Clavius, Christoph, Geometria practica

Table of contents

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[201.] FINIS LIBRI QVARTI.
Page: 233 (203)
[202.] GEOMETRIÆ PRACTICÆ LIBER QVINTVS.
Page: 234 (204)
[203.] AREAS Solidorum, corporumue perſcrutans.
Page: 234 (204)
[204.] DE AREA PARALLELEPIP EDO-rum, Priſmatum, & Cylindrorum. Capvt I.
Page: 234 (204)
[205.] DE AREA PYRAMIDVM & Conorum. Capvt II.
Page: 236 (206)
[206.] DL AREA FRVSTI PYRA-midis, & Coni. Capvt III.
Page: 237 (207)
[207.] SCHOLIVM.
Page: 239 (209)
[208.] DE AREA QVINQVE COR-porum regularium. Capvt IV.
Page: 240 (210)
[209.] Capvt V.
Page: 248 (218)
[210.] PROPOSITIO I.
Page: 248 (218)
[211.] COROLLARIVM.
Page: 249 (219)
[212.] PROPOSITIO II.
Page: 249 (219)
[213.] COROLLARIVM.
Page: 249 (219)
[214.] PROPOSITIO III.
Page: 250 (220)
[215.] COROLLARIVM.
Page: 250 (220)
[216.] PROPOSITIO IV.
Page: 251 (221)
[217.] PROPOSITIO V.
Page: 251 (221)
[218.] PROPOSITIO VI.
Page: 251 (221)
[219.] PROPOSITIO VII.
Page: 252 (222)
[220.] I.
Page: 253 (223)
[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)
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              <pb o="143" file="173" n="173" rhead="LIBER TERTIVS."/>
              <note style="it" position="right" xlink:label="note-173-01" xlink:href="note-173-01a" xml:space="preserve">
                <lb/>
              Vt A C, nota in parti- \\ b{us} A B, # ad A B, notarum \\ partium: # Ita C D, nota in data \\ menſura # ad B G,
                <lb/>
              </note>
            cognoſcetur diſtantia B G, in partibus C D. </s>
            <s xml:id="echoid-s5552" xml:space="preserve">Vt ſi A C, eſt quinta pars ipſius A B,
              <lb/>
            & </s>
            <s xml:id="echoid-s5553" xml:space="preserve">C D, contineat 1. </s>
            <s xml:id="echoid-s5554" xml:space="preserve">pedem, & </s>
            <s xml:id="echoid-s5555" xml:space="preserve">inſuper {2/3}. </s>
            <s xml:id="echoid-s5556" xml:space="preserve">ſi 1 {2/3}. </s>
            <s xml:id="echoid-s5557" xml:space="preserve">quinquies ſumatur, efficietur di-
              <lb/>
            ſtantia B G, pedum 8 {1/3}.</s>
            <s xml:id="echoid-s5558" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s5559" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5560" xml:space="preserve">
              <emph style="sc">Non</emph>
            aliter diſtantia b F, ex maioris montis cacumine G, mueſtigabitur,
              <lb/>
            vt figura indicat.</s>
            <s xml:id="echoid-s5561" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5562" xml:space="preserve">
              <emph style="sc">Eodem</emph>
            modo procedes, ſi puncta F, G, ſint faſtigia duarum turrium, aut ſi
              <lb/>
            vnum ſit faſtigium turris, & </s>
            <s xml:id="echoid-s5563" xml:space="preserve">alterum, cacumen montis, vt conſtat.</s>
            <s xml:id="echoid-s5564" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5565" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5566" xml:space="preserve">
              <emph style="sc">Idem</emph>
            hoc per quadratum fiet hoc modo. </s>
            <s xml:id="echoid-s5567" xml:space="preserve">Sit quadratum a b f g, ſtatua-
              <lb/>
            turque angulus b, in cacumine G, & </s>
            <s xml:id="echoid-s5568" xml:space="preserve">latus b f, deprimatur, ita vtrecta in cacu-
              <lb/>
            men F, tendat, ſi productum intelligatur, obſeruetur que vmbra verſa abſciſ-
              <lb/>
            ſa g h, à radio viſuali a B. </s>
            <s xml:id="echoid-s5569" xml:space="preserve">Nam quia triangula a g h, B b a, æquiangula ſunt,
              <lb/>
            ſi fiat.</s>
            <s xml:id="echoid-s5570" xml:space="preserve">
              <note symbol="a" position="right" xlink:label="note-173-02" xlink:href="note-173-02a" xml:space="preserve">4. ſexti.</note>
              <note style="it" position="right" xlink:label="note-173-03" xlink:href="note-173-03a" xml:space="preserve">
                <lb/>
              Vt g h, vmbra \\ verſa # ad g a, lat{us} \\ quadrati # ita lat{us} quadrati \\ a b, # ad B b,
                <lb/>
              </note>
            hoc eſt, ſi quadratus numerus lateris, nimirum 1000000. </s>
            <s xml:id="echoid-s5571" xml:space="preserve">diuidatur per vmbram
              <lb/>
            verſam, gignetur in Quotiente diſtantia B b.</s>
            <s xml:id="echoid-s5572" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5573" xml:space="preserve">
              <emph style="sc">Idemqve</emph>
            fieret, ſi angulus quadrati in B, collocaretur, infimum que latus
              <lb/>
            recta à B, in cacumen G, tenderet, &</s>
            <s xml:id="echoid-s5574" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5575" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5576" xml:space="preserve">LONGITVDINEM aſcenſus alicuius montis, ſi eius cacumen ab
              <lb/>
            oculo in radice conſtituto videatur, eiuſdem inſtrumenti beneficio
              <lb/>
            cognoſcere.</s>
            <s xml:id="echoid-s5577" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div374" type="section" level="1" n="156">
          <head xml:id="echoid-head159" xml:space="preserve">PROBLEMA XXXVIII.</head>
          <p>
            <s xml:id="echoid-s5578" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5579" xml:space="preserve">
              <emph style="sc">Accommodetvr</emph>
            prædictum inſtrumen-
              <lb/>
              <figure xlink:label="fig-173-01" xlink:href="fig-173-01a" number="106">
                <image file="173-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/173-01"/>
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            tum, vt punctum B, in radice montis ſtatuatur,
              <lb/>
            & </s>
            <s xml:id="echoid-s5580" xml:space="preserve">baculus B E, beneficio duorum clauiculorum
              <lb/>
            infixorum, vt Num. </s>
            <s xml:id="echoid-s5581" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5582" xml:space="preserve">problem. </s>
            <s xml:id="echoid-s5583" xml:space="preserve">31. </s>
            <s xml:id="echoid-s5584" xml:space="preserve">dictum eſt, re-
              <lb/>
            cta in cacumen F, vergat; </s>
            <s xml:id="echoid-s5585" xml:space="preserve">notetur que interſe-
              <lb/>
            ctio D, radij viſualis cum baculo C D, inſpecto
              <lb/>
            cacumine F, ex A. </s>
            <s xml:id="echoid-s5586" xml:space="preserve"> Nam iterum triangula A C
              <note symbol="b" position="right" xlink:label="note-173-04" xlink:href="note-173-04a" xml:space="preserve">coroll. 4.
                <lb/>
              ſexti.</note>
            A B F. </s>
            <s xml:id="echoid-s5587" xml:space="preserve">Similia erunt. </s>
            <s xml:id="echoid-s5588" xml:space="preserve"> Quare ſi
              <note symbol="c" position="right" xlink:label="note-173-05" xlink:href="note-173-05a" xml:space="preserve">4. ſexti.</note>
              <note style="it" position="right" xlink:label="note-173-06" xlink:href="note-173-06a" xml:space="preserve">
                <lb/>
              Vt A C, nota in parti- \\ b{us} A B, # ad A B, notarum \\ partium: # Ita C D, nota in data \\ menſura # ad B F,
                <lb/>
              </note>
            cognoſcetur aſcenſus obliquus montis B, F, in partibus C D.</s>
            <s xml:id="echoid-s5589" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5590" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5591" xml:space="preserve">
              <emph style="sc">Pari</emph>
            ratione, ſi F, ſit faſtigium alicuius turris, inueſtigabis diſtantiam à
              <lb/>
            puncto B, in terra, vel alibi poſito, vſque ad F, hoc eſt, hypotenuſam B F, vt per-
              <lb/>
            ſpicuum eſt. </s>
            <s xml:id="echoid-s5592" xml:space="preserve">Atque hoc eodem inſtrumento complures aliæ dimenſiones ab-
              <lb/>
            ſolui poterunt, quod prudens Lector facilè perſpiciet.</s>
            <s xml:id="echoid-s5593" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5594" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5595" xml:space="preserve">
              <emph style="sc">Idem</emph>
            aſſequemur quadrato A B G H, ſi eius angulus B, in radice ſta-
              <lb/>
            @uatur, & </s>
            <s xml:id="echoid-s5596" xml:space="preserve">latus B G, eleuetur ita, vtrecta tendat in cacumen F. </s>
            <s xml:id="echoid-s5597" xml:space="preserve">Obſeruara </s>
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