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]

Page concordance

< >
Scan Original
141 129
142 130
143 131
144 132
145 133
146 134
147 135
148 136
149 137
150 138
151 139
152 140
153 141
154 142
155 143
156 144
157 145
158 146
159 147
160 148
161 149
162 150
163 151
164 152
165 153
166 154
167 155
168 156
169 157
170 158
< >
page |< < (129) of 445 > >|
DE PERSPECT.
    <echo version="1.0">
      <text type="book" xml:lang="la">
        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div308" type="chapter" level="2" n="2">
            <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>
            </div>
          </div>
        </div>
      </text>
    </echo>