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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DE PERSPECT.
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              <p>
                <s xml:id="echoid-s1502" xml:space="preserve">
                  <pb o="121" rhead="DE PERSPECT." n="133" file="0133" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0133"/>
                cundum figuram quadrilateram
                  <var>.q.d.r.e</var>
                . </s>
                <s xml:id="echoid-s1503" xml:space="preserve">Communis autem ſectio ſuperficiei
                  <var>.p.t.</var>
                  <lb/>
                cum dicto plano, ſit
                  <var>.i.x.</var>
                quæ
                  <var>.i.x.</var>
                perpendicularis erit
                  <var>.s.a.</var>
                ſuperficiei orizontali ex
                  <lb/>
                19. lib. 11. quia
                  <var>.p.t.</var>
                eſt etiam orizonti perpendicularis ex .18. eiuſdem, cum
                  <var>.o.p.</var>
                ei-
                  <lb/>
                dem perpendicularis exiſtat. </s>
                <s xml:id="echoid-s1504" xml:space="preserve">Vnde
                  <var>.i.x.</var>
                erit altitudo trianguli
                  <var>.i.q.d.</var>
                & æqualis ipſi
                  <var>.
                    <lb/>
                  o.p.</var>
                ex
                  <ref id="ref-0019">.34. primi</ref>
                . </s>
                <s xml:id="echoid-s1505" xml:space="preserve">Sit deinde
                  <var>.o.l.</var>
                  <reg norm="communis" type="context">cõmunis</reg>
                ſectio ſuperficiei triangularis
                  <var>.o.a.u.</var>
                  <reg norm="cum" type="context">cũ</reg>
                  <lb/>
                ſuperficie
                  <var>.p.t.</var>
                quæ
                  <var>.o.l.</var>
                ſecando lineam
                  <var>.e.r.</var>
                in puncto
                  <var>.Z.</var>
                nobis oſtendet quantum di-
                  <lb/>
                ſtare ſeu eminens eſſe debeat latus
                  <var>.e.r.</var>
                in plano ab
                  <var>.q.d.</var>
                medio ipſius
                  <var>.z.x</var>
                . </s>
                <s xml:id="echoid-s1506" xml:space="preserve">Et quia
                  <lb/>
                præſuppoſuimus
                  <var>.p.l.</var>
                in eodem medio, inter
                  <var>.u.s.</var>
                et
                  <var>.a.n.</var>
                ideo
                  <var>.x.q.</var>
                ęqualis erit
                  <var>.x.d.</var>
                  <lb/>
                & ex .4. lib. primi
                  <var>.i.q.</var>
                ipſi
                  <var>.i.d.</var>
                et
                  <var>.e.r.</var>
                parallela ipſi
                  <var>.q.d.</var>
                ex .6. lib. 11. cum ipſa quoque
                  <lb/>
                ſit perpendicularis ſuperficiei
                  <var>.p.t.</var>
                ex
                  <ref id="ref-0020">.19. eiuſdem</ref>
                . </s>
                <s xml:id="echoid-s1507" xml:space="preserve">Hucuſque igitur in figura cor-
                  <lb/>
                porea
                  <var>.A.</var>
                prodeunt in lucem omnes cauſæ effectuum figuræ ſuperficialis
                  <var>.A.</var>
                ideſt vn
                  <lb/>
                de fiat, vt in ipſa figura ſuperficiali, triangulum
                  <var>.o.p.l.</var>
                tale conſurgat, & quid ſignifi-
                  <lb/>
                cet
                  <var>.o.</var>
                et
                  <var>.o.p.</var>
                et
                  <var>.p.l.</var>
                et
                  <var>.o.l.</var>
                & quam ob cauſam tale quoque formetur triangulum
                  <var>.i.
                    <lb/>
                  q.d.</var>
                atque in tantam altitudinem, quantam obtinet
                  <var>.o.p.</var>
                & quid ſint latera
                  <var>.i.q.</var>
                et
                  <var>.i.
                    <lb/>
                  d.</var>
                & quare erigatur
                  <var>.x.i.</var>
                parallela ipſi
                  <var>.p.o.</var>
                ab eadem
                  <var>.p.o.</var>
                tanto ſpatio diſtans, & qua
                  <lb/>
                ratione producatur à puncto
                  <var>.Z.</var>
                ipſa
                  <var>.Z.r.e.</var>
                parallela ipſi
                  <var>.q.d</var>
                .</s>
              </p>
              <div xml:id="echoid-div308" type="float" level="4" n="1">
                <figure xlink:label="fig-0132-01" xlink:href="fig-0132-01a">
                  <image file="0132-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0132-01"/>
                </figure>
              </div>
              <p>
                <s xml:id="echoid-s1508" xml:space="preserve">Nunc obſeruandum eſt, quòd ſi planum ipſius
                  <var>.i.q.d.</var>
                in figura corporea aliquan-
                  <lb/>
                tulum inclinatum eſſet orizontem verſus, anguli
                  <var>.i.q.d.</var>
                et
                  <var>.i.d.q.</var>
                maiores exiſterent,
                  <lb/>
                quàm cum idem eſt ipſi orizonti perpendiculare, quemadmodum clarè demonſtra-
                  <lb/>
                tum fuit in .39. primi Vitelionis.</s>
              </p>
              <p>
                <s xml:id="echoid-s1509" xml:space="preserve">Non igitur rectè fit ſi in figura ſuperficiali ducatur à puncto
                  <var>.B.</var>
                parallela ipſi
                  <var>.q.d.</var>
                  <lb/>
                abſque maiori apertura angulorum
                  <var>.i.q.d.</var>
                et
                  <var>.i.d.q</var>
                .</s>
              </p>
              <figure position="here">
                <image file="0133-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0133-01"/>
                <caption xml:id="echoid-caption3" xml:space="preserve">SVPERFICIALIS.</caption>
              </figure>
            </div>
            <div xml:id="echoid-div310" type="section" level="3" n="2">
              <head xml:id="echoid-head178" xml:space="preserve">CAP. II.</head>
              <p>
                <s xml:id="echoid-s1510" xml:space="preserve">CVM verò duæ præcedentes figuræ intellectæ erunt, facilè quoque erit intel-
                  <lb/>
                ligere duas ſubſequentes
                  <var>.B.B.</var>
                in corporea quarum
                  <var>.p.l.</var>
                extra lineas
                  <var>.u.s.</var>
                et
                  <var>.a.n.</var>
                  <lb/>
                reperitur, vbi enim aduertendum erit oportere ſumere ſemper
                  <var>.p.x.</var>
                figuræ ſuperfi-
                  <lb/>
                cialis æqualem ei, quæ eſt corporeæ, & eidem ſuperficiali, adiungere
                  <var>.x.d.</var>
                æqualem
                  <lb/>
                ei, quæ eſt corporeæ, & compoſito
                  <var>.p.d.</var>
                ex dictis duabus lineis, in figura ſuperficiali,
                  <lb/>
                addere
                  <var>.d.q.</var>
                æqualem ei, quæ eſt figuræ corporeæ, deinde accipere punctum
                  <var>.l.</var>
                in fu-
                  <lb/>
                perficiali </s>
              </p>
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