Clavius, Christoph, Geometria practica

Page concordance

< >
Scan Original
261 231
262 232
263 233
264 234
265 235
266 236
267 237
268 238
269 239
270 240
271 241
272 242
273 243
274 244
275 245
276 246
277 247
278 248
279 249
280 250
281 251
282 252
283 253
284 254
285 255
286 256
287 257
288 258
289 259
290 260
< >
page |< < (207) of 450 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div565" type="section" level="1" n="205">
          <p>
            <s xml:id="echoid-s9272" xml:space="preserve">
              <pb o="207" file="237" n="237" rhead="LIBER QVINTVS."/>
            quinque triangula ABF, BCF, CDF, DEF, AEF, tot nimirum, quot in baſe ſunt
              <lb/>
            latera, dicitur pyramis.</s>
            <s xml:id="echoid-s9273" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9274" xml:space="preserve">
              <emph style="sc">Convs</emph>
            autem eſt figura ſolida rotunda ad vnum punctum conſtituta, ſu-
              <lb/>
              <note position="right" xlink:label="note-237-01" xlink:href="note-237-01a" xml:space="preserve">Area pyra-
                <lb/>
              midis, & co-
                <lb/>
              ni.</note>
            pra baſem circularem, inſtar pyramidis rotundæ,
              <lb/>
              <figure xlink:label="fig-237-01" xlink:href="fig-237-01a" number="153">
                <image file="237-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/237-01"/>
              </figure>
            qualis eſt figura ABCDE.</s>
            <s xml:id="echoid-s9275" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9276" xml:space="preserve">
              <emph style="sc">Tam</emph>
            autem pyramidis, quam Coni area pro-
              <lb/>
            ducitur ex multiplicatione baſis in tertiã partem
              <lb/>
            altitudinis. </s>
            <s xml:id="echoid-s9277" xml:space="preserve">Cũ enim, vt in præcedenti cap. </s>
            <s xml:id="echoid-s9278" xml:space="preserve">oſten-
              <lb/>
            dimus, ex baſe in totam altitudinem gignatur
              <lb/>
            priſma vel Cylindrus eandem habens cum pyra-
              <lb/>
            mide, & </s>
            <s xml:id="echoid-s9279" xml:space="preserve">cono altitudinem; </s>
            <s xml:id="echoid-s9280" xml:space="preserve"> producetur ex eadem baſe in tertiam partem
              <note symbol="a" position="right" xlink:label="note-237-02" xlink:href="note-237-02a" xml:space="preserve">ſchol. 14.
                <lb/>
              duodec.</note>
            titudinis tertia pars illius priſmatis, vel Cylindri. </s>
            <s xml:id="echoid-s9281" xml:space="preserve">, Cum ergo pyramisſit
              <handwritten xlink:label="hd-237-2" xlink:href="hd-237-2a" number="71"/>
              <handwritten xlink:label="hd-237-2" xlink:href="hd-237-2a" number="72"/>
            pars illius priſmatis, & </s>
            <s xml:id="echoid-s9282" xml:space="preserve">Conus tertia pars Cylindri, liquet tam pyramidẽ,
              <note symbol="b" position="right" xlink:label="note-237-03" xlink:href="note-237-03a" xml:space="preserve">corol. 7.
                <lb/>
              duodec.</note>
            Conum produci ex baſe in tertiam partem altitudinis. </s>
            <s xml:id="echoid-s9283" xml:space="preserve">Ex quo fit, ſi baſis duca-
              <lb/>
            tur in totam altitudinem, tertiam partem numeri producti, eſſe quoque aream
              <lb/>
              <note symbol="c" position="right" xlink:label="note-237-04" xlink:href="note-237-04a" xml:space="preserve">10. duodec.
                <lb/>
              Areapyrami-
                <lb/>
              dis, & coni
                <lb/>
              aliter.</note>
            pyramidis, vel Coni. </s>
            <s xml:id="echoid-s9284" xml:space="preserve">Item eandem produci ex tota altitudine in tertiam par-
              <lb/>
            tem baſis: </s>
            <s xml:id="echoid-s9285" xml:space="preserve"> quod hac ratione tertia pars priſmatis, vel Conigignatur.</s>
            <s xml:id="echoid-s9286" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9287" xml:space="preserve">2. </s>
            <s xml:id="echoid-s9288" xml:space="preserve">
              <emph style="sc">Basis</emph>
            porro pyramidis, ſi triangularis eſt, cognoſcetur, vt lib. </s>
            <s xml:id="echoid-s9289" xml:space="preserve">4. </s>
            <s xml:id="echoid-s9290" xml:space="preserve">2. </s>
            <s xml:id="echoid-s9291" xml:space="preserve">tra-
              <lb/>
            ditum eſt: </s>
            <s xml:id="echoid-s9292" xml:space="preserve">ſi multilatera, reperietur, per ea, quæ eodem lib. </s>
            <s xml:id="echoid-s9293" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s9294" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9295" xml:space="preserve">4. </s>
            <s xml:id="echoid-s9296" xml:space="preserve">& </s>
            <s xml:id="echoid-s9297" xml:space="preserve">5. </s>
            <s xml:id="echoid-s9298" xml:space="preserve">ſcripſi-
              <lb/>
              <note symbol="d" position="right" xlink:label="note-237-05" xlink:href="note-237-05a" xml:space="preserve">1. ſchol. 7.
                <lb/>
              duodec. & 11.
                <lb/>
              duodec.</note>
            mus. </s>
            <s xml:id="echoid-s9299" xml:space="preserve">Baſis autem Coni inueſtigabitur ex cap. </s>
            <s xml:id="echoid-s9300" xml:space="preserve">7. </s>
            <s xml:id="echoid-s9301" xml:space="preserve">eiuſdem lib. </s>
            <s xml:id="echoid-s9302" xml:space="preserve">At verò altitudo
              <lb/>
            tam pyramidis, quam Coni, obtinebitur, ſi in vertice ſtatuatur planum baſi æ-
              <lb/>
            quidiſtans, ab eoque ad planum, in quo baſis, perpendicularis demittatur, ea-
              <lb/>
              <note position="right" xlink:label="note-237-06" xlink:href="note-237-06a" xml:space="preserve">Altitudo py-
                <lb/>
              ramidis, &
                <lb/>
              coni.</note>
              <handwritten xlink:label="hd-237-2" xlink:href="hd-237-2a" number="71"/>
              <handwritten xlink:label="hd-237-2" xlink:href="hd-237-2a" number="72"/>
            que exquiſitè menſuretur. </s>
            <s xml:id="echoid-s9303" xml:space="preserve">Quamuis enim eadem hæc altitudo inda
              <unsure/>
            gari poſsit
              <lb/>
            Geo metrice, ſi inclinatio vnius lateris ad baſem, & </s>
            <s xml:id="echoid-s9304" xml:space="preserve">magnitudo quoque eiuſdem
              <lb/>
            lateris cognoſcatur: </s>
            <s xml:id="echoid-s9305" xml:space="preserve">quia tamen hęc ipſa exploranda ſunt materialiter per ali-
              <lb/>
            quodinſtrumentum, præſtatipſam quoque altitudinem ſtatim per inſtrumen-
              <lb/>
            tum exquirere, pręſertim per inſtrumentum partium, quod lib. </s>
            <s xml:id="echoid-s9306" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9307" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s9308" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9309" xml:space="preserve">deſcri
              <lb/>
            pſimus: </s>
            <s xml:id="echoid-s9310" xml:space="preserve">cum inuentio illa Geometrica difficilior ſit, procedatq; </s>
            <s xml:id="echoid-s9311" xml:space="preserve">ex inclinatio-
              <lb/>
            ne, ac latere per inſtrumentum cognitis.</s>
            <s xml:id="echoid-s9312" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9313" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9314" xml:space="preserve">
              <emph style="sc">Atqve</emph>
            hæc, quę diximus, intelligivolumus tam de pyramidibus, C@-
              <lb/>
            niſque rectis, quam de obliquis, & </s>
            <s xml:id="echoid-s9315" xml:space="preserve">Scalenis.</s>
            <s xml:id="echoid-s9316" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div570" type="section" level="1" n="206">
          <head xml:id="echoid-head221" xml:space="preserve">DL AREA FRVSTI PYRA-
            <lb/>
          midis, & Coni.</head>
          <head xml:id="echoid-head222" xml:space="preserve">
            <emph style="sc">Capvt</emph>
          III.</head>
          <p>
            <s xml:id="echoid-s9317" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9318" xml:space="preserve">
              <emph style="sc">FRvstvm</emph>
            pyramidis, & </s>
            <s xml:id="echoid-s9319" xml:space="preserve">Coni appello id, quod alij pyramidem decur-
              <lb/>
            tatam, & </s>
            <s xml:id="echoid-s9320" xml:space="preserve">Conum decurtatum dicunt. </s>
            <s xml:id="echoid-s9321" xml:space="preserve">Sit ergo fruſtum pyramidis
              <lb/>
            ABCDEF, cuius baſes ABC, DEF, ſint parallelæ, & </s>
            <s xml:id="echoid-s9322" xml:space="preserve">ſimiles, & </s>
            <s xml:id="echoid-s9323" xml:space="preserve">cuius
              <lb/>
            area inueſtiganda ſit. </s>
            <s xml:id="echoid-s9324" xml:space="preserve">Quod duobus modis fieri poteſt. </s>
            <s xml:id="echoid-s9325" xml:space="preserve">Primũ cogitetur integra
              <lb/>
            pyramis ABCH, cuius altitudinẽ HG, perpendicularem ad baſem (licet pyramis
              <lb/>
            actu nõ ſit integrata) ita inueniem
              <emph style="sub">9</emph>
            . </s>
            <s xml:id="echoid-s9326" xml:space="preserve"> Quoniã eſt, vt ab AB, ad AH, ita DE, ad
              <note symbol="e" position="right" xlink:label="note-237-07" xlink:href="note-237-07a" xml:space="preserve">4. ſexti.</note>
            & </s>
            <s xml:id="echoid-s9327" xml:space="preserve">permutando, vt AB, ad DE, ita AH, ad DH; </s>
            <s xml:id="echoid-s9328" xml:space="preserve">erit quoq; </s>
            <s xml:id="echoid-s9329" xml:space="preserve">diuidẽdo (ſumpta </s>
          </p>
        </div>
      </text>
    </echo>
Impressum