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
131 119
132 120
133 121
134 122
135 123
136 124
137 125
138 126
139 127
140 128
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
< >
page |< < (120) of 445 > >|
IO. BAPT. BENED.
    <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-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/>
                  <anchor type="figure" xlink:label="fig-0132-01a" xlink:href="fig-0132-01"/>
                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>
            </div>
          </div>
        </div>
      </text>
    </echo>