Clavius, Christoph, Geometria practica

List of thumbnails

< >
151
151 (121) 		152
152 (122)
153
153 (123) 		154
154 (124)
155
155 (125) 		156
156 (126)
157
157 (127) 		158
158 (128)
159
159 (129) 		160
160 (130)
< >
page |< < (229) of 450 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div657" type="section" level="1" n="231">
          <p>
            <s xml:id="echoid-s10606" xml:space="preserve">
              <pb o="229" file="259" n="259" rhead="LIBER QVINTVS."/>
            cap Num. </s>
            <s xml:id="echoid-s10607" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10608" xml:space="preserve">minor ſit proportio cubi datæ diametri ad ſphæram, quàm 426. </s>
            <s xml:id="echoid-s10609" xml:space="preserve">ad
              <lb/>
            223. </s>
            <s xml:id="echoid-s10610" xml:space="preserve">Sit autem cubus diametri datæ ad procreatum numerum, vt 426. </s>
            <s xml:id="echoid-s10611" xml:space="preserve">ad 223.
              <lb/>
            </s>
            <s xml:id="echoid-s10612" xml:space="preserve">habebit quo que cubus datæ diametri ad ſphæram, proportionem minorem,
              <lb/>
              <note symbol="a" position="right" xlink:label="note-259-01" xlink:href="note-259-01a" xml:space="preserve">10. quinti.</note>
            quàm idem cubus ad numerum genitum. </s>
            <s xml:id="echoid-s10613" xml:space="preserve"> Quare minor erit numerus produ- ctus, quàm vera ſoliditas ſphęræ.</s>
            <s xml:id="echoid-s10614" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div659" type="section" level="1" n="232">
          <head xml:id="echoid-head249" xml:space="preserve">DE AREA SEGMENTO-
            <lb/>
          rum ſphæræ.</head>
          <head xml:id="echoid-head250" xml:space="preserve">
            <emph style="sc">Capvt</emph>
          VI.</head>
          <p style="it">
            <s xml:id="echoid-s10615" xml:space="preserve">I. </s>
            <s xml:id="echoid-s10616" xml:space="preserve">HEMISPHER II ſuperfici{es} conuexa, excluſa baſe, gignitur ex area ma-
              <lb/>
              <note position="right" xlink:label="note-259-02" xlink:href="note-259-02a" xml:space="preserve">Superfici{es} cõ-
                <lb/>
              uexa Hemi-
                <lb/>
              ſphærii.</note>
            ximi circuli per 2. </s>
            <s xml:id="echoid-s10617" xml:space="preserve">multiplicata. </s>
            <s xml:id="echoid-s10618" xml:space="preserve">Vel ex ſemidiametro in circumferentiã ma-
              <lb/>
            ximi circuli. </s>
            <s xml:id="echoid-s10619" xml:space="preserve">Vel denique ex tota diametro in ſemiſſem circumferentiæ ma-
              <lb/>
            ximi circuli. </s>
            <s xml:id="echoid-s10620" xml:space="preserve">Quæ omnia perſpicua ſunt ex 1. </s>
            <s xml:id="echoid-s10621" xml:space="preserve">regula Num. </s>
            <s xml:id="echoid-s10622" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10623" xml:space="preserve">capitis 5. </s>
            <s xml:id="echoid-s10624" xml:space="preserve">propterea
              <lb/>
            quod hi numeri producti ſunt ſemiſſes illorum, qui ſuperficiem conuexam to-
              <lb/>
            tius ſphęræ in earegula exhibuerunt.</s>
            <s xml:id="echoid-s10625" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10626" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10627" xml:space="preserve">SVPERFICIES conuexa cuiuſlibet portionis ſphæræ hemiſphærio minoris,
              <lb/>
              <note position="right" xlink:label="note-259-03" xlink:href="note-259-03a" xml:space="preserve">Superfici{es} cõ-
                <lb/>
              uexæ portio-
                <lb/>
              nis ſphæræ.</note>
            velmaioris, dempta baſe, æqualis eſt circulo, cui{us} ſemidiameter æqualis eſt rectæ lineæ,
              <lb/>
            quæ à vertice portionis ad circumferentiam baſis ducitur. </s>
            <s xml:id="echoid-s10628" xml:space="preserve">ex propoſ. </s>
            <s xml:id="echoid-s10629" xml:space="preserve">40. </s>
            <s xml:id="echoid-s10630" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s10631" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10632" xml:space="preserve">Archime-
              <lb/>
            dis de ſphæra, & </s>
            <s xml:id="echoid-s10633" xml:space="preserve">cylindro. </s>
            <s xml:id="echoid-s10634" xml:space="preserve">Sit enim maximus in ſphęra circulus ABCD, cuius dia-
              <lb/>
            meter AC, quàm in E, ad angulos rectos ſecet B D, recta, per quam intelligatur
              <lb/>
            duciplanum diametro ad angulos rectos, ſecans ſphæram in duas portiones,
              <lb/>
            quarum baſis communis circulus diametri B D, & </s>
            <s xml:id="echoid-s10635" xml:space="preserve">A, vertex minoris portionis,
              <lb/>
            maioris autem vertex C. </s>
            <s xml:id="echoid-s10636" xml:space="preserve">Iunctis autem rectis AB, CB; </s>
            <s xml:id="echoid-s10637" xml:space="preserve">erit circulus ſemidiametri
              <lb/>
            A B, ſuperficiei conuexæ minoris portionis, & </s>
            <s xml:id="echoid-s10638" xml:space="preserve">circulus ſemidiametri C B, con-
              <lb/>
            uexę ſuperficiei maioris portionis ęqualis, ex dicta propoſ. </s>
            <s xml:id="echoid-s10639" xml:space="preserve">Ar-
              <lb/>
              <figure xlink:label="fig-259-01" xlink:href="fig-259-01a" number="165">
                <image file="259-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/259-01"/>
              </figure>
            chimedis. </s>
            <s xml:id="echoid-s10640" xml:space="preserve">Quare ſi vtraque AB, CB, in partibus diametri A C,
              <lb/>
            fiat nota, præſertim ope inſtrumenti partium cap. </s>
            <s xml:id="echoid-s10641" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10642" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s10643" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10644" xml:space="preserve">con-
              <lb/>
            ſtructi, & </s>
            <s xml:id="echoid-s10645" xml:space="preserve">areę circulorum ad interualla ſemidiametrorum AB,
              <lb/>
            CB, deſciptorum inueſtigentur, per ea, quę lib. </s>
            <s xml:id="echoid-s10646" xml:space="preserve">4. </s>
            <s xml:id="echoid-s10647" xml:space="preserve">capit. </s>
            <s xml:id="echoid-s10648" xml:space="preserve">7. </s>
            <s xml:id="echoid-s10649" xml:space="preserve">ſcri-
              <lb/>
            pſimus; </s>
            <s xml:id="echoid-s10650" xml:space="preserve">notæ erunt ſuperficies conuexæ dictarum portionum
              <lb/>
            ſphęræ.</s>
            <s xml:id="echoid-s10651" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10652" xml:space="preserve">
              <emph style="sc">Eadem</emph>
            ſuperficies conuexa portionis ſphærę hemiſphęrio minoris, vel ma-
              <lb/>
            ioris, ita quoque cognoſcetur. </s>
            <s xml:id="echoid-s10653" xml:space="preserve">Ex demonſtratis ab Archimede propoſ. </s>
            <s xml:id="echoid-s10654" xml:space="preserve">3. </s>
            <s xml:id="echoid-s10655" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s10656" xml:space="preserve">2.
              <lb/>
            </s>
            <s xml:id="echoid-s10657" xml:space="preserve">de ſphęra, & </s>
            <s xml:id="echoid-s10658" xml:space="preserve">cylindro, eandem proportionem habet EC, ad EA, quam ſuperfi-
              <lb/>
            cies conuexa portionis ſphęræ baſem habentis circulum diametri BD, & </s>
            <s xml:id="echoid-s10659" xml:space="preserve">verticẽ
              <lb/>
            C, ad ſuperficiem conuexam portionis baſem habentis eundem circulum dia-
              <lb/>
            metri BD, & </s>
            <s xml:id="echoid-s10660" xml:space="preserve">verticem A. </s>
            <s xml:id="echoid-s10661" xml:space="preserve">Igitur componendo quoq; </s>
            <s xml:id="echoid-s10662" xml:space="preserve">erit, vt tota diameter A C,
              <lb/>
            ad AE, ita ſuperficies conuexa totius ſphęræ ad ſuperficiem cõuexam portionis
              <lb/>
            B A D. </s>
            <s xml:id="echoid-s10663" xml:space="preserve">Eademq; </s>
            <s xml:id="echoid-s10664" xml:space="preserve">ratione erit, vt tota diameter A C, ad E C, ita conuexa ſuperfici-
              <lb/>
            es totius ſphęræ ad ſuperficiem conuexam portionis BCD. </s>
            <s xml:id="echoid-s10665" xml:space="preserve">Quo circainueſti-
              <lb/>
            gata proportione diametri A C, ad ſegmenta AE, EC, per inſtrumentum partium
              <lb/>
            cap. </s>
            <s xml:id="echoid-s10666" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10667" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s10668" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10669" xml:space="preserve">conſtructum; </s>
            <s xml:id="echoid-s10670" xml:space="preserve">ſi fiat, vt diameter AC, ad AE, ita ſuperficies conuexa
              <lb/>
            totius ſphęræ, (quæ ex regula 1. </s>
            <s xml:id="echoid-s10671" xml:space="preserve">Nume. </s>
            <s xml:id="echoid-s10672" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10673" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s10674" xml:space="preserve">5. </s>
            <s xml:id="echoid-s10675" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s10676" xml:space="preserve">cognita fiet) ad </s>
          </p>
        </div>
      </text>
    </echo>
Impressum