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="175" file="205" n="205" rhead="LIBER QVARTVS."/>
            ueniemus ei quadratum æquale, ſi, ducta perpendiculari F N, circa rectam ex
              <lb/>
            F N, & </s>
            <s xml:id="echoid-s7301" xml:space="preserve">ſemiſſe baſis E Z, conflatam ſemicirculus deſcribatur, &</s>
            <s xml:id="echoid-s7302" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7303" xml:space="preserve">Sint ergo a, b,
              <lb/>
            c, latera quadratorum trapeziis, ABCG, CDEG, & </s>
            <s xml:id="echoid-s7304" xml:space="preserve">triangulo EFG, æqualium;
              <lb/>
            </s>
            <s xml:id="echoid-s7305" xml:space="preserve">quibus omnibus quadratis vnum ęquale exhibebimus hac arte. </s>
            <s xml:id="echoid-s7306" xml:space="preserve">Fiat angulus
              <lb/>
            rectus def, & </s>
            <s xml:id="echoid-s7307" xml:space="preserve">lateribus a, b, æquales ſumantur rectę ed, eg, eritque
              <note symbol="a" position="right" xlink:label="note-205-01" xlink:href="note-205-01a" xml:space="preserve">47. primi.</note>
            tum ductę rectę d g, quadratis rectarum ed, eg, hoc eſt, laterum a, b, æquale.
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            </s>
            <s xml:id="echoid-s7308" xml:space="preserve">Capiatur rurſus e k, lateric, & </s>
            <s xml:id="echoid-s7309" xml:space="preserve">recta e h, rectę d g, ęqualis; </s>
            <s xml:id="echoid-s7310" xml:space="preserve"> eritque rurſus
              <note symbol="b" position="right" xlink:label="note-205-02" xlink:href="note-205-02a" xml:space="preserve">47. primi.</note>
            dratum ex kh, ęquale quadratis ex k e, e h, id eſt ex c, eh, nimirum tribus ex a,
              <lb/>
            b, c. </s>
            <s xml:id="echoid-s7311" xml:space="preserve">Siigitur latus ex k h, menſuretur, & </s>
            <s xml:id="echoid-s7312" xml:space="preserve">in ſe ducatur, ginetur area figurę pro-
              <lb/>
            poſitæ A B C D E F G.</s>
            <s xml:id="echoid-s7313" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7314" xml:space="preserve">
              <emph style="sc">Eodem</emph>
            artificio, ſi plura ſint latera, inueniemus quadratum omnibus qua-
              <lb/>
            dratis ęquale. </s>
            <s xml:id="echoid-s7315" xml:space="preserve">Vt ſi foret alterum latus q, acciperemus ei æqualem rectam
              <lb/>
            e p. </s>
            <s xml:id="echoid-s7316" xml:space="preserve">Item rectam ef, rectę k h, æqualem. </s>
            <s xml:id="echoid-s7317" xml:space="preserve">Nam quadratum ex p f, quadratis ex
              <lb/>
            e p, hoc eſt, ex q, & </s>
            <s xml:id="echoid-s7318" xml:space="preserve">ex ef, id eſt, ex a, b, c, erit ęquale, & </s>
            <s xml:id="echoid-s7319" xml:space="preserve">ſic de pluribus.
              <lb/>
            </s>
            <s xml:id="echoid-s7320" xml:space="preserve">
              <note position="right" xlink:label="note-205-03" xlink:href="note-205-03a" xml:space="preserve">Facilis ratio
                <lb/>
              menſurandi
                <lb/>
              trapezii irre-
                <lb/>
              gularis.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s7321" xml:space="preserve">
              <emph style="sc">Ex</emph>
            his colligitur facilis ratio metiendi trapezij irregularis, cuiuſmo di eſt in
              <lb/>
            proxima figura trapezium A B C G. </s>
            <s xml:id="echoid-s7322" xml:space="preserve">Nam ducta diametro B G, ſi ad eam duę
              <lb/>
            perpendiculares demiſſę A L, CH, menſurentur, earumque aggregatum in me-
              <lb/>
            dietatem diametri B G, multiplicetur, procreabitur area trapezij, vt demonſtra-
              <lb/>
            tum eſt.</s>
            <s xml:id="echoid-s7323" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7324" xml:space="preserve">
              <emph style="sc">In</emph>
            octauo porrò lib. </s>
            <s xml:id="echoid-s7325" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s7326" xml:space="preserve">6. </s>
            <s xml:id="echoid-s7327" xml:space="preserve">docebimus quo que, qua ratione datę figu-
              <lb/>
            rę rectilineę rectangulum æquale conſtruatur. </s>
            <s xml:id="echoid-s7328" xml:space="preserve">quod ſi fiat hoc loco, effi cietur
              <lb/>
            illi rectangulo quadratum ęquale, per vltimam propoſ. </s>
            <s xml:id="echoid-s7329" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s7330" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7331" xml:space="preserve">Euclidis, ſine vl-
              <lb/>
            lo negotio, aut moleſtia.</s>
            <s xml:id="echoid-s7332" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div472" type="section" level="1" n="175">
          <head xml:id="echoid-head180" xml:space="preserve">DE AREA MVLTILATERA-
            <lb/>
          rum figurarum regularium.</head>
          <head xml:id="echoid-head181" xml:space="preserve">
            <emph style="sc">Capvt</emph>
          V.</head>
          <p>
            <s xml:id="echoid-s7333" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7334" xml:space="preserve">
              <emph style="sc">QVanqvam</emph>
            regulares figurę, quę ſcilicet ſunt & </s>
            <s xml:id="echoid-s7335" xml:space="preserve">æquilaterę & </s>
            <s xml:id="echoid-s7336" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s7337" xml:space="preserve">æquiangulę, menſurari poſ@int, vt irregulares pręcedentis capi-
              <lb/>
            tis, reſoluendo eas in triangula, &</s>
            <s xml:id="echoid-s7338" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7339" xml:space="preserve">ſolet tamen dari propria ac pe-
              <lb/>
            culiaris regula, qua cuiuſque figurę regularis area inuenitur: </s>
            <s xml:id="echoid-s7340" xml:space="preserve">quę ita ſe habet.</s>
            <s xml:id="echoid-s7341" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7342" xml:space="preserve">SEMISSIS ambit{us} figuræ multiplicetur in perpendicularem è centro figuræ ad
              <lb/>
            vnum lat{us} cadentem. </s>
            <s xml:id="echoid-s7343" xml:space="preserve">Numer{us} enim product{us} area erit figuræ.</s>
            <s xml:id="echoid-s7344" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7345" xml:space="preserve">
              <emph style="sc">Nam</emph>
            vt lib. </s>
            <s xml:id="echoid-s7346" xml:space="preserve">7. </s>
            <s xml:id="echoid-s7347" xml:space="preserve">de Iſoperimetris propoſ. </s>
            <s xml:id="echoid-s7348" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7349" xml:space="preserve">demonſtrabimus, area cuiuslibet
              <lb/>
              <note position="right" xlink:label="note-205-04" xlink:href="note-205-04a" xml:space="preserve">Area figura
                <lb/>
              regularis.</note>
            figurę regularis ęqualis eſt rectangulo contento ſub perpendiculari à centro fi-
              <lb/>
            gurę ad vnum latus ducta, & </s>
            <s xml:id="echoid-s7350" xml:space="preserve">ſub dimidiato ambitu eiuſdem figurę.</s>
            <s xml:id="echoid-s7351" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7352" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7353" xml:space="preserve">
              <emph style="sc">Perpendicvlaris</emph>
            porrò è centro figurę in vnum latus cadens,
              <lb/>
              <note position="right" xlink:label="note-205-05" xlink:href="note-205-05a" xml:space="preserve">Perpendicu-
                <lb/>
              laris & ſemi-
                <lb/>
              diameter fi-
                <lb/>
              guræ regula-
                <lb/>
              ris quo pacto
                <lb/>
              inueniatur.</note>
            vna cum ſemidiametro circuli figuram ambientis ſic reperietur. </s>
            <s xml:id="echoid-s7354" xml:space="preserve">Numerus late-
              <lb/>
            rum, ſiue angulorum duplicetur, & </s>
            <s xml:id="echoid-s7355" xml:space="preserve">à duplo auferantur 4. </s>
            <s xml:id="echoid-s7356" xml:space="preserve">Nam reliquus nu-
              <lb/>
            merus indicabit, quot rectis angulis omnes anguli figurę ęquiualeant, per ea,
              <lb/>
            quę in ſcholio propoſ. </s>
            <s xml:id="echoid-s7357" xml:space="preserve">32. </s>
            <s xml:id="echoid-s7358" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s7359" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7360" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s7361" xml:space="preserve">demonſtrata ſunt. </s>
            <s xml:id="echoid-s7362" xml:space="preserve">Hic idem nume-
              <lb/>
            @us reliquus, videlicet, numerus angulorum rectorum, per numerum angulo-
              <lb/>
            rum diuidatur, vt Quotiens vnius anguli figurę magnitudinem exhibeat, qui</s>
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