.i.</var>
                & per conſequens ipſum quoque
                  <var>.o.</var>
                duplo grauius erit
                  <reg norm="quam" type="context">quã</reg>
                  <lb/>
                ſit ipſum
                  <var>.i.</var>
                ex .7. libr. quinti Euclidis. </s>
                <s xml:id="echoid-s2122" xml:space="preserve">Ipſum ergo corpus
                  <var>.o.</var>
                duplo velocius erit,
                  <lb/>
                quàm ipſum
                  <var>.i.</var>
                ex primo ſuppoſito cap .2. huius lib. </s>
                <s xml:id="echoid-s2123" xml:space="preserve">Vnde ex .9. quinti, velocitas ipſius
                  <lb/>
                i. æqualis eſſet ei, quæ eſt ipſius u. cum Ariſtoteles ſcribat
                  <var>.o.</var>
                quoque futurum duplo
                  <lb/>
                velocius ipſo
                  <var>.u.</var>
                  <reg norm="quod" type="simple">ꝙ</reg>
                cap .7. huius lib. falſum eſſe demonſtraui.</s>
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            <div xml:id="echoid-div413" type="section" level="3" n="17">
              <head xml:id="echoid-head275" style="it" xml:space="preserve">De alio Aristo. lapſu.</head>
              <head xml:id="echoid-head276" xml:space="preserve">CAP. XVII.</head>
              <p>
                <s xml:id="echoid-s2124" xml:space="preserve">SCribit Ariſtoteles in ultimo cap. lib. 7. phyſicorum in hunc modum.
                  <lb/>
                </s>
                <s xml:id="echoid-s2125" xml:space="preserve">Si duo quædam ſeorſum per tantum ſpatium tanto tempore duo ſeorſum pon
                  <lb/>
                dera mouent, & compoſita per longitudinem æqualem,
                  <reg norm="ęqualiuem" type="context">ęqualiuẽ</reg>
                in tempore, com-
                  <lb/>
                poſitum ex ponderibus
                  <reg norm="vtriſque" type="simple">vtriſq;</reg>
                mouebunt, eſt enim in eis eadem ratio.</s>
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