Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Page concordance

< >
Scan Original
101 64
102 65
103 66
104 67
105 68
106 69
107 70
108 71
109 72
110 73
111 74
112 75
113 76
114 77
115 78
116 79
117 80
118 81
119 82
120 83
121 84
122 85
123 86
124 87
125 88
126 89
127 90
128 91
129 92
130 93
< >
page |< < (100) of 525 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div262" type="section" level="1" n="90">
          <p>
            <s xml:id="echoid-s4837" xml:space="preserve">
              <pb o="100" file="136" n="137" rhead="Comment. in I. Cap. Sphæræ"/>
            des (nempe corpus A B C D, ex illis compoſitum) æquales ſolido rectangu-
              <lb/>
            lo L R. </s>
            <s xml:id="echoid-s4838" xml:space="preserve">Quamobrem area cuiuſlibet corporis planis ſuperficiebus contenti,
              <lb/>
            &</s>
            <s xml:id="echoid-s4839" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4840" xml:space="preserve">quod demonſtrandum erat.</s>
            <s xml:id="echoid-s4841" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div265" type="section" level="1" n="91">
          <head xml:id="echoid-head95" style="it" xml:space="preserve">THEOR. 14. PROPOS. 16.</head>
          <p style="it">
            <s xml:id="echoid-s4842" xml:space="preserve">
              <emph style="sc">Area</emph>
            cuiuslibet ſphærę æqualis eſt ſolido rectangulo comprehenſo
              <lb/>
              <note position="left" xlink:label="note-136-01" xlink:href="note-136-01a" xml:space="preserve">Sphę ra q̃li
                <lb/>
              bet cui pa-
                <lb/>
              rallel epipe
                <lb/>
              do ſit ęqua
                <lb/>
              lis.</note>
            ſub ſemidiametro ſphæræ, & </s>
            <s xml:id="echoid-s4843" xml:space="preserve">tertia parte ambitus ſphæræ.</s>
            <s xml:id="echoid-s4844" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4845" xml:space="preserve">
              <emph style="sc">Esto</emph>
            ſphæra A B C, cuius centrum D, ſemidiameter A D: </s>
            <s xml:id="echoid-s4846" xml:space="preserve">Solidum au-
              <lb/>
            tem rectangulum E, contentum ſub ſemidiametro A D, & </s>
            <s xml:id="echoid-s4847" xml:space="preserve">tertia parte ambi-
              <lb/>
            tus ſpæræ A B C. </s>
            <s xml:id="echoid-s4848" xml:space="preserve">Dico corpus E, ſphæræ A B C, eſſe æquale. </s>
            <s xml:id="echoid-s4849" xml:space="preserve">Nam ſi non eſt
              <lb/>
            æquale; </s>
            <s xml:id="echoid-s4850" xml:space="preserve">ſit, ſi fieri poteſt, primum maius, ſitq́ue exceſfus corporis E, ſupra
              <lb/>
            ſphęram A B C, quantitas F. </s>
            <s xml:id="echoid-s4851" xml:space="preserve">Intelligatur circa ccntrum D, deſcripta ſphæ-
              <lb/>
            ra GHK, maior quàm ſphæra A B C, ita tamen, ut exceſſus ſphęrę G H K,
              <lb/>
            ſupra ſphęram A B C, non ſit maior quantitate F, ſed uel æqualis, uel mi-
              <lb/>
            nor, hoc eſt, vt ſphæra G H K, ſit uel ęqualis ſolido E, quando nimirum
              <lb/>
              <figure xlink:label="fig-136-01" xlink:href="fig-136-01a" number="38">
                <image file="136-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/136-01"/>
              </figure>
            ipſa excedit ſphæram A B C, præciſe
              <lb/>
            quantitate F; </s>
            <s xml:id="echoid-s4852" xml:space="preserve">uel minor, ſi nimirum
              <lb/>
            ipſa excedit ſphęram A B C, mino-
              <lb/>
            ri quantitate, quàm F. </s>
            <s xml:id="echoid-s4853" xml:space="preserve">Neceſlario
              <lb/>
            enim aliqua ſphæra erit, quæ uel
              <lb/>
            æqualis ſit magnitudini E, atque
              <lb/>
            adeo maior, quàm ſphæra A B C;
              <lb/>
            </s>
            <s xml:id="echoid-s4854" xml:space="preserve">uel maior quidem quã ſphęra A B C,
              <lb/>
            minor vero quàm magnitudo E, quæ
              <lb/>
            maior ponitur, quàm ſphæra A B C. </s>
            <s xml:id="echoid-s4855" xml:space="preserve">
              <lb/>
            Inſcribatur deinde intra ſphæram
              <lb/>
            G H K, corpus, quod non tangat
              <lb/>
            ſphæram A B C, ita ut unaquæque
              <lb/>
              <note position="left" xlink:label="note-136-02" xlink:href="note-136-02a" xml:space="preserve">37. duod.</note>
            perpendicularium ex centro D, ad
              <lb/>
            baſes iſtius corporis eductarum ma-
              <lb/>
            ior fit ſemidiametro A D. </s>
            <s xml:id="echoid-s4856" xml:space="preserve">Si igitur
              <lb/>
            à centro D, ad omnes angulos di-
              <lb/>
            cti corporis ducantur lineæ rectæ,
              <lb/>
            ut totum corpus in pyramides di-
              <lb/>
            uidatur, quarum baſes ſunt eædem,
              <lb/>
            quæ corporis G H K, uertex au-
              <lb/>
            tem communis centrum D; </s>
            <s xml:id="echoid-s4857" xml:space="preserve">erit quæ
              <lb/>
            libet pyramis (per 14. </s>
            <s xml:id="echoid-s4858" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4859" xml:space="preserve">hu-
              <lb/>
            ius) æqualis ſolido rectangulo contento ſub eius perpendiculari, & </s>
            <s xml:id="echoid-s4860" xml:space="preserve">tertia
              <lb/>
            parte baſis; </s>
            <s xml:id="echoid-s4861" xml:space="preserve">A tque idcirco ſolidum rectangulum contentum ſub ſemidiame-
              <lb/>
            tro A D & </s>
            <s xml:id="echoid-s4862" xml:space="preserve">tertia parte baſis cuiuſlibet pyramidis, minus ipſa pyramide
              <lb/>
            erit. </s>
            <s xml:id="echoid-s4863" xml:space="preserve">Et quoniam omnia ſolida rectangula contenta ſub ſingulis perpendi-
              <lb/>
            cularibus ex centro D, ad baſes corporis dicti protractis, & </s>
            <s xml:id="echoid-s4864" xml:space="preserve">ſingulis ter-
              <lb/>
            tijs partibus baſium, ſimul ęqualia ſunt toti corpori, efficiunt autem om-
              <lb/>
            @es tertiæ partes baſium ſimul tertiam partem ambitus corporis, erit </s>
          </p>
        </div>
      </text>
    </echo>
Impressum