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-div314" type="section" level="3" n="4">
              <p>
                <s xml:id="echoid-s1533" xml:space="preserve">
                  <pb o="124" rhead="IO. BAPT. BENED." n="136" file="0136" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0136"/>
                  <var>.p.u.</var>
                & imaginemur
                  <var>.o.q.</var>
                in ſuperficie
                  <var>.t.s.</var>
                vnde trianguli
                  <var>.o.p.q.</var>
                et
                  <var>.o.p.u.</var>
                erunt perpen
                  <lb/>
                diculares orizonti ex
                  <ref id="ref-0021">.18. lib. 11.</ref>
                et
                  <var>.ω.m.</var>
                et. α. e. communes ſectiones dictorum
                  <reg norm="duorum" type="context">duorũ</reg>
                  <lb/>
                triangulorum cum plano trianguli
                  <var>.i.q.x.</var>
                ipſi quoque plano ex .19. eiuſdem lib. erunt
                  <lb/>
                perpendiculares. </s>
                <s xml:id="echoid-s1534" xml:space="preserve">Nuncautem ſecetur
                  <var>.q.x.</var>
                ſuperficialis in punctis
                  <var>.ω.</var>
                et .α. eadem ra-
                  <lb/>
                tione; </s>
                <s xml:id="echoid-s1535" xml:space="preserve">qua corporea ſecta ſuit à duabus
                  <var>.p.q.</var>
                et
                  <var>.p.u.</var>
                à quibus punctis
                  <var>.ω.</var>
                et. α. ſuperficia
                  <lb/>
                libus ductæ ſint duæ
                  <var>ω.m.</var>
                et .α.e. perpendiculares vſque ad latus
                  <var>.i.q.</var>
                in punctis
                  <var>.m.</var>
                et
                  <var>.
                    <lb/>
                  e.</var>
                quę ſitum habebunt in
                  <var>.i.q.</var>
                ſuperficiali pręcisè, vt in corporea, ex .26. primi, du-
                  <lb/>
                cendo deinde in ſuperficiali duas
                  <var>.m.f.</var>
                et
                  <var>.e.Z.</var>
                eæ æquales erunt corporeis ex .4. pri-
                  <lb/>
                mi, & ſic anguli
                  <var>.i.e.z.</var>
                et
                  <var>.i.m.f.</var>
                & eę duę lineę
                  <var>.e.z.</var>
                et
                  <var>.m.f.</var>
                fectę erunt à linea
                  <var>.i.d.</var>
                in duo
                  <lb/>
                  <figure xlink:label="fig-0136-01" xlink:href="fig-0136-01a" number="186">
                    <image file="0136-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0136-01"/>
                    <caption xml:id="echoid-caption9" xml:space="preserve">CORPOREA.</caption>
                  </figure>
                bus punctis
                  <var>.r.</var>
                et
                  <var>.c.</var>
                vnde
                  <var>.e.r.</var>
                et
                  <var>.m.c.</var>
                æquales
                  <lb/>
                erunt corporeis ex .26. primi, ſed ita quo-
                  <lb/>
                que ſe habent duę
                  <var>.e.m.</var>
                et
                  <var>.r.c.</var>
                ſi verum eſt
                  <reg norm="quod" type="simple">ꝙ</reg>
                dif
                  <lb/>
                ferentię rerum æqualium ſint adinuicem etiam
                  <lb/>
                æquales. </s>
                <s xml:id="echoid-s1536" xml:space="preserve">Hac ratione igitur habebimus figu-
                  <lb/>
                ram quadrilateram
                  <var>.m.e.r.c.</var>
                ſuperficialem om
                  <lb/>
                ninò ſinlilem, & ęqualem corporeæ. </s>
                <s xml:id="echoid-s1537" xml:space="preserve">Is tamen
                  <lb/>
                modus prolixus eſt, & arduus, quam ob cau-
                  <lb/>
                ſam neque ego vnquam
                  <reg norm="eum" type="context">eũ</reg>
                viui accommo-
                  <lb/>
                darem, neque alijs, vt eodem vterentur ſua-
                  <lb/>
                derem.</s>
              </p>
              <figure position="here" number="187">
                <image file="0136-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0136-02"/>
                <caption xml:id="echoid-caption10" xml:space="preserve">SVPERFICIALIS.</caption>
              </figure>
            </div>
            <div xml:id="echoid-div316" type="section" level="3" n="5">
              <head xml:id="echoid-head181" xml:space="preserve">CAP.V.</head>
              <p>
                <s xml:id="echoid-s1538" xml:space="preserve">
                  <emph style="sc">ESt</emph>
                igitur ſciendum, quòd qui ſciuerit vnum ſolum punctum locare in perſpe
                  <lb/>
                ctiua, eo modo quem nunc proponam, facilè quoque ſciet ſupra quoduis
                  <reg norm="planum" type="context">planũ</reg>
                  <lb/>
                (quod tamen ſit perpendiculare orizonti) quamlibet rem locare. </s>
                <s xml:id="echoid-s1539" xml:space="preserve">Quam ob cauſam
                  <lb/>
                imaginemur hic ſubſcriptas duas figuras
                  <var>.E.</var>
                  <reg norm="corpoream" type="context">corporeã</reg>
                , & E. ſuperficialem, & in qua-
                  <lb/>
                drilatero rectangulo orizontali
                  <var>.a.u.q.d.</var>
                imaginemur eſſe punctum
                  <var>.b.</var>
                quodlibet col-
                  <lb/>
                locandum in aliquo plano perpendiculari orizonti locato, quemadmodum ſuppo-
                  <lb/>
                nebatur in figura
                  <var>.A.</var>
                corporea. </s>
                <s xml:id="echoid-s1540" xml:space="preserve">Imaginemur ergo in ipſa figura
                  <var>.E.</var>
                corporea radi-
                  <lb/>
                um viſualem
                  <var>.o.b.</var>
                qui ſectus ſit à noſtro plano in
                  <var>.k.</var>
                quod quidem
                  <var>.k.</var>
                quærendum eſt
                  <lb/>
                in triangulo
                  <var>.i.q.d.</var>
                ipſius plani. </s>
                <s xml:id="echoid-s1541" xml:space="preserve">Volo ob hanc igitur rem, vt à puncto
                  <var>.b.</var>
                in figura
                  <var>.E.</var>
                  <lb/>
                ſuperficiali ducatur
                  <var>.b.c.</var>
                ad rectos
                  <reg norm="cum" type="context">cũ</reg>
                  <var>.q.d.</var>
                & à puncto
                  <var>.c.</var>
                ad
                  <var>.i.</var>
                ducatur linea
                  <var>.c.i.</var>
                et
                  <var>.b.m.</var>
                  <lb/>
                parallela ipſi
                  <var>.q.d.</var>
                quę ab ipſa
                  <var>.x.l.</var>
                in puncto
                  <var>.m.</var>
                erit diuiſa, & hęc
                  <var>.x.m.</var>
                è directo con-
                  <lb/>
                iuncta cum
                  <var>.p.x.</var>
                ducatur
                  <var>.o.m.</var>
                quæ ab
                  <var>.i.x.</var>
                ſecta erit in puncto
                  <var>.f.</var>
                à quo ducendo dein-
                  <lb/>
                de
                  <var>.f.g.h.</var>
                parallela
                  <var>.q.d.</var>
                ab
                  <var>.i.c.</var>
                in puncto
                  <var>.K.</var>
                erit diuiſa. </s>
                <s xml:id="echoid-s1542" xml:space="preserve">Atque id erit quod nobis
                  <lb/>
                inquirendum propoſueramus.</s>
              </p>
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