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-div340" type="chapter" level="2" n="3">
            <div xml:id="echoid-div356" type="section" level="3" n="9">
              <pb o="152" rhead="IO. BAPT. BENED." n="164" file="0164" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0164"/>
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            <div xml:id="echoid-div358" type="section" level="3" n="10">
              <head xml:id="echoid-head212" style="it" xml:space="preserve">Quòd line a circularis non habe at concauum cum con-
                <lb/>
              uexo coniunctum, & quod Aristo. cir caproportio
                <lb/>
              nes motuum aberrauerit.</head>
              <head xml:id="echoid-head213" xml:space="preserve">CAP.X.</head>
              <p>
                <s xml:id="echoid-s1808" xml:space="preserve">ARiſtoteles in principio quæſtionum Mechanicarum ait lineam, quæ terminat
                  <lb/>
                  <handwritten xlink:label="hd-0164-01" xlink:href="hd-0164-01a" number="11"/>
                circulum videtur conuexum habere coniunctum cum concauo, quod falſum
                  <lb/>
                eſt: </s>
                <s xml:id="echoid-s1809" xml:space="preserve">quia huiuſmodi linea partes nullas ſecundum latitudinem habet, (vt ipſe etiam
                  <lb/>
                confirmat) ſed eſt idem conuexum circuli: </s>
                <s xml:id="echoid-s1810" xml:space="preserve">linea verò quæ terminus eſt ſuperficiei
                  <lb/>
                ambientis, & amplectentis circulum eſt eadem concauitas dictæ ſuperficiei eun-
                  <lb/>
                dem circulum ambientis, quæ nullam conuexitatem habet. </s>
                <s xml:id="echoid-s1811" xml:space="preserve">& hæ duæ ſunt lineæ,
                  <lb/>
                quarum vna diuerſa eſt ab alia, neque altera alterius, quod ad conuexum, & ad con-
                  <lb/>
                cauum attinet.</s>
              </p>
              <p>
                <s xml:id="echoid-s1812" xml:space="preserve">Sed illud, quod Ariſtoteles ſcribit de duplici reſpectu motus vnius puncti ſecun
                  <lb/>
                dum vnam datam pro portionem, non ſufficit, ille enim ſic ait.</s>
              </p>
              <p>
                <s xml:id="echoid-s1813" xml:space="preserve">Sit proportio ſecundum quam latum fertur, quam habet
                  <var>.A.B.</var>
                ad
                  <var>.A.C.</var>
                et
                  <var>.A.</var>
                qui
                  <lb/>
                dem feratur verſus .B:
                  <var>A.B.</var>
                verò ſubterferatur verſus
                  <var>.M.C.</var>
                latum autem ſit
                  <var>.A.</var>
                  <reg norm="quidem" type="context">quidẽ</reg>
                  <lb/>
                ad
                  <var>.D.</var>
                vbi autem eſt
                  <var>.A.B.</var>
                verſus
                  <var>.E</var>
                . </s>
                <s xml:id="echoid-s1814" xml:space="preserve">Quoniam igitur lationis erat proportio, quam
                  <var>.
                    <lb/>
                  A.B.</var>
                habet ad
                  <var>.A.C.</var>
                neceſſe eſt &
                  <var>.A.D.</var>
                ad
                  <var>.A.E.</var>
                hanc habere rationem. </s>
                <s xml:id="echoid-s1815" xml:space="preserve">Simile igi
                  <lb/>
                  <handwritten xlink:label="hd-0164-02" xlink:href="hd-0164-02a" number="12"/>
                tur eſt pro portione paruum quadr ilaterum maiori. </s>
                <s xml:id="echoid-s1816" xml:space="preserve">Quamobrem etc.</s>
              </p>
              <p>
                <s xml:id="echoid-s1817" xml:space="preserve">Cui reſpondeo, punctum
                  <var>.A.</var>
                quod mouetur in linea
                  <var>.A.M.</var>
                ab
                  <var>.A.</var>
                verſus
                  <var>.M.</var>
                vſque
                  <lb/>
                ad
                  <var>.F.</var>
                non moueriab aliqua proportione determinata magis quàm ab alia: </s>
                <s xml:id="echoid-s1818" xml:space="preserve">vnde
                  <reg norm="non" type="context">nõ</reg>
                  <lb/>
                ſolum poſſumus imaginari dictum punctum
                  <var>.A.</var>
                moueri ab
                  <var>.A.</var>
                vſque ad
                  <var>.F.</var>
                eiuſdem
                  <lb/>
                velocitatis ſub alia quadam proportione, ſed etiam ſub alia, quæ iam datæ contraria
                  <lb/>
                ſit, vt eſt proportio ipſius
                  <var>.A.C.</var>
                ad
                  <var>.A.B.</var>
                  <reg norm="imaginantes" type="context">imaginãtes</reg>
                moueri
                  <var>.A.</var>
                verſus
                  <var>.C.</var>
                et
                  <var>.A.C.</var>
                ver
                  <lb/>
                ſus
                  <var>.B.M.</var>
                delatam. </s>
                <s xml:id="echoid-s1819" xml:space="preserve">Dico etiam idem
                  <var>.A.</var>
                moueri vſque ad
                  <var>.F.</var>
                ſecundum proportio-
                  <lb/>
                nem ipſius
                  <var>.A.O.</var>
                ad
                  <var>.A.N</var>
                . </s>
                <s xml:id="echoid-s1820" xml:space="preserve">Quamobrem imaginemur à puncto
                  <var>.F.</var>
                lineam
                  <var>.F.H.</var>
                cum
                  <lb/>
                linea
                  <var>.F.A.</var>
                efficere angu-
                  <lb/>
                lum æqualem angulo
                  <var>.O.
                    <lb/>
                  P.A.</var>
                & à puncto
                  <var>.A.</var>
                  <reg norm="lineam" type="context">lineã</reg>
                  <lb/>
                  <figure xlink:label="fig-0164-01" xlink:href="fig-0164-01a" number="222">
                    <image file="0164-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0164-01"/>
                  </figure>
                  <var>A.H.</var>
                  <reg norm="cum" type="context">cũ</reg>
                linea
                  <var>.A.F.</var>
                face-
                  <lb/>
                re
                  <reg norm="angulum" type="context">angulũ</reg>
                  <reg norm="æqualem" type="context">æqualẽ</reg>
                angulo
                  <lb/>
                  <var>O.A.P.</var>
                unde angulus
                  <var>.H.</var>
                  <lb/>
                æqualis erit angulo
                  <var>.O.</var>
                  <lb/>
                ex .32. libr. primi Eucl.
                  <lb/>
                </s>
                <s xml:id="echoid-s1821" xml:space="preserve">&
                  <reg norm="triangulum" type="context">triangulũ</reg>
                  <var>.A.H.F.</var>
                ęqui
                  <lb/>
                angulum erit triangulo
                  <var>.
                    <lb/>
                  A.O.P</var>
                . </s>
                <s xml:id="echoid-s1822" xml:space="preserve">Quam ob
                  <reg norm="causam" type="context">causã</reg>
                  <lb/>
                  <reg norm="eadem" type="context">eadẽ</reg>
                proportio erit
                  <reg norm="ipſius" type="simple">ipſiꝰ</reg>
                  <lb/>
                  <var>A.H.</var>
                ad
                  <var>.F.H.</var>
                quę
                  <reg norm="enipſius" type="context">ẽipſius</reg>
                  <lb/>
                  <var>A.O.</var>
                ad
                  <var>.O.P.</var>
                punctum
                  <lb/>
                igitur
                  <var>.A.</var>
                vſque ad
                  <var>.F.</var>
                mouetur ſecundum proportionem etiam ipſius
                  <var>.A.O.</var>
                ad
                  <var>.O.P.</var>
                  <lb/>
                Huiuſmodi igitur conſideratio, ab Ariſtotele facta, nullius eſt momenti.</s>
              </p>
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