Clavius, Christoph, Geometria practica

Table of figures

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            <s xml:id="echoid-s11410" xml:space="preserve">9. </s>
            <s xml:id="echoid-s11411" xml:space="preserve">
              <emph style="sc">Ex</emph>
            his puto ſatis ſtudio ſum Lectorem intelligere, quo pacto in alijs e-
              <lb/>
            xemplis ſe gerere debeat. </s>
            <s xml:id="echoid-s11412" xml:space="preserve">Nam ſi verbi gratia ex hoc propoſito rectilineo irre-
              <lb/>
            gulariſsimo per lineam lateri AM, parallelam abſcindenda ſit portio æqualis al-
              <lb/>
            teri cuipiam rectilineo minori, producemus MA, vſ-
              <lb/>
              <figure xlink:label="fig-275-01" xlink:href="fig-275-01a" number="178">
                <image file="275-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/275-01"/>
              </figure>
            que ad N. </s>
            <s xml:id="echoid-s11413" xml:space="preserve">Et ſi quidem deprehenſum fuerit trian-
              <lb/>
            gulum A B N, eſſe æquale dato rectilineo minori,
              <lb/>
            (quod ſcietur, ſi quadratum triangulo æquale con-
              <lb/>
            ſtructum, fuerit æquale quadrato, quod dato recti-
              <lb/>
            lineo minori conſtruitur æquale) recta AN, proble-
              <lb/>
            ma efficiet. </s>
            <s xml:id="echoid-s11414" xml:space="preserve">Siverò maius, conſtruemus ſuper AN,
              <lb/>
            verſus B, trapezium per parallelam ipſi A N, æquale exceſſui: </s>
            <s xml:id="echoid-s11415" xml:space="preserve">At ſi minus, du-
              <lb/>
            cemus L O, parallelam. </s>
            <s xml:id="echoid-s11416" xml:space="preserve">Nam ſi fuerit deprehenſum rectilineum NL, æquale
              <lb/>
            defectui, problema efficiet parallela L O: </s>
            <s xml:id="echoid-s11417" xml:space="preserve">Si verò maius, conſtituemus ſuper
              <lb/>
            L O, verſus MN, per parallelam ipſi MN, trapezium exceſſui æquale. </s>
            <s xml:id="echoid-s11418" xml:space="preserve">Ea enim
              <lb/>
            parallela problema ſoluet: </s>
            <s xml:id="echoid-s11419" xml:space="preserve">At ſi minus, producemus OL, ad P: </s>
            <s xml:id="echoid-s11420" xml:space="preserve">Etſi quidem
              <lb/>
            triangulum KLP, fuerit æquale defectui, tota parallela O P, quæſtioni ſatisfa-
              <lb/>
            ciet: </s>
            <s xml:id="echoid-s11421" xml:space="preserve">Si verò maius, conſtituemus in angulo K, triangulum ſimile
              <note symbol="a" position="right" xlink:label="note-275-01" xlink:href="note-275-01a" xml:space="preserve">25. ſexti.</note>
            KLP, & </s>
            <s xml:id="echoid-s11422" xml:space="preserve">exceſſuiæquale; </s>
            <s xml:id="echoid-s11423" xml:space="preserve">ita vt hoc triangulum vna cum rectilineo per paralle-
              <lb/>
            lam L O, abſciſſo ſit dato rectilineo minori æquale. </s>
            <s xml:id="echoid-s11424" xml:space="preserve">Ex quo colliges, proble-
              <lb/>
            ma in hoc caſu ſolui non poſſe, cum duæ parallelæ, nimirum L O, & </s>
            <s xml:id="echoid-s11425" xml:space="preserve">illa, quæ
              <lb/>
            triangulum ipſi KLP, ſimile aufert, reſecent ex toto rectilineo BG, partem dato
              <lb/>
            rectilineo minori æqualem. </s>
            <s xml:id="echoid-s11426" xml:space="preserve">At ſi triangulum KLP, fuerit minus defectu præ-
              <lb/>
            dicto, ita vt hoc triangulum vna cum rectilineo per parallelam L O, abſciſſo ſit
              <lb/>
            minus dato rectilineo minore, ducemus per D, parallelam Q R. </s>
            <s xml:id="echoid-s11427" xml:space="preserve">Et ſi quidem
              <lb/>
            rectilineum P R, æquale fuerit defectui, quo figura KPLMABNO, à dato re-
              <lb/>
            ctilineo minore deficit, factum erit per parallelam QR, quod iubetur: </s>
            <s xml:id="echoid-s11428" xml:space="preserve">Siverò
              <lb/>
            maius, parallela, quæ cum QR, verſus OP, auferet rectilineum huic exceſſuiæ-
              <lb/>
            quale, ſatisfaciet problemati: </s>
            <s xml:id="echoid-s11429" xml:space="preserve">At ſi rectilineum PR, fuerit minus prædicto de-
              <lb/>
            fectu, & </s>
            <s xml:id="echoid-s11430" xml:space="preserve">triangulum C D R, inuentũ fuerit vltimo huic defectui, quo rectiline-
              <lb/>
            um PR, à prædicto defectu deficit, æquale, parallela DQ@ quæſtionem diſſoluet:
              <lb/>
            </s>
            <s xml:id="echoid-s11431" xml:space="preserve">Si autem triangulum CDR, fuerit maius hoc vltimo defectu, ſi ad C,
              <note symbol="b" position="right" xlink:label="note-275-02" xlink:href="note-275-02a" xml:space="preserve">25. ſexti.</note>
            atur triangulum exceſſui æquale, & </s>
            <s xml:id="echoid-s11432" xml:space="preserve">ſimile triangulo CDR, ſatisfacient quæſtio-
              <lb/>
            ni duæ parallelæ, videlicet D Q. </s>
            <s xml:id="echoid-s11433" xml:space="preserve">& </s>
            <s xml:id="echoid-s11434" xml:space="preserve">baſis prædictitrianguli conſtituti; </s>
            <s xml:id="echoid-s11435" xml:space="preserve">atque in
              <lb/>
            hoc caſu per vnicam parallelam ſatisfieri problemati nequit: </s>
            <s xml:id="echoid-s11436" xml:space="preserve">Si denique trian-
              <lb/>
            gulum CDR, minus extiterit eo dem illo vltimo defectu, ducemus parallelam
              <lb/>
            IS. </s>
            <s xml:id="echoid-s11437" xml:space="preserve">Et ſi quidẽ rectilineum DI, æquale fuerit illi, quo triangulum CDR, minus
              <lb/>
            eſt vltimo illo defectu, erit totum rectilineum ISDCBAMLKI, dato minori re-
              <lb/>
            ctilineo æquale: </s>
            <s xml:id="echoid-s11438" xml:space="preserve">Si autem rectilineum DI, inæquale fuerit, progrediemur vlte-
              <lb/>
            rius, vt iam ſæpius dictum eſt, donec rectilineum inueniamus dato minori recti-
              <lb/>
            lineo æquale; </s>
            <s xml:id="echoid-s11439" xml:space="preserve">Inuenietur autem omnino vnum æquale, cum totũ rectilineum
              <lb/>
            BG, maius ponatur. </s>
            <s xml:id="echoid-s11440" xml:space="preserve">Vides igitur, facilè conijci poſſe, quando problema per v-
              <lb/>
            nicam parallelam ſolui poſsit, & </s>
            <s xml:id="echoid-s11441" xml:space="preserve">quando non, ſed per duas: </s>
            <s xml:id="echoid-s11442" xml:space="preserve">Quotieſcunque
              <lb/>
            enimincidemus in eiuſmo ditriangulum in ipſa conſtructione, qualia fu-
              <lb/>
            erunt K L P, & </s>
            <s xml:id="echoid-s11443" xml:space="preserve">C D R, ex quo auferendum ſit triangulum ſimile, & </s>
            <s xml:id="echoid-s11444" xml:space="preserve">
              <lb/>
            æquale exceſſui alicui, ſolui problema nequit, niſi per
              <lb/>
            duas parallelas.</s>
            <s xml:id="echoid-s11445" xml:space="preserve"/>
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