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-s1521" xml:space="preserve">
                  <pb o="123" rhead="DE PERSPECT." n="135" file="0135" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0135"/>
                aliud eſt, quàm punctum, varijs ſectionibus commune, & huiuſmodi punctum, ocu
                  <lb/>
                lus non eſt, quemadmodum multi Pictores, Sculptores, Architecti, & Perſpectiui
                  <lb/>
                ignari, ipſum punctum, oculum appellando, falsò crediderunt, quaſi
                  <reg norm="punctum" type="context">punctũ</reg>
                  <var>.i.</var>
                per-
                  <lb/>
                ſpectiuæ oculus eſſet.</s>
              </p>
              <p>
                <s xml:id="echoid-s1522" xml:space="preserve">In ſupradictis igitur figuris manifeſte eluceſcit cauſa diminutionis obiectorum,
                  <lb/>
                & altitudinis trianguli æqualis ei, quæ eſt oculi à plano orizontali, vt etiam diſtantię
                  <var>.
                    <lb/>
                  p.l.p.x.</var>
                & cuiuſuis tandem rei. </s>
                <s xml:id="echoid-s1523" xml:space="preserve">Sed vt huius effectus ſcientia magis in vniuerſum pa-
                  <lb/>
                retur. </s>
                <s xml:id="echoid-s1524" xml:space="preserve">Volo duas hic ſubſcriptas figuras
                  <var>.D.</var>
                corpoream, &
                  <var>.D.</var>
                ſuperficialem à vo-
                  <lb/>
                bis conſiderari, in quarum corporea, linea
                  <var>.p.l.</var>
                ſit extra duas
                  <var>.u.s.</var>
                et
                  <var>.a.n.</var>
                vt in figu-
                  <lb/>
                ra
                  <var>.B.</var>
                locata, ita tamen vt planum trianguli
                  <var>.i.q.d.</var>
                diſiunctum ſit à rectangulo ſuper-
                  <lb/>
                ficiali, ideſt, vt ſeparatum exiſtat à linea
                  <var>.q.d.</var>
                latere ipſius rectanguli, & ſit etiam obli
                  <lb/>
                quum, reſpectu ipſius rectanguli, ideſt vt communis ſectio dicti plani cum ſuperficie
                  <lb/>
                  <var>a.s.</var>
                orizontalis ipſi
                  <var>.u.a.</var>
                parallela non ſit, ſed ſit obliqua, ſi tamen idem planuni per-
                  <lb/>
                pendiculare dictæ ſuperficiei orizontali
                  <var>.a.s.</var>
                erit: </s>
                <s xml:id="echoid-s1525" xml:space="preserve">& dicta communis ſectio exprima­
                  <lb/>
                tur characteribus .q.ω.α.d.x. nunc in figura corporea habebimus figuram
                  <var>.e.r.c.m.</var>
                  <lb/>
                in plano, quod viſualem pyramidem ſecat, medio cuius figuræ
                  <var>.e.r.c.m.</var>
                oculus po-
                  <lb/>
                ſitus in
                  <var>.o.</var>
                rectangulum orizontale conſpicit. </s>
                <s xml:id="echoid-s1526" xml:space="preserve">Volentes vero nunc in figura
                  <var>.D.</var>
                ſuper-
                  <lb/>
                ficiali eam deſcribere, faciem us
                  <var>.p.x.</var>
                ſuperficialem, æqualem corporeæ, eiq́ue
                  <lb/>
                addemus
                  <var>.x.l.</var>
                æqualem corporeæ, aut ſumemus
                  <var>.p.l.</var>
                eidem corporeæ
                  <reg norm="aequa- lem" type="simple">ęqua-
                    <lb/>
                  lem</reg>
                , quam ſecabimus in puncto
                  <var>.x.</var>
                eodem planè modo, quo corporea reperi-
                  <lb/>
                tur diuiſa; </s>
                <s xml:id="echoid-s1527" xml:space="preserve">erigemus deinde
                  <var>.p.o.</var>
                et
                  <var>.x.i.</var>
                æquales corporeis. </s>
                <s xml:id="echoid-s1528" xml:space="preserve">Secabimus deinde
                  <var>.x.q.</var>
                  <lb/>
                æqualem corporeæ, & ducemus
                  <var>.q.i.</var>
                et
                  <var>.l.o.</var>
                vnde habebimus triangulos
                  <var>.o.p.l.</var>
                et
                  <var>.i.x.
                    <lb/>
                  q.</var>
                ſimiles & æquales corporeis ex .4. primi Eucli. </s>
                <s xml:id="echoid-s1529" xml:space="preserve">Secabimus deinde
                  <var>.q.x.</var>
                in pun-
                  <lb/>
                cto
                  <var>.d.</var>
                eadem ratione, qua ſecta fuit corporea, & ducemus lineam
                  <var>.d.i.</var>
                vnde habebi-
                  <lb/>
                mus triangulos
                  <var>.i.d.q.</var>
                et
                  <var>.i.d.x.</var>
                ſimiles corporeis. </s>
                <s xml:id="echoid-s1530" xml:space="preserve">& mediante triangulo
                  <var>.i.q.d.</var>
                hu-
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0135-01a" xlink:href="fig-0135-01"/>
                cuſque habebimus ſitus duorum laterum figurę
                  <lb/>
                rectanguli degradati, ideſt ſitus ipſius
                  <var>.e.m.</var>
                et
                  <var>.r.
                    <lb/>
                  c.</var>
                etiam ſi adhuc neſciatur in qua parte ipſius
                  <var>.i.
                    <lb/>
                  q.</var>
                & ipſius
                  <var>.i.d.</var>
                eſſe
                  <reg norm="debeant" type="context">debeãt</reg>
                . </s>
                <s xml:id="echoid-s1531" xml:space="preserve">Quod ſi ſcire volue
                  <lb/>
                rimus
                  <reg norm="ſecabitur" type="simple">ſecabit̃</reg>
                .
                  <var>p.l.</var>
                in
                  <reg norm="puncto" type="context">pũcto</reg>
                  <var>.g.</var>
                ſimilis corporeæ,
                  <lb/>
                ſi in ipſa tamen corporea prius protraxerimus
                  <lb/>
                lineam
                  <var>.q.d.</var>
                latus rectanguli vſque ad
                  <var>.p.l.</var>
                in pun
                  <lb/>
                cto
                  <var>.g</var>
                . </s>
                <s xml:id="echoid-s1532" xml:space="preserve">Ducetur deinde linea
                  <var>.o.g.</var>
                ſuperficialis,
                  <lb/>
                quæ ſecabit lineam
                  <var>.i.x.</var>
                in puncto
                  <var>.f.</var>
                linea vero
                  <var>.
                    <lb/>
                  o.l.</var>
                in puncto
                  <var>.z.</var>
                punctis ſitis in
                  <var>.i.x.</var>
                ſuperficiali,
                  <lb/>
                pręcisè vt in corporea,
                  <reg norm="quemadmodum" type="context">quemadmodũ</reg>
                quilibet
                  <lb/>
                ex ſe facilè cognoſcere poteſt. </s>
                <s xml:id="echoid-s1533" xml:space="preserve">Deinde in cor
                  <lb/>
                porea, in ſuperficie orizontali ducatur
                  <var>.p.q.</var>
                et
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0135-02a" xlink:href="fig-0135-02"/>
                </s>
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