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-div322" type="section" level="3" n="8">
              <p>
                <s xml:id="echoid-s1573" xml:space="preserve">
                  <pb o="129" rhead="DE PERSPECT." n="141" file="0141" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0141"/>
                vera altitudo ipſius
                  <var>.M.T.</var>
                et
                  <var>I.s.</var>
                duxi ſupponendo eſſe
                  <var>.I.</var>
                  <reg norm="punctum" type="context">punctũ</reg>
                pſpectiuæ
                  <reg norm="ſecundum" type="context">ſecundũ</reg>
                  <lb/>
                antiquos, ideſt angulum ſupremum trianguli antiquorum à punctoq́ue
                  <var>.k.</var>
                meo duxi
                  <lb/>
                  <var>k.f.</var>
                parallelam ipſi
                  <var>.c.m.p.</var>
                vſque ad
                  <var>.i.x.</var>
                in puncto
                  <var>.f.</var>
                & à puncto à communi ipſis
                  <var>.k.f.</var>
                  <lb/>
                et
                  <var>.i.x.</var>
                vſque ad
                  <var>.I.s.</var>
                duxi quoque
                  <var>.A.B.</var>
                parallelam ipſi
                  <var>.i.x.</var>
                atque hæc omnia ex more
                  <lb/>
                antiquo præſtiti.</s>
              </p>
              <div xml:id="echoid-div322" type="float" level="4" n="1">
                <figure xlink:label="fig-0140-02" xlink:href="fig-0140-02a">
                  <image file="0140-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0140-02"/>
                </figure>
              </div>
              <p>
                <s xml:id="echoid-s1574" xml:space="preserve">Nunc verò eum conſiderans modum, quem ego de figuris
                  <var>.G.H.</var>
                antecedentibus
                  <lb/>
                præſcripſi, videndum eſt, an punctum
                  <var>.B.</var>
                tribus lineis
                  <var>.A.B.I.s.</var>
                et
                  <var>.R.V.</var>
                quarum hęc vl
                  <lb/>
                tima à me iam ducta fuit, commune exiſtat, ideſt vtrum
                  <var>.A.B.</var>
                æqualis exiſtat ipſi
                  <var>.K.
                    <lb/>
                  R.</var>
                quam ſecundum modum à me adinuentum, reuera ſcimus eſſe deſideratam altitu
                  <lb/>
                dinem in perſpectiua. </s>
                <s xml:id="echoid-s1575" xml:space="preserve">Quod tunc à nobis probatum erit, quando rationibus clarè
                  <lb/>
                patebit ipſam
                  <var>.A.B.</var>
                æqualem eſſe ipſi
                  <var>.f.V</var>
                . </s>
                <s xml:id="echoid-s1576" xml:space="preserve">Quamobrem ducamus
                  <var>.I.f.</var>
                vſque ad
                  <var>.ω.</var>
                  <lb/>
                lineæ
                  <var>.c.p.</var>
                vnde ratione ſimilitudinis triangulorum manifeſtè intelligemus, eandem
                  <lb/>
                proportionem eſſe ipſius
                  <var>.m.T.</var>
                ad
                  <var>.f.V.</var>
                quæ eſt
                  <var>.m.o.</var>
                ad
                  <var>.f.o.</var>
                & eius, quæ eſt
                  <var>.m.o.</var>
                ad
                  <var>.f.
                    <lb/>
                  o.</var>
                quæ eſt
                  <var>.ω.I.</var>
                ad
                  <var>.f.I.</var>
                & eius, quæ eſt
                  <var>.ω.I.</var>
                ad
                  <var>.f.I.</var>
                quæ eſt
                  <var>.x.I.</var>
                ad
                  <var>.A.I.</var>
                & eius, quæ eſt
                  <var>.x.
                    <lb/>
                  I.</var>
                ad
                  <var>.A.I.</var>
                quæ eſt
                  <var>.x.s.</var>
                ad
                  <var>.A.B.</var>
                ideſt vt eius, quæ eſt
                  <var>.m.T.</var>
                ad
                  <var>.A.B.</var>
                ſed idem
                  <reg norm="quoque" type="simple">quoq;</reg>
                erat
                  <lb/>
                de
                  <var>.m.T.</var>
                ad
                  <var>.f.V</var>
                . </s>
                <s xml:id="echoid-s1577" xml:space="preserve">Vnde ſequitur
                  <var>.A.B.</var>
                æqualem eſſe
                  <var>.f.V.</var>
                ex .9. quinti Eucli.
                  <reg norm="atque" type="simple">atq;</reg>
                etiam
                  <lb/>
                ipſi
                  <var>.k.R.</var>
                quod à nobis propoſitum eſt inquirendum.</s>
              </p>
            </div>
            <div xml:id="echoid-div324" type="section" level="3" n="9">
              <head xml:id="echoid-head185" xml:space="preserve">CAP. IX.</head>
              <figure position="here">
                <image file="0141-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0141-01"/>
              </figure>
              <p>
                <s xml:id="echoid-s1578" xml:space="preserve">
                  <emph style="sc">INstitvens</emph>
                etiam ſermonem de figuris ſu-
                  <lb/>
                perficialibus orizontalibus, ſeu de plantis,
                  <lb/>
                pulcherrimum quendam modum, quem ego ad
                  <lb/>
                locandum quodlibet punctum in perſpectiua,
                  <lb/>
                (degradatum cum fuerit
                  <reg norm="parallelogrammum" type="context">parallelogrãmum</reg>
                quod
                  <lb/>
                dam rectangulum, in noſtro plano perpendicula
                  <lb/>
                ri orizonti, quemadmodum in ſuperioribus figu-
                  <lb/>
                ris
                  <var>.A.</var>
                demonſtrauimus) conſideraui, ſilentio
                  <lb/>
                haud prætereundum eſſe.</s>
              </p>
              <p>
                <s xml:id="echoid-s1579" xml:space="preserve">Sit igitur in ſubſcripta hîc figura
                  <var>.K.</var>
                in paralle
                  <lb/>
                  <reg norm="logrammo" type="context">logrãmo</reg>
                perfecto
                  <reg norm="punctum" type="context">pũctum</reg>
                  <var>.b.</var>
                quod locari debeat
                  <lb/>
                in degradato
                  <var>.e.q.d.r</var>
                . </s>
                <s xml:id="echoid-s1580" xml:space="preserve">Nunc à duobus quorumli-
                  <lb/>
                bet quatuor angulorum
                  <var>.q.u.a.d.</var>
                ducuntur duæ li-
                  <lb/>
                neæ occultæ
                  <var>.q.g.</var>
                et
                  <var>.u.f.</var>
                per punctum
                  <var>.b.</var>
                vſque ad
                  <lb/>
                latera
                  <var>.q.d.</var>
                et
                  <var>.u.a.</var>
                ita tamen vt eorum extremita-
                  <lb/>
                tes
                  <var>.g.</var>
                et
                  <var>.f.</var>
                intus cadant inter
                  <var>.q.d.</var>
                et
                  <var>.u.a.</var>
                ipſorum
                  <lb/>
                laterum, ideſt vt non ſecent duo latera
                  <var>.q.u.</var>
                aut
                  <var>.d.
                    <lb/>
                  a</var>
                . </s>
                <s xml:id="echoid-s1581" xml:space="preserve">Deinde punctum
                  <var>.f.</var>
                inter
                  <var>.q.</var>
                et
                  <var>.d.</var>
                  <reg norm="coniungatur" type="context">cõiungatur</reg>
                oc-
                  <lb/>
                cultè cum angulo degradato
                  <var>.e.</var>
                qui
                  <reg norm="correſpondet" type="context">correſpõdet</reg>
                  <var>.
                    <lb/>
                  u.</var>
                perfecti, mediante linea
                  <var>.e.f.</var>
                quæ erit
                  <var>.u.f.</var>
                degra
                  <lb/>
                dita in noſtro plano. </s>
                <s xml:id="echoid-s1582" xml:space="preserve">Deinde ſumatur punctum
                  <var>.
                    <lb/>
                  n.</var>
                in linea
                  <var>.q.d.</var>
                tam diſtans à
                  <var>.q.</var>
                quàm.g. diſtat ab
                  <var>.
                    <lb/>
                  u.</var>
                ducaturq́ue linea
                  <var>.i.n.</var>
                quæ lineam
                  <var>.e.r.</var>
                in puncto
                  <lb/>
                c. diuidet, quod exijs, quæ ſuperius iam diximus
                  <lb/>
                ad ipſum
                  <var>.g.</var>
                referetur. </s>
                <s xml:id="echoid-s1583" xml:space="preserve">Ducendo poſtea lineam oc
                  <lb/>
                cultam
                  <var>.q.c.</var>
                patebit eam correſpondere lineæ
                  <var>.q.g.</var>
                quæ ſecans lineam
                  <var>.e.f.</var>
                in puncto
                  <var>.
                    <lb/>
                  t.</var>
                hoc, communi ſcientiæ ratione, reſpondebit ipſi
                  <var>.b.</var>
                vt omnes cognoſcent.</s>
              </p>
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