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-div308" type="chapter" level="2" n="2">
            <div xml:id="echoid-div316" type="section" level="3" n="5">
              <p>
                <s xml:id="echoid-s1548" xml:space="preserve">
                  <pb o="126" rhead="IO. BAPT. BENED." n="138" file="0138" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0138"/>
                æqualis ſit ipſi
                  <var>.b.c.</var>
                )
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0138-01a" xlink:href="fig-0138-01"/>
                  <var>o.m.</var>
                etiam
                  <var>.i.c</var>
                : et
                  <var>.f.
                    <lb/>
                  k.</var>
                vt in figura
                  <var>.F.</var>
                cla
                  <lb/>
                riſſimè patet. </s>
                <s xml:id="echoid-s1549" xml:space="preserve">Alias
                  <lb/>
                  <reg norm="autem" type="context">autẽ</reg>
                multas lineas in
                  <lb/>
                alijs figuris non
                  <reg norm="aliam" type="context">aliã</reg>
                  <lb/>
                ob
                  <reg norm="camm" type="context">cãm</reg>
                duxi,
                  <reg norm="quam" type="context">quã</reg>
                ad
                  <lb/>
                facilius
                  <reg norm="eruendas" type="context">eruẽdas</reg>
                è te-
                  <lb/>
                nebris ignorantiæ, &
                  <lb/>
                in cognitionis lucem
                  <lb/>
                proferendas horum
                  <lb/>
                effectuum cauſas, vt
                  <lb/>
                dixi.</s>
              </p>
              <div xml:id="echoid-div316" type="float" level="4" n="1">
                <figure xlink:label="fig-0137-01" xlink:href="fig-0137-01a">
                  <image file="0137-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0137-01"/>
                  <caption xml:id="echoid-caption11" xml:space="preserve">CORPOREA.</caption>
                </figure>
                <figure xlink:label="fig-0137-02" xlink:href="fig-0137-02a">
                  <image file="0137-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0137-02"/>
                  <caption xml:id="echoid-caption12" xml:space="preserve">SVPERFICIALIS.</caption>
                </figure>
                <figure xlink:label="fig-0138-01" xlink:href="fig-0138-01a">
                  <image file="0138-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0138-01"/>
                </figure>
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            <div xml:id="echoid-div318" type="section" level="3" n="6">
              <head xml:id="echoid-head182" xml:space="preserve">CAP. VI.</head>
              <p>
                <s xml:id="echoid-s1550" xml:space="preserve">
                  <emph style="sc">SEd</emph>
                vtlocum altitudinis, in noſtro plano perpendiculari orizonti, & ita
                  <reg norm="locatum" type="context">locatũ</reg>
                  <unsure/>
                ,
                  <lb/>
                vt poſtremo diximus, inueniamus; </s>
                <s xml:id="echoid-s1551" xml:space="preserve">duas hîc ſubſcriptas figuras conſiderabimus
                  <var>.
                    <lb/>
                  G.</var>
                corpoream, & G. ſuperficialem, ſimiles duabus
                  <var>.E.E.</var>
                proximè præcedentibus,
                  <lb/>
                in quarum corporea ſit linea
                  <var>.b.M.</var>
                altitudinis perpendicularis orizonti. </s>
                <s xml:id="echoid-s1552" xml:space="preserve">Quare ſi
                  <lb/>
                deſiderabis inuenire in noſtro plano ſitum puncti
                  <var>.M.</var>
                ideſt punctum radij
                  <var>.o.M.</var>
                vi-
                  <lb/>
                ſualis in quo ipſe radius à plano eſt diuiſus, quod ſit
                  <var>.R.</var>
                quamuis extra
                  <reg norm="triangulum" type="context">triangulũ</reg>
                  <lb/>
                  <var>i.q.d.</var>
                tibi imaginatione confige ductam eſſe lineam
                  <var>.p.b.</var>
                quæ erit ſectio commu-
                  <lb/>
                nis orizontis cum ſuperficie
                  <var>.o.p.b.M.</var>
                quæ ſuperficies erit perpendicularis ipſi ori-
                  <lb/>
                zonti ex .18. lib 11. </s>
                <s xml:id="echoid-s1553" xml:space="preserve">Quòd autemnon minus
                  <var>.o.p.</var>
                quàm.M.b. ſit in vna eademq́ue
                  <lb/>
                ſuperficie dubitandum non eſt, quia ſi imaginabimur ductam eſſe lineam
                  <var>.p.M.</var>
                ha
                  <lb/>
                bebimus triangulum
                  <var>.o.p.b.</var>
                cum triangulo
                  <var>.M.b.p.</var>
                communibus partibus in vna ea-
                  <lb/>
                demq́ue ſuperficie conſtantem, vt triangulum quoque
                  <var>.o.p.M.</var>
                cum triangulo
                  <var>M.b.</var>
                  <lb/>
                o & triangulum
                  <var>.o.p.b.</var>
                cum triangulo
                  <var>.o.p.M.</var>
                & triangulum
                  <var>.M.b.p.</var>
                cum triangulo
                  <var>.
                    <lb/>
                  M.b.o</var>
                . </s>
                <s xml:id="echoid-s1554" xml:space="preserve">Vnde cum quilibet triangulus in vnica tantum ſuperficie ſit ex .2. lib. 11. ſe-
                  <lb/>
                quetur ſuperficiem
                  <var>.o.p.b.M.</var>
                planam eſſe, & vnicam, cuius communis ſectio cum no-
                  <lb/>
                ſtro plano ſit. θ.K.R. quæ perpendicularis orizonti exiſtet ex .19. lib. 11. eritq́ue pa-
                  <lb/>
                rallela ipſi
                  <var>.i.x.</var>
                ex .6. eiuſdem. </s>
                <s xml:id="echoid-s1555" xml:space="preserve">Imaginare nunc erectam eſſe
                  <var>.m.T.</var>
                æqualem ipſi
                  <var>.
                    <lb/>
                  b.M.</var>
                orizonti perpendicularem, quæ extenſa erit in ſuperficie
                  <var>.p.t.</var>
                quod ex ſe ad
                  <lb/>
                conſiderandum admodum facilè, clarumq́ue exiſtit, reducendo ad impoſſibilia
                  <lb/>
                quemlibet hæc negare volentem. </s>
                <s xml:id="echoid-s1556" xml:space="preserve">Imaginemur quoque ductam eſſe lineam
                  <var>.M.
                    <lb/>
                  T.</var>
                quæ
                  <var>.b.m.</var>
                ex .33. primi erit parallela, quia
                  <var>.m.T.</var>
                ęqualis
                  <var>.b.M.</var>
                parallela eſt
                  <lb/>
                ipſi
                  <var>.b.M.</var>
                ex .6. lib. 11. præter hæc
                  <var>.b.m.</var>
                parallela eſt ipſi
                  <var>.q.d.</var>
                quia ſic fuit ducta
                  <lb/>
                ſuperius, vnde
                  <var>.M.T.</var>
                parallela erit ipſi
                  <var>.q.d.</var>
                ex .9. vndecimi, & obid perpendi-
                  <lb/>
                cularis erit ſuperficiei
                  <var>.b.t.</var>
                ex .8. eiuſdem. </s>
                <s xml:id="echoid-s1557" xml:space="preserve">Nunc ſit
                  <var>.R.V.</var>
                communis ſectio trian-
                  <lb/>
                guli
                  <var>.o.M.T.</var>
                cum noſtro plano, vnde
                  <var>.R.V.</var>
                perpendicularis erit ſuperficiei
                  <var>.p.t.</var>
                  <lb/>
                ex .19. lib. 11. quam ob cauſam parallela erit ipſi
                  <var>.q.d.</var>
                ex .6. aut ex .9. eiuſdem
                  <lb/>
                quia ex .6. dicta, parallela eſt ipſi
                  <var>.M.T</var>
                . </s>
                <s xml:id="echoid-s1558" xml:space="preserve">Atſi
                  <var>.R.V.</var>
                parallela eſt ipſi
                  <var>.q.d.</var>
                  <lb/>
                etiam
                  <var>.f.K.</var>
                probatum iam fuit parallelam eſſe eidem, ergo
                  <var>.R.V.</var>
                parallela erit
                  <lb/>
                ipſi
                  <var>.K.f.</var>
                ex .30. primi, </s>
                <s xml:id="echoid-s1559" xml:space="preserve">Vnde ex .34. æqualis erit ipſi
                  <var>.K.f</var>
                . </s>
                <s xml:id="echoid-s1560" xml:space="preserve">Accedamus nunc
                  <lb/>
                ad
                  <reg norm="figuram" type="context">figurã</reg>
                  <var>.G.</var>
                  <reg norm="extructam" type="context">extructã</reg>
                ſupra figuram
                  <var>.E.</var>
                ſuperficialem, & erigamus
                  <var>.m.T.</var>
                perpendi-
                  <lb/>
                cularem ipſi
                  <var>.m.p.</var>
                ſed æqualem perfectæ altitudini, & ducamus
                  <var>.T.o.</var>
                vt ſecet li-
                  <lb/>
                neam
                  <var>.i.x.</var>
                in puncto
                  <var>.V.</var>
                ab ipſo ducentes
                  <var>.V.R.</var>
                parallelam ipſi
                  <var>.q.d.</var>
                ducendo de- </s>
              </p>
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