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
121 109
122 110
123 111
124 112
125 113
126 114
127 115
128 116
129 117
130 118
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
< >
page |< < (139) of 445 > >|
    <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-div333" type="section" level="3" n="14">
              <pb o="139" rhead="DE PERSPECT." n="151" file="0151" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0151"/>
              <p>
                <s xml:id="echoid-s1675" xml:space="preserve">Ad habendam deinde quantitatem diſtantiæ, aut interualli ſimul cum ſitu, in fa-
                  <lb/>
                cie
                  <var>.q.d.k.</var>
                quem latus
                  <var>.p.l.</var>
                perpendiculariter reſpicit. </s>
                <s xml:id="echoid-s1676" xml:space="preserve">Imaginemur à puncto
                  <var>.u.</var>
                ſuper
                  <lb/>
                  <var>q.a.</var>
                cad ere lineam perpendicularem
                  <var>.u.o.</var>
                quæ illico reperitur cum triangulum
                  <var>.a.
                    <lb/>
                  u.q.</var>
                ex lateribus datis & cognitis conſtet,
                  <reg norm="quodquidem" type="context">quodquidẽ</reg>
                triangulum, medietas eſt qua-
                  <lb/>
                drilateri, ſeu. rumbi
                  <var>.q.a.b.u.</var>
                cui vnaquæque dictarum quatuor facierum perpendi-
                  <lb/>
                cularis exiſtit ex .4. ct .18. lib. 11. & ob id linea
                  <var>.u.o.</var>
                extenſa in ſuperficie dicti quadri-
                  <lb/>
                lateri, & perpendicularis lineæ
                  <var>.q.a.</var>
                perpendicularis erit faciei
                  <var>.q.d.k.</var>
                & ex .29.
                  <lb/>
                primi, angulus
                  <var>.b.u.o.</var>
                rectus erit, ut
                  <reg norm="etiam" type="context">etiã</reg>
                angulus
                  <var>.o.u.l.</var>
                ex .2. definitione lib. 11. vnde
                  <lb/>
                ex .4. eiuſdem lib
                  <var>.o.u.</var>
                perpendicularis erit faciei
                  <var>.b.p.l</var>
                . </s>
                <s xml:id="echoid-s1677" xml:space="preserve">Ha bebimus ergo ſitum in fa-
                  <lb/>
                cie
                  <var>.q.d.k.</var>
                qui reſpicietur ad angulos rectos à linea
                  <var>.p.l.</var>
                quiquidem erit in perpendi-
                  <lb/>
                culari à puncto
                  <var>.o.</var>
                ad
                  <var>.q.a.</var>
                ducta.</s>
              </p>
              <p>
                <s xml:id="echoid-s1678" xml:space="preserve">Quòd autem
                  <var>.a.o.</var>
                ſit latus exagoni æquilateris circumſcrip tibilis ab eodem circu
                  <lb/>
                lo, qui vnam ex faciebus triangularibus æquilateribus propoſiti corporis circunſcri-
                  <lb/>
                bere pot eſt, ita oſtenditur. ſit
                  <reg norm="comprehenſum" type="context">cõprehenſum</reg>
                imaginatione, triangulum
                  <var>.a.q.u.</var>
                ſepara
                  <lb/>
                tim, cuius latus
                  <var>.a.u.</var>
                æquale eſt vni ex lateribus
                  <reg norm="triangulorum" type="context">triangulorũ</reg>
                eiuſdem corporis ex .33.
                  <lb/>
                primi, quo dlibet verò aliorum duorum æquale perpendicularibus dictorum trian-
                  <lb/>
                gulorum, in quo triangulo
                  <var>.a.u.q.</var>
                ducta ſit perpendicularis
                  <var>.u.o.</var>
                ab vna
                  <reg norm="extremitatum" type="context">extremitatũ</reg>
                  <lb/>
                lateris maioris, ad vnum ex minoribus lateribus, quę perpendicularis intra triangu-
                  <lb/>
                lum cadet, quia dictum triangulum oxigonium eſt. </s>
                <s xml:id="echoid-s1679" xml:space="preserve">quod autem attinet ad duos angu
                  <lb/>
                los
                  <var>.a.</var>
                et
                  <var>.u.</var>
                cum æquales ſint ex quinta lib. primi; </s>
                <s xml:id="echoid-s1680" xml:space="preserve">17. nos certiores facit; </s>
                <s xml:id="echoid-s1681" xml:space="preserve">quod verò an­
                  <lb/>
                gulus
                  <var>.q.</var>
                ſit
                  <reg norm="etiam" type="context">etiã</reg>
                acutus: </s>
                <s xml:id="echoid-s1682" xml:space="preserve">30. lib. tertii nos cer-
                  <lb/>
                tos reddit,
                  <reg norm="quia" type="simple">ꝗa</reg>
                  <var>.a.u.</var>
                minor eſt diametro
                  <reg norm="ſphae­ ræ" type="simple">ſphę­
                    <lb/>
                    <figure xlink:label="fig-0151-01" xlink:href="fig-0151-01a" number="206">
                      <image file="0151-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0151-01"/>
                    </figure>
                  ræ</reg>
                datum corpus circumſcribentis, cum
                  <var>.q.</var>
                  <lb/>
                dictæ ſphęrę ſuperficiem tangat.</s>
              </p>
              <p>
                <s xml:id="echoid-s1683" xml:space="preserve">Ad probandum
                  <var>.a.o.</var>
                ęqualem eſſe lateri
                  <lb/>
                exagoni dicti, ſatis erit probare
                  <var>.a.q.</var>
                ſeſqui
                  <lb/>
                alteram eſſe ad
                  <var>.a.o.</var>
                quia ſi in ſubſcripto
                  <lb/>
                hîc circulo ducemus duas ſemidiametros
                  <var>.
                    <lb/>
                  n.p.</var>
                et
                  <var>.n.l.</var>
                ad. angulos
                  <reg norm="trianguli" type="context">triãguli</reg>
                ęquilateri
                  <var>.p.</var>
                  <lb/>
                et
                  <var>.l.</var>
                & cum quodlibet laterum ipſius exago
                  <lb/>
                ni, ęquale ſit ſemidiametro circuli ex .15.
                  <lb/>
                lib. 4. habebimus ex .8. primi, angulum
                  <var>.n.
                    <lb/>
                  p.l.</var>
                æqualem angulo
                  <var>.q.p.l</var>
                . </s>
                <s xml:id="echoid-s1684" xml:space="preserve">Vnde ex .4. eiuſ
                  <lb/>
                dem
                  <var>.o.n.</var>
                ęqualiserit ipſi
                  <var>.o.q.</var>
                ideſt
                  <var>.q.a.</var>
                ſeſ
                  <lb/>
                quialtera erit ad
                  <var>.a.o</var>
                .</s>
              </p>
              <p>
                <s xml:id="echoid-s1685" xml:space="preserve">Ad probandum nunc in triangulo
                  <var>.a.q.
                    <lb/>
                  u</var>
                :
                  <var>a.q.</var>
                ſeſquialteram eſſe ad
                  <var>.a.o.</var>
                eſt
                  <reg norm="quoque" type="simple">quoq;</reg>
                  <lb/>
                ſciendum primò omne latus trianguli ęquilateri in potentia ſeſquitertium eſſe ad
                  <lb/>
                perpendicularem eiuſdem trianguli, quod vndecima lib. 14. Eucli. breuiter demon
                  <lb/>
                ſtratum eſt.</s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>