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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            <div xml:id="echoid-div316" type="section" level="3" n="5">
              <pb o="125" rhead="DE PERSPECT." n="137" file="0137" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0137"/>
              <p>
                <s xml:id="echoid-s1543" xml:space="preserve">Ad cuius rei
                  <reg norm="ſpeculationem" type="context">ſpeculationẽ</reg>
                , imaginatione con
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0137-01a" xlink:href="fig-0137-01"/>
                cipiamus lineam
                  <var>.b.c.</var>
                corpoream, protractam eſ
                  <lb/>
                ſe vſque ad
                  <var>.y.</var>
                lineæ
                  <var>.s.n.</var>
                & imaginatione ſit com
                  <lb/>
                  <reg norm="præhenſa" type="context">præhẽſa</reg>
                linea
                  <var>.y.o.</var>
                et
                  <var>.b.</var>
                R
                  <unsure/>
                . parallela eidem, ideo
                  <lb/>
                ob rationes iam dictas de figura
                  <var>.A.</var>
                hæ tres li-
                  <lb/>
                neæ
                  <var>.o.y</var>
                :
                  <var>i.c</var>
                : et. </s>
                <s xml:id="echoid-s1544" xml:space="preserve">R
                  <unsure/>
                  <var>.b.</var>
                ſimul cum linea
                  <var>.o.b.</var>
                erunt
                  <lb/>
                in vna eademq́ue ſuperficie plana, quam cha-
                  <lb/>
                racteribus
                  <var>.y.</var>
                R
                  <unsure/>
                . notemus .et
                  <var>.i.c.</var>
                eius erit ſe-
                  <lb/>
                ctio communis cum plano, in quo quæritur
                  <reg norm="pun- ctum" type="context">pũ-
                    <lb/>
                  ctum</reg>
                , et
                  <var>.f.k.</var>
                ipſius plani cum triangulo
                  <var>.o.b.m.</var>
                  <lb/>
                erit ſectio communis, & parallela ipſi
                  <var>.q.d.</var>
                ex
                  <ref id="ref-0022">.
                    <lb/>
                  6. lib. 11.</ref>
                quia
                  <var>.k.f.</var>
                perpendicularis eſt ſuperfi-
                  <lb/>
                ciei
                  <var>.p.t.</var>
                ex .19. eiuſdem cum triangulus
                  <var>.o.
                    <lb/>
                  b.m.</var>
                eidem ſuperficiei
                  <var>.p.t.</var>
                ex .18. eiuſdem
                  <lb/>
                perpendicularis exiſtat. </s>
                <s xml:id="echoid-s1545" xml:space="preserve">Vnde perſpicuè pa-
                  <lb/>
                tet ratio quare protracta
                  <unsure/>
                ſit parallela
                  <var>.b.c.</var>
                et
                  <lb/>
                quare ducta ſit
                  <var>.i.c.</var>
                et coniuncta
                  <var>.x.m.</var>
                cum
                  <var>.x.
                    <lb/>
                  p.</var>
                directè, & quare ducta ſit
                  <var>.o.m.</var>
                et
                  <var>.f.k</var>
                . </s>
                <s xml:id="echoid-s1546" xml:space="preserve">Lau-
                  <lb/>
                do igitur vt ſemper præſupponatur
                  <var>.p.x.</var>
                perpen
                  <lb/>
                dicularis baſi ipſius plani & præſupponatur, (vt
                  <lb/>
                rem totam vnò verbo complectar) ſuperficies
                  <var>.
                    <lb/>
                  p.t.</var>
                perpendicularis plano, & orizonti. </s>
                <s xml:id="echoid-s1547" xml:space="preserve">Quod
                  <lb/>
                reliquum eſt, neceſſariv
                  <unsure/>
                m non eſt, niſi ad ſpe-
                  <lb/>
                culandum. </s>
                <s xml:id="echoid-s1548" xml:space="preserve">Neceſſariæ ergo non ſunt aliæli-
                  <lb/>
                neæ, quàm.p.x:
                  <var>p.o.x.i</var>
                :
                  <var>b.c</var>
                : et
                  <var>.x.m.</var>
                è dire-
                  <lb/>
                cto coniuncta cum
                  <var>.p.x.</var>
                (quæ
                  <var>.x.m.</var>
                coniuncta
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0137-02a" xlink:href="fig-0137-02"/>
                </s>
              </p>
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