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]

Table of handwritten notes

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            <div xml:id="echoid-div367" type="section" level="3" n="14">
              <p>
                <pb o="156" rhead="IO. BAPT. BENED." n="168" file="0168" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0168"/>
                <s xml:id="echoid-s1854" xml:space="preserve">
                  <reg norm="Sitque" type="simple">Sitq;</reg>
                ſemper diuiſum à linea
                  <var>.a.o.e.</var>
                per medium, ſequitur communi quodam con-
                  <lb/>
                ceptu, nullam nobis difficultatem oborituram, dictum centrum ad quam volueri-
                  <lb/>
                mus partem ducendo, quemadmodum à qualibet alia figura, quæ perfectè rotunda
                  <lb/>
                non eſſet, emergeret; </s>
                <s xml:id="echoid-s1855" xml:space="preserve">Vt
                  <reg norm="exempli" type="context">exẽpli</reg>
                gratia, ſi imaginabimur pentagonum
                  <var>.K.i.h.f.l.</var>
                quie
                  <lb/>
                ſcere
                  <reg norm="ſuper" type="simple">ſuꝑ</reg>
                  <reg norm="eandem" type="context">eandẽ</reg>
                  <reg norm="lineam" type="context">lineã</reg>
                  <var>.a.b.K.</var>
                ita ut
                  <reg norm="primum" type="context">primũ</reg>
                  <reg norm="totum" type="context">totũ</reg>
                latus
                  <var>.i.K.</var>
                in linea
                  <var>.b.K.</var>
                  <reg norm="extendatur" type="context simple">extẽdat̃</reg>
                ,
                  <reg norm="ducen- do" type="context">ducẽ-
                    <lb/>
                  do</reg>
                poſteà centrum
                  <var>.o.</var>
                (ponamus.) verſus
                  <var>.l.</var>
                dubium non eſt, quin oporteat, vt dictum
                  <lb/>
                centrum
                  <var>.o.</var>
                à linea
                  <var>.b.d.</var>
                eleuetur, ab
                  <reg norm="eademque" type="simple">eademq;</reg>
                magis diſtet, voluens ſe per
                  <reg norm="arcum" type="context">arcũ</reg>
                vnum
                  <lb/>
                circuli,
                  <reg norm="qui" type="simple">ꝗ</reg>
                  <reg norm="pro" type="simple">ꝓ</reg>
                ſuo ſemidiametro habeat
                  <var>.o.K.</var>
                quę maior eſt ipſa
                  <var>.o.a.</var>
                ex .18. li. primi Eu
                  <lb/>
                cli. vnde ſi à puncto
                  <var>.K.</var>
                imaginabimur lineam
                  <var>.K.c.</var>
                reſpicientem centrum regionis
                  <lb/>
                elementaris, dubium non eſt, quin ſi velimus transferre
                  <reg norm="centrum" type="context">cẽtrum</reg>
                hoc à priori ſitu
                  <reg norm="vſque" type="simple">vſq;</reg>
                  <lb/>
                ad dictam lineam, oporteat addere pondus parti ipſius
                  <var>.l.</var>
                quæ à linea
                  <var>.K.c.</var>
                fuit ſecta,
                  <lb/>
                aut aliquid de ipſo pondere partis centri detrahere. </s>
                <s xml:id="echoid-s1856" xml:space="preserve">quod quibuſuis modis fiat, ar-
                  <lb/>
                duum certè eſt ad efficiendum; </s>
                <s xml:id="echoid-s1857" xml:space="preserve">neque hoc etiam accidit figuræ perfectè rotundæ,
                  <lb/>
                cum
                  <reg norm="centrum" type="context">cẽtrum</reg>
                  <reg norm="quod" type="simple">ꝙ</reg>
                perfectè in medio ipſius ponderis eſt, reperiatur ſemper in linea per-
                  <lb/>
                pendiculari ipſi plano, in quo animaduertendum eſt,
                  <reg norm="quod" type="simple">ꝙ</reg>
                etiam ſi ipſum planum ap-
                  <lb/>
                pellem; </s>
                <s xml:id="echoid-s1858" xml:space="preserve">pro plano tamen perfecto intelligi nolo, ſed pro ſuperficie perfectè
                  <reg norm="ſphaeri- ca" type="simple">ſphęri-
                    <lb/>
                  ca</reg>
                circa centrum à corporibus grauibus expetitum; </s>
                <s xml:id="echoid-s1859" xml:space="preserve">nam ratione magnæ amplitudi-
                  <lb/>
                nis huiuſmodi ſuperficiei, nullam differentiam notatu dignam à perfecto aliquo pla
                  <lb/>
                no exigui interualli ad curuitatem eiuſdem ſuperficiei imaginari poterimus. </s>
                <s xml:id="echoid-s1860" xml:space="preserve">Sed ut
                  <lb/>
                redeamus ad ſermonem de reuolutione figuræ rotundæ ſuſceptum,
                  <reg norm="clarum" type="context">clarũ</reg>
                igitur erit
                  <lb/>
                quamlibet minimam vim (vt ita dicam) quę trahat, aut impellat centrum
                  <var>.o.</var>
                verſus
                  <var>.u.</var>
                  <lb/>
                huiuſmodi figuram reuoluturam, cuius media pars ad trahendum, aut impellendum
                  <lb/>
                punctum
                  <var>.e.</var>
                ſufficiere; </s>
                <s xml:id="echoid-s1861" xml:space="preserve">Imaginemur autem
                  <reg norm="quod" type="simple">ꝙ</reg>
                li
                  <lb/>
                nea
                  <var>.n.o.u.</var>
                eſſet libra
                  <reg norm="quędam" type="context">quędã</reg>
                in figura perfectè
                  <lb/>
                  <figure xlink:label="fig-0168-01" xlink:href="fig-0168-01a" number="226">
                    <image file="0168-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0168-01"/>
                  </figure>
                rotunda
                  <var>.a.n.e.u.</var>
                poſita, & vis, quę trahere cen
                  <lb/>
                trum deberet, diuiſa eſſet per medium, cuius
                  <lb/>
                medietas appenſa eſſet extremitati
                  <var>.u.</var>
                diame-
                  <lb/>
                tri
                  <var>.n.o.u.</var>
                  <reg norm="clarum" type="context">clarũ</reg>
                erit,
                  <reg norm="quod" type="simple">ꝙ</reg>
                abſque vlla difficultate
                  <lb/>
                reuolueret figuram ſuper lineam
                  <var>.b.a.d.</var>
                verſus
                  <var>.
                    <lb/>
                  d.</var>
                quia huius vis, aut pondus
                  <reg norm="nullum" type="context">nullũ</reg>
                contra pon
                  <lb/>
                dus haberet vltra centrum
                  <var>.o.</var>
                uerſus
                  <var>.n.</var>
                  <reg norm="quod" type="simple">ꝙ</reg>
                cen-
                  <lb/>
                trum
                  <var>.o.</var>
                perpetuo quieſcit
                  <reg norm="ſuper" type="simple">ſuꝑ</reg>
                . a. in linea
                  <var>.e.o.
                    <lb/>
                  a.</var>
                per medium diuidente ſemper totum pon-
                  <lb/>
                dus figurę ſuppoſitę. </s>
                <s xml:id="echoid-s1862" xml:space="preserve">Tantò facilius ergo tota
                  <lb/>
                dicta vis ap
                  <lb/>
                  <figure xlink:label="fig-0168-02" xlink:href="fig-0168-02a" number="227">
                    <image file="0168-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0168-02"/>
                  </figure>
                  <figure xlink:label="fig-0168-03" xlink:href="fig-0168-03a" number="228">
                    <image file="0168-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0168-03"/>
                  </figure>
                plicata cen
                  <lb/>
                tro,
                  <reg norm="ipsum" type="context">ipsũ</reg>
                ver
                  <lb/>
                ſus
                  <var>.u.</var>
                  <reg norm="trahens" type="context">trahẽs</reg>
                  <lb/>
                per lineam
                  <lb/>
                  <reg norm="parallelam" type="context">parallelã</reg>
                ip
                  <lb/>
                ſi
                  <var>.a.d.</var>
                  <reg norm="dictam" type="context">dictã</reg>
                  <lb/>
                figuram re-
                  <lb/>
                uolueret. </s>
                <s xml:id="echoid-s1863" xml:space="preserve">Et
                  <lb/>
                ſi linea qua
                  <lb/>
                dictum cen
                  <lb/>
                trum trahi-
                  <lb/>
                tur ab ipſo </s>
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