Clavius, Christoph, Geometria practica

Table of contents

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[221.] II.
Page: 253 (223)
[222.] ALITER.
Page: 255 (225)
[223.] ALITER.
Page: 255 (225)
[224.] I.
Page: 256 (226)
[225.] II.
Page: 257 (227)
[226.] III.
Page: 257 (227)
[227.] IIII.
Page: 257 (227)
[228.] I.
Page: 258 (228)
[229.] II.
Page: 258 (228)
[230.] III.
Page: 258 (228)
[231.] IIII.
Page: 258 (228)
[232.] DE AREA SEGMENTO-rum ſphæræ. Capvt VI.
Page: 259 (229)
[233.] ALITER.
Page: 261 (231)
[234.] DE AREA SPHÆROIDIS, EIVSDEM-que portionum. Capvt VII.
Page: 262 (232)
[235.] DE AREA CONOIDIS parabolici. Capvt VIII.
Page: 262 (232)
[236.] DE AREA CONOIDIS Hyperbolici. Capvt IX.
Page: 263 (233)
[237.] DE AREA DOLIORVM. Capvt X.
Page: 263 (233)
[238.] DE AREA CORPORVM. omnino irregularium. Capvt XI.
Page: 264 (234)
[239.] DE SVPERFICIE CONVEXA coni & cylindri recti. Capvt XII.
Page: 265 (235)
[240.] FINIS LIBRI QVINTI.
Page: 265 (235)
[241.] GEOMETRIÆ PRACTICÆ LIBER SEXTVS.
Page: 266 (236)
[242.] THOREMA 1. PROPOSITIO 1.
Page: 267 (237)
[243.] PROBLEMA 1. PROPOSITIO 2.
Page: 269 (239)
[244.] PROBL. 2. PROPOS. 3.
Page: 276 (246)
[245.] ALITER.
Page: 276 (246)
[246.] ALITER.
Page: 277 (247)
[247.] PROBL. 3. PROPOS. 4.
Page: 278 (248)
[248.] SCHOLIVM.
Page: 282 (252)
[249.] PROBLEMA 4. PROPOSITIO 5.
Page: 283 (253)
[250.] ALITER.
Page: 284 (254)
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            <s xml:id="echoid-s10676" xml:space="preserve">
              <pb o="230" file="260" n="260" rhead="GEOMETR. PRACT."/>
            proueniet conuexa ſuperficies portionis minoris BAD. </s>
            <s xml:id="echoid-s10677" xml:space="preserve">Similiq; </s>
            <s xml:id="echoid-s10678" xml:space="preserve">modò ſuperfi-
              <lb/>
            cies conuexa maioris portionis B C D, cognoſcetur; </s>
            <s xml:id="echoid-s10679" xml:space="preserve">ſi fiat, vt diameter A C, ad
              <lb/>
            EC, ita ſuperficies conuexa totius ſphæræ ad aliud.</s>
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          </p>
          <p>
            <s xml:id="echoid-s10681" xml:space="preserve">
              <emph style="sc">Et</emph>
            quia, vt ex Archimede oſtendimus, ita eſt diameter A C, ad A E, vel ad
              <lb/>
            EC, vt tota ſuperficies ſphæræ ad ſuperficiẽ portionis BAD, vel BCD: </s>
            <s xml:id="echoid-s10682" xml:space="preserve">erit quo-
              <lb/>
            que ita AF, ſemiſsis diametri ad AE, vel EC, vt hemiſphęrij ſuperficies GAH, ad
              <lb/>
            ſuperficiem portionis B A D, vel B C D, quod oſtendetur eodem modo, quo
              <lb/>
            ſcholium propoſ. </s>
            <s xml:id="echoid-s10683" xml:space="preserve">22. </s>
            <s xml:id="echoid-s10684" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s10685" xml:space="preserve">5. </s>
            <s xml:id="echoid-s10686" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s10687" xml:space="preserve">eſt demonſtratum: </s>
            <s xml:id="echoid-s10688" xml:space="preserve">Si fiat, vt ſemidiameter
              <lb/>
            ſphæræ A F, ad A E, vel E C, altitudinem portionis, ita hemiſphęrij G A H, ſu-
              <lb/>
            perficies ad aliud; </s>
            <s xml:id="echoid-s10689" xml:space="preserve">producetur rurſus conuexa ſuperficies portionis minoris B-
              <lb/>
            AD, vel maioris BCD.</s>
            <s xml:id="echoid-s10690" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10691" xml:space="preserve">
              <emph style="sc">Immo</emph>
            cum ſit vt AF, ſemidiameter ad AE, ita hemiſphęrij GAH, ſuperfici-
              <lb/>
              <note symbol="a" position="left" xlink:label="note-260-01" xlink:href="note-260-01a" xml:space="preserve">corol. 19.
                <lb/>
              quinti.</note>
            es ad ſuperficiem portionis BAD, erit per conuerſionem rationis, vt AF, ſemi- diameter ad EF, ita ſuperficies hemiſphęrij GAH, ad ſuperficiem fruſti GBDH,
              <lb/>
            demptis baſibus. </s>
            <s xml:id="echoid-s10692" xml:space="preserve">Ergo EF, eadem pars erit, vel partes diametri AC, vel ſemidia-
              <lb/>
            metri AF, quæ pars eſt, vel partes ſuperficies fruſtri GBDH, demptis baſibus, ſu-
              <lb/>
            perficiei totius ſphęræ, vel hemiſphærij GAH. </s>
            <s xml:id="echoid-s10693" xml:space="preserve">Quam obrem cognito, quæ pars
              <lb/>
            ſit EF, vel partes ſemidiametri AF, ſi ex ſuperficie hemiſphærij G A H, eadẽ pars
              <lb/>
            auferatur, vel partes, reliqua fiet ſuperficies conuexa minoris portionis B A D.
              <lb/>
            </s>
            <s xml:id="echoid-s10694" xml:space="preserve">Et ſi ad hemiſphærij GCH, ſuperficiem adij ciatur eadem pars, vel partes, con-
              <lb/>
            flabitur conuexa ſuperficies portionis maioris BCD. </s>
            <s xml:id="echoid-s10695" xml:space="preserve">Verbi gratia, ſi E F, conti-
              <lb/>
            neat {3/5}. </s>
            <s xml:id="echoid-s10696" xml:space="preserve">ſemidiametri AF, & </s>
            <s xml:id="echoid-s10697" xml:space="preserve">ex ſuperficie hemiſphærij G A H, tollantur {3/5}. </s>
            <s xml:id="echoid-s10698" xml:space="preserve">reli-
              <lb/>
            qua fiet ſuperficies conuexa portionis minoris BAD: </s>
            <s xml:id="echoid-s10699" xml:space="preserve">Et ſi {3/5}. </s>
            <s xml:id="echoid-s10700" xml:space="preserve">ſuperficiei hemi-
              <lb/>
            ſphærij adij ciantur ad ſuperficiẽ hemiſpherij GCH, cõficietur ſuperficies cõue-
              <lb/>
            xa maioris portionis BCD. </s>
            <s xml:id="echoid-s10701" xml:space="preserve">Sic ſi EF, eſſet ſemiſsis ſemidiametri, auferenda eſ@et
              <lb/>
            ex hemiſphærij ſuperficie ſemiſsis ipſius, vel adijcenda: </s>
            <s xml:id="echoid-s10702" xml:space="preserve">Et ſic de cæteris.</s>
            <s xml:id="echoid-s10703" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s10704" xml:space="preserve">3. </s>
            <s xml:id="echoid-s10705" xml:space="preserve">
              <emph style="sc">Hemisphærii</emph>
            ſoliditas producitur ex ſemidiametro in tertiam par-
              <lb/>
              <note position="left" xlink:label="note-260-02" xlink:href="note-260-02a" xml:space="preserve">Solidit{as} he-
                <lb/>
              miſphærij.</note>
            tem ſuperficiei hemiſphærij: </s>
            <s xml:id="echoid-s10706" xml:space="preserve">Vel in ſextam partem ſuperficiei totius ſphæræ. </s>
            <s xml:id="echoid-s10707" xml:space="preserve">Vel
              <lb/>
            ex {1/4}. </s>
            <s xml:id="echoid-s10708" xml:space="preserve">totius diametri in {2/3}. </s>
            <s xml:id="echoid-s10709" xml:space="preserve">ſuperficiei hemiſphærij.</s>
            <s xml:id="echoid-s10710" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10711" xml:space="preserve">
              <emph style="sc">Item</emph>
            ex duabus tertijs partibus diametri in ſemiſſem areæ circuli maximi.</s>
            <s xml:id="echoid-s10712" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10713" xml:space="preserve">
              <emph style="sc">Vel</emph>
            ex duabus tertijs partibus areæ circuli maximi in ſemidiametrum: </s>
            <s xml:id="echoid-s10714" xml:space="preserve">Aut
              <lb/>
            ex tertia parte areæ circuli maximi in totam diametrum.</s>
            <s xml:id="echoid-s10715" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10716" xml:space="preserve">
              <emph style="sc">Vel</emph>
            ex {1/4}. </s>
            <s xml:id="echoid-s10717" xml:space="preserve">totius diametri in {4/5
              <unsure/>
            }. </s>
            <s xml:id="echoid-s10718" xml:space="preserve">areæ circuli maximi.</s>
            <s xml:id="echoid-s10719" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10720" xml:space="preserve">
              <emph style="sc">Vel</emph>
            ex ſemiſſe areæ circuli maximi in {2/3
              <unsure/>
            }. </s>
            <s xml:id="echoid-s10721" xml:space="preserve">diametri.</s>
            <s xml:id="echoid-s10722" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10723" xml:space="preserve">
              <emph style="sc">Vel</emph>
            ex dupla diametro in {1/6}. </s>
            <s xml:id="echoid-s10724" xml:space="preserve">areæ circuli maximi.</s>
            <s xml:id="echoid-s10725" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10726" xml:space="preserve">
              <emph style="sc">Vel</emph>
            ex ſemidiametro in ſextam partem ſuperficiei ſphęræ.</s>
            <s xml:id="echoid-s10727" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10728" xml:space="preserve">
              <emph style="sc">Vel</emph>
            denique ex {1/6}. </s>
            <s xml:id="echoid-s10729" xml:space="preserve">diametri in ſuperficiem hemiſphærij conuexam. </s>
            <s xml:id="echoid-s10730" xml:space="preserve">quæ
              <lb/>
            omnia ex 2. </s>
            <s xml:id="echoid-s10731" xml:space="preserve">regula Num. </s>
            <s xml:id="echoid-s10732" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10733" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s10734" xml:space="preserve">5. </s>
            <s xml:id="echoid-s10735" xml:space="preserve">colliguntur: </s>
            <s xml:id="echoid-s10736" xml:space="preserve">cum omnes hi numeri producti
              <lb/>
            ſint ſemiſſes illorum, qui ſoliditatem totius ſphæræ in ea regula indicant.</s>
            <s xml:id="echoid-s10737" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10738" xml:space="preserve">4. </s>
            <s xml:id="echoid-s10739" xml:space="preserve">
              <emph style="sc">Soliditas</emph>
            ſectoris ſphęræ (quinimirum componitur ex minore por-
              <lb/>
              <note position="left" xlink:label="note-260-03" xlink:href="note-260-03a" xml:space="preserve">Solidit{as} ſe-
                <lb/>
              ctoris ſphæræ.</note>
            tione ſphęræ, & </s>
            <s xml:id="echoid-s10740" xml:space="preserve">cono baſem habente eandem cum portione, & </s>
            <s xml:id="echoid-s10741" xml:space="preserve">altitudinem æ-
              <lb/>
            qualem perpendiculari ex centro in baſem portionis deductæ; </s>
            <s xml:id="echoid-s10742" xml:space="preserve">Vel quirelin qui-
              <lb/>
            tur, ſi idem conus ex portione maiore ſubtrahitur. </s>
            <s xml:id="echoid-s10743" xml:space="preserve">Vt in proxima figura, ſolidũ
              <lb/>
            compoſitum ex portione ſphęræ B A D, baſem habente circulum diametri B D,
              <lb/>
            & </s>
            <s xml:id="echoid-s10744" xml:space="preserve">ex cono habente eandem baſem, & </s>
            <s xml:id="echoid-s10745" xml:space="preserve">verticemin centro F: </s>
            <s xml:id="echoid-s10746" xml:space="preserve">Item ſolidũ, quod
              <lb/>
            relinquitur, ſi conus idem ex portione maiore B C D, dematur, appellamus </s>
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