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-div308" type="section" level="3" n="1">
              <pb o="120" rhead="IO. BAPT. BENED." n="132" file="0132" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0132"/>
              <p>
                <s xml:id="echoid-s1494" xml:space="preserve">Pro cuius rei ſpeculatione imaginemur in figura corporea .A:
                  <var>q.a.</var>
                eſſe figuram re-
                  <lb/>
                ctangulam
                  <reg norm="orizontalemque" type="simple">orizontalemq́;</reg>
                ad degradandam ſuper aliquod planum perpendiculare
                  <lb/>
                orizonti, & cum eo primum coniunctam in linea
                  <var>.q.d.</var>
                cuius plani triangulum
                  <var>.i.q.d.</var>
                  <lb/>
                pars erit, ſit autem oculus reſpicientis
                  <var>.o.</var>
                cuius altitudo
                  <var>.o.p.</var>
                ab orizonte, qui
                  <reg norm="quidem" type="context">quidẽ</reg>
                  <lb/>
                conſpicit rectangulum dictum orizontale
                  <var>.q.a.</var>
                in pyramide
                  <var>.o.q</var>
                :
                  <var>o.u</var>
                :
                  <var>o.a.</var>
                et
                  <var>.o.d.</var>
                  <lb/>
                terminata quatuor triangulis
                  <var>.o.q.u</var>
                :
                  <var>o.u.a</var>
                :
                  <var>o.a.d.</var>
                et
                  <var>.o.d.q.</var>
                ſit verò primum ita
                  <lb/>
                collocatus pes
                  <var>.p.</var>
                eius qui reſpicit, vt linea
                  <var>.p.l.</var>
                perpendicularis ipſi
                  <var>.u.a.</var>
                lateri re-
                  <lb/>
                ctanguli, medio loco poſita ſit, inter
                  <var>.a.n.</var>
                et
                  <var>.u.s</var>
                . </s>
                <s xml:id="echoid-s1495" xml:space="preserve">
                  <reg norm="Idque" type="simple">Idq́;</reg>
                primum nobis erit exem-
                  <lb/>
                plum.</s>
              </p>
              <p>
                <s xml:id="echoid-s1496" xml:space="preserve">Imaginemur nunc lineas
                  <var>.u.q.</var>
                et
                  <var>.a.d.</var>
                indefinitè productas eſſe, quæ in ſuperficie-
                  <lb/>
                bus duorum triangulorum
                  <var>.o.u.q.</var>
                et
                  <var>.o.a.d.</var>
                & rectanguli orizontalis
                  <var>.q.a.</var>
                ex
                  <ref id="ref-0018">prima
                    <lb/>
                  vndecimi Euclid.</ref>
                poſitæ erunt. </s>
                <s xml:id="echoid-s1497" xml:space="preserve">Imaginemur etiam lineam
                  <var>.p.s.n.</var>
                perpendicula-
                  <lb/>
                rem ipſi
                  <var>.p.l.</var>
                quæ etiam cum duabus
                  <var>.u.q.s.</var>
                et
                  <var>.a.d.n.</var>
                ex .34. primi Euclid. angulos
                  <lb/>
                rectos conſtituet, cum ex .28. duæ
                  <var>.u.q.s.</var>
                et
                  <var>.a.d.n.</var>
                ſint parallelæ ipſi
                  <var>.p.l.</var>
                et
                  <var>.s.n.</var>
                ipſi
                  <var>.u.
                    <lb/>
                  a.</var>
                & quia ſupponitur
                  <var>.o.p.</var>
                perpendicularis plano orizontali, Angulus ergò
                  <var>.o.p.l.</var>
                re-
                  <lb/>
                ctus erit ex ſecunda definitione .11. Euclid. </s>
                <s xml:id="echoid-s1498" xml:space="preserve">Imaginemur quoque ductas eſſe
                  <lb/>
                duas
                  <var>.o.s.</var>
                et
                  <var>.o.n.</var>
                vnde
                  <var>.l.p.</var>
                ei ſuperficiei, in qua ſunt duæ lineæ
                  <var>.o.p.</var>
                et
                  <var>.s.n.</var>
                ex .4.
                  <lb/>
                11. perpendicularis erit, & ſuperficies orizontalis
                  <var>.a.s.</var>
                perpendicularis erit cum dicta
                  <lb/>
                  <var>o.s.n.</var>
                ex .18. eiuſdem lib. vnde ex dicta definitione
                  <var>.o.s.u.</var>
                et
                  <var>.o.n.a.</var>
                erunt anguli recti
                  <lb/>
                et
                  <var>.o.s.</var>
                et
                  <var>.o.n.</var>
                ex communi ſcientia, in ſuperficiebus duorum triangulorum
                  <var>.o.u.q.</var>
                et
                  <var>.
                    <lb/>
                  o.a.d.</var>
                erunt, ſi noluerimus cogere aduerſarium ad confitendum duas lineas rectas in-
                  <lb/>
                cludere ſuperficiem, quemadmodum cogere-
                  <lb/>
                  <figure xlink:label="fig-0132-01" xlink:href="fig-0132-01a" number="179">
                    <image file="0132-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0132-01"/>
                  </figure>
                tur facere, ſi opinaretur duas alias rectas per
                  <lb/>
                eadem puncta
                  <var>.o.s.n.</var>
                tranſire, quæſunt in di-
                  <lb/>
                ctis ſuperficiebus. </s>
                <s xml:id="echoid-s1499" xml:space="preserve">Vnde
                  <var>.o.s.</var>
                et
                  <var>.o.n.</var>
                communes
                  <lb/>
                erunt ſectiones duarum dictarum
                  <reg norm="ſuperficierum" type="context">ſuperficierũ</reg>
                  <lb/>
                cum ſuperficie
                  <var>.o.s.n</var>
                . </s>
                <s xml:id="echoid-s1500" xml:space="preserve">Imaginemur nunc has
                  <lb/>
                duas ſuperficies
                  <var>.o.u.</var>
                et
                  <var>.o.a.</var>
                quarum commu-
                  <lb/>
                nis ſectio ſit
                  <var>.o.t.</var>
                (quæ erit linea recta ex .3. lib.
                  <lb/>
                II.) quæ erunt perpendiculares ſuperficiei
                  <var>.o.s.
                    <lb/>
                  n.</var>
                ex .4. et .14. iam dictis. </s>
                <s xml:id="echoid-s1501" xml:space="preserve">& ex .19. eiuſdem
                  <lb/>
                  <var>o.t.</var>
                perpendicularis eidem ſuperficiei
                  <var>.o.s.n.</var>
                  <lb/>
                erit, & ex .6. eiuſdem hæc linea
                  <var>.o.t.</var>
                duabus
                  <var>.u.
                    <lb/>
                  q.s.</var>
                et
                  <var>.a.d.n.</var>
                parallela exiſter, & ex .9. eiuſdem
                  <lb/>
                hæc linea
                  <var>.o.t.</var>
                duabus
                  <var>.u.q.s.</var>
                et
                  <var>.a.d.n.</var>
                parallela
                  <lb/>
                exiſtet, & ex eadem .9. erit parallela ipſi
                  <var>.p.l.</var>
                  <lb/>
                Imaginemur nunc planum, ſuper quod deſide
                  <lb/>
                remus videre quadrangulum orizontale, quod
                  <lb/>
                planum, exempli gratia, ſit primo, vt iam dixi-
                  <lb/>
                mus, locatum in linea
                  <var>.q.d.</var>
                ad angulos rectos
                  <lb/>
                cum plano orizontali, cuius communes ſectio
                  <lb/>
                nes cum ſuperficiebus
                  <var>.s.t.</var>
                et
                  <var>.n.t.</var>
                viſionis la-
                  <lb/>
                terum
                  <var>.u.q.</var>
                et
                  <var>.a.d.</var>
                ſint
                  <var>.i.q.</var>
                et
                  <var>.i.d.</var>
                & com-
                  <lb/>
                munis ſectio trianguli
                  <var>.o.u.a.</var>
                ideſt viſionis
                  <lb/>
                lateris
                  <var>.a.u.</var>
                cum dicto plano, ſit
                  <var>.r.e</var>
                . </s>
                <s xml:id="echoid-s1502" xml:space="preserve">Vnde ex
                  <lb/>
                communi ſcientia rectangulum orizontale,
                  <lb/>
                oculo
                  <var>.o.</var>
                ſeipſum patefaciet in plano
                  <var>.i.q.d.</var>
                ſe- </s>
              </p>
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