Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Page concordance

< >
Scan Original
121 84
122 85
123 86
124 87
125 88
126 89
127 90
128 91
129 92
130 93
131 94
132 95
133 96
134 97
135 98
136 99
137 100
138 101
139 102
140 103
141 104
142 105
143 106
144 107
145 108
146 109
147 110
148 111
149 112
150 113
< >
page |< < (93) of 525 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div244" type="section" level="1" n="84">
          <p>
            <s xml:id="echoid-s4529" xml:space="preserve">
              <pb o="93" file="129" n="130" rhead="Ioan. de Sacro Boſco."/>
            vna linea, deſcripto. </s>
            <s xml:id="echoid-s4530" xml:space="preserve">& </s>
            <s xml:id="echoid-s4531" xml:space="preserve">quadrato ex K M, M H, tanquam ex una linea deſcri-
              <lb/>
            pto, hoc eſt, quadrato K H, vtriuſque ſimul. </s>
            <s xml:id="echoid-s4532" xml:space="preserve">Ablato ergo communi quadrato
              <lb/>
            K H, erit quadratum ex F K, G H, tanquam ex una linea, deſcriptum maius
              <lb/>
            quadrato ex B K, D H, tanquam ex una linea, deſcripto; </s>
            <s xml:id="echoid-s4533" xml:space="preserve">ideòque maiores e-
              <lb/>
            runt rectæ linea F K, G H, ſimul rectis B K, D H, ſimnl: </s>
            <s xml:id="echoid-s4534" xml:space="preserve">Ac propterea, demptis
              <lb/>
            communibus B K, G H, erit F B, reliqua maior quàm reliqua D G. </s>
            <s xml:id="echoid-s4535" xml:space="preserve">Eſt autem
              <lb/>
            & </s>
            <s xml:id="echoid-s4536" xml:space="preserve">K C, maior quàm H C, eò quòd tota A C, cuius dimidium eſt K C, maior
              <lb/>
            ponitur, quam tota C E,
              <lb/>
              <figure xlink:label="fig-129-01" xlink:href="fig-129-01a" number="31">
                <image file="129-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/129-01"/>
              </figure>
            cuius dimidium eſt H C.
              <lb/>
            </s>
            <s xml:id="echoid-s4537" xml:space="preserve">Qua propter rectangulũ
              <lb/>
            ſub F B, K C, contentum,
              <lb/>
            maius erit rectangulo
              <lb/>
            ſub D G, H C, contẽto. </s>
            <s xml:id="echoid-s4538" xml:space="preserve">
              <lb/>
            Et quoniam triangulum
              <lb/>
            F B C, dimidium eſt re,
              <lb/>
            ctanguli ſub F B, K C, con
              <lb/>
            tenti; </s>
            <s xml:id="echoid-s4539" xml:space="preserve">(Nam ſi ſuper F B,
              <lb/>
            conſtituatur rectangu--
              <lb/>
            lum altitudinem habens
              <lb/>
            K C, ita ut triangulum,
              <lb/>
            & </s>
            <s xml:id="echoid-s4540" xml:space="preserve">rectangulum inter eaſ-
              <lb/>
            dem ſint parallelas; </s>
            <s xml:id="echoid-s4541" xml:space="preserve">erit
              <lb/>
              <note position="right" xlink:label="note-129-01" xlink:href="note-129-01a" xml:space="preserve">41. primi.</note>
            triangulum parallelo--
              <lb/>
            grammi dimidium. </s>
            <s xml:id="echoid-s4542" xml:space="preserve">quod
              <lb/>
            quidem parallelogram-
              <lb/>
            mum idem eſt, quod re-
              <lb/>
            ctangulum ſub F B, K C,
              <lb/>
            contentum, ut conſtat.
              <lb/>
            </s>
            <s xml:id="echoid-s4543" xml:space="preserve">Triangulum uero D G C, dimidium eſt rectanguli contenti ſub, D G, H C; </s>
            <s xml:id="echoid-s4544" xml:space="preserve">(ſi
              <lb/>
            enim ſuper D G, conſtituatur rectangulum altitudinem habens H C, ita vt
              <lb/>
            triangulum, & </s>
            <s xml:id="echoid-s4545" xml:space="preserve">rectangulum inter eaſdem ſint parallelas; </s>
            <s xml:id="echoid-s4546" xml:space="preserve">erit triangulum pa-
              <lb/>
            rallelogrammi dimidium. </s>
            <s xml:id="echoid-s4547" xml:space="preserve">quod quidem parallelogrammum idem eſt, quod
              <lb/>
              <note position="right" xlink:label="note-129-02" xlink:href="note-129-02a" xml:space="preserve">41. primi.</note>
            rectangulum ſub D H, H C, contentum, ut conſtat. </s>
            <s xml:id="echoid-s4548" xml:space="preserve">(erit quoque triangulum
              <lb/>
            FBC, maius triangulo D G C, ac propterea duplum trianguli F B C, nimirũ
              <lb/>
            rectilineum A F C B A, maius erit duplo trianguli D G C, ut pote rectilineo
              <lb/>
            erunt triangula A F C, C G E, utraque ſimul maiora triangulis A B C, C D E,
              <lb/>
            utriuſque ſimul. </s>
            <s xml:id="echoid-s4549" xml:space="preserve">Duo ergo triangula Iſoſcelia ſimilia ſuper inæqualibus baſi-
              <lb/>
            bus conſtituta, &</s>
            <s xml:id="echoid-s4550" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4551" xml:space="preserve">quod oſtendendum erat.</s>
            <s xml:id="echoid-s4552" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div247" type="section" level="1" n="85">
          <head xml:id="echoid-head89" style="it" xml:space="preserve">THEOR. 10. PROPOS. 52</head>
          <note position="right" xml:space="preserve">Inter Iſope-
            <lb/>
          rimetras fi-
            <lb/>
          guras ęqua-
            <lb/>
          lia numero
            <lb/>
          habentes la
            <lb/>
          tera maxi-
            <lb/>
          ma & æqui
            <lb/>
          latera eſt,
            <lb/>
          & æquian-
            <lb/>
          gula.</note>
          <p style="it">
            <s xml:id="echoid-s4553" xml:space="preserve">ISOPERIMETR ARVM figur arum latera numero ęqualia ha-
              <lb/>
            bentium maxima & </s>
            <s xml:id="echoid-s4554" xml:space="preserve">æqualiter eſt, & </s>
            <s xml:id="echoid-s4555" xml:space="preserve">æquiangula.</s>
            <s xml:id="echoid-s4556" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4557" xml:space="preserve">
              <emph style="sc">Esto</emph>
            figura quotcunq; </s>
            <s xml:id="echoid-s4558" xml:space="preserve">laterum ABCDEF, maxima inter omnes totidem
              <lb/>
            laterum ſibi iſoperimetras; </s>
            <s xml:id="echoid-s4559" xml:space="preserve">ita ut maior dari non poſſit. </s>
            <s xml:id="echoid-s4560" xml:space="preserve">Dico eam eſſe æquila-
              <lb/>
            terã, & </s>
            <s xml:id="echoid-s4561" xml:space="preserve">æquiãgulã. </s>
            <s xml:id="echoid-s4562" xml:space="preserve">Sit enim, ſi fieri poteſt, primũ nõ æquilatera, ſed ſint </s>
          </p>
        </div>
      </text>
    </echo>
Impressum