Clavius, Christoph, Geometria practica

Table of Notes

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            <s xml:id="echoid-s11314" xml:space="preserve">
              <pb o="243" file="273" n="273" rhead="LIBER SEXTVS."/>
            deinde quadrato G, quod rectilineo A, ſit æquale, reperiatur tribus rectis BC, X,
              <lb/>
            & </s>
            <s xml:id="echoid-s11315" xml:space="preserve">HI, quarta proportionalis IY, agaturque Y Z, lateribus quadrati parallela, ita
              <lb/>
            vt rurſus ſit triangulum BCF, ad triangulum V C T, ſicut quadratum G, ad re-
              <lb/>
            ctangulum I Z. </s>
            <s xml:id="echoid-s11316" xml:space="preserve">Poſt hæc, vt Num. </s>
            <s xml:id="echoid-s11317" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11318" xml:space="preserve">præcepimus, rectangulo IZ, conſtruatur
              <lb/>
            trapezium æquale V e, & </s>
            <s xml:id="echoid-s11319" xml:space="preserve">tribus rectis C V, V d, CB, inuenta quarta proportionali
              <lb/>
            B R, (tranſibit autem recta C d, ducta per R: </s>
            <s xml:id="echoid-s11320" xml:space="preserve">ſi quarta BR, rectè inuenta eſt:</s>
            <s xml:id="echoid-s11321" xml:space="preserve">
              <note symbol="a" position="right" xlink:label="note-273-01" xlink:href="note-273-01a" xml:space="preserve">ſchol. 4.
                <lb/>
              ſexti.</note>
            ita vt viciſsim recta C d, ſi accuratè ducatur, abſcindat quartam proportiona- lem quæſitam BR,) demittatur R S, ipſi BC, parallela. </s>
            <s xml:id="echoid-s11322" xml:space="preserve">Dico trapezium B S, recti-
              <lb/>
              <note symbol="b" position="right" xlink:label="note-273-02" xlink:href="note-273-02a" xml:space="preserve">4. ſexti.</note>
            lineo A, æquale eſſe. </s>
            <s xml:id="echoid-s11323" xml:space="preserve">Quoniam enim trapezium B S, trapezio V e, ſimile eſt, per
              <lb/>
            ea, quæ in ſcholio propoſ. </s>
            <s xml:id="echoid-s11324" xml:space="preserve">18. </s>
            <s xml:id="echoid-s11325" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11326" xml:space="preserve">6. </s>
            <s xml:id="echoid-s11327" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s11328" xml:space="preserve">monſtrata ſunt à nobis; </s>
            <s xml:id="echoid-s11329" xml:space="preserve"> erit
              <note symbol="c" position="right" xlink:label="note-273-03" xlink:href="note-273-03a" xml:space="preserve">coroll. 20.
                <lb/>
              ſexti.</note>
            zium B S, ad trapezium V e, vt recta BC, ad rectam X, hoc eſt, vt recta H I, ad
              <lb/>
            rectam IY, hoc eſt, vt quadratum G, ad rectangulum IZ. </s>
            <s xml:id="echoid-s11330" xml:space="preserve">Cum ergo
              <note symbol="d" position="right" xlink:label="note-273-04" xlink:href="note-273-04a" xml:space="preserve">1. ſexti.</note>
            V e, rectangulo I Z, æqualeſit; </s>
            <s xml:id="echoid-s11331" xml:space="preserve"> erit quo que trapezium B S, quadrato G,
              <note symbol="e" position="right" xlink:label="note-273-05" xlink:href="note-273-05a" xml:space="preserve">14. quinti.</note>
            eſt, rectilineo A, æquale. </s>
            <s xml:id="echoid-s11332" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s11333" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11334" xml:space="preserve">7. </s>
            <s xml:id="echoid-s11335" xml:space="preserve">
              <emph style="sc">Iam</emph>
            verò datis duobus rectilineis quibuſcunque A, & </s>
            <s xml:id="echoid-s11336" xml:space="preserve">BCDEFGHI, ſit
              <lb/>
            ex poſteriore: </s>
            <s xml:id="echoid-s11337" xml:space="preserve">quod maius ponatur, auferendum rectilineum habens latus la-
              <lb/>
            teri BI, parallelum, æquale priori A, quod minus ſtatuatur, ſi fieri quidem id po-
              <lb/>
            terit. </s>
            <s xml:id="echoid-s11338" xml:space="preserve">Fieri autem poterit ſemper in figuris omnes angulos habentibus intror-
              <lb/>
            ſum, in aliis verò non ſemper. </s>
            <s xml:id="echoid-s11339" xml:space="preserve">Per ea, quæ in ſcholio propoſ. </s>
            <s xml:id="echoid-s11340" xml:space="preserve">14 lib. </s>
            <s xml:id="echoid-s11341" xml:space="preserve">2. </s>
            <s xml:id="echoid-s11342" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s11343" xml:space="preserve">vel
              <lb/>
            potius per ea, quæ Num. </s>
            <s xml:id="echoid-s11344" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11345" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s11346" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11347" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11348" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11349" xml:space="preserve">huius tradidimus, conſtruatur quadra-
              <lb/>
            tum K M, rectilineo minori A, æquale. </s>
            <s xml:id="echoid-s11350" xml:space="preserve">Deinde ex angulo C, quilateri BI, pro-
              <lb/>
            ximus eſt, ducta lateri B I, parallela C O, conſtituatur rectilineo B O, ea-
              <lb/>
            dem ratione quadratum æquale P Q R; </s>
            <s xml:id="echoid-s11351" xml:space="preserve">& </s>
            <s xml:id="echoid-s11352" xml:space="preserve">duabus rectis K N, PQ, inuenta ter-
              <lb/>
            tia proportionali K S, ducatur S T, ipſi K L, parallela: </s>
            <s xml:id="echoid-s11353" xml:space="preserve"> Erit que
              <note symbol="f" position="right" xlink:label="note-273-06" xlink:href="note-273-06a" xml:space="preserve">17. ſexti.</note>
            K T, contentum ſub prima linea KL, & </s>
            <s xml:id="echoid-s11354" xml:space="preserve">tertia K S, quadrato mediæ PQ, hoc eſt,
              <lb/>
            rectilineo B O, æquale. </s>
            <s xml:id="echoid-s11355" xml:space="preserve">Et quoniam KS, inuenta eſt in hoc exemplo minor late-
              <lb/>
            re KN: </s>
            <s xml:id="echoid-s11356" xml:space="preserve">ideo que & </s>
            <s xml:id="echoid-s11357" xml:space="preserve">rectangulum K T, minus quadrato K M, hoc eſt, rectilineo
              <lb/>
            A; </s>
            <s xml:id="echoid-s11358" xml:space="preserve">erit etiam rectilineum B O, minus rectilineo A. </s>
            <s xml:id="echoid-s11359" xml:space="preserve">Ex propinquiore ergo an-
              <lb/>
            gulo H, ducta rurſum ipſi CO, vel BI, parallela H V, fiat iterum rectilineo C H,
              <lb/>
            æquale quadratum, cuius latus X: </s>
            <s xml:id="echoid-s11360" xml:space="preserve">Et duabus rectis K N, & </s>
            <s xml:id="echoid-s11361" xml:space="preserve">X, inuenta tertia
              <lb/>
            proportionali S N, quæ in hoc exemplo terminatur in extremo lateris K N;
              <lb/>
            </s>
            <s xml:id="echoid-s11362" xml:space="preserve"> erit rurſum rectangulum SM, ſub prima linea ST, & </s>
            <s xml:id="echoid-s11363" xml:space="preserve">tertia SN,
              <note symbol="g" position="right" xlink:label="note-273-07" xlink:href="note-273-07a" xml:space="preserve">17. ſexti.</note>
            æquale quadrato mediæ X, hoc eſt, rectilineo C H. </s>
            <s xml:id="echoid-s11364" xml:space="preserve">Cum ergo & </s>
            <s xml:id="echoid-s11365" xml:space="preserve">K T, ipſi
              <lb/>
            B O, ſit oſtenſum æquale: </s>
            <s xml:id="echoid-s11366" xml:space="preserve">erit totum quadratum K M, hoc eſt, rectilineum A,
              <lb/>
            toti rectilineo BCVHOI, æquale; </s>
            <s xml:id="echoid-s11367" xml:space="preserve">ac proinde ex maiori rectilineo per rectam
              <lb/>
            HV, lateri B I, parallelam rectilineum detraximus minori rectilineo A, æquale.
              <lb/>
            </s>
            <s xml:id="echoid-s11368" xml:space="preserve">quod faciendum erat.</s>
            <s xml:id="echoid-s11369" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11370" xml:space="preserve">8. </s>
            <s xml:id="echoid-s11371" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi duabus rectis K N, & </s>
            <s xml:id="echoid-s11372" xml:space="preserve">X, inuenta tertia proportionalis fuiſ-
              <lb/>
            ſet minor, quam SN, nimirum æqualis ipſi S Y, ita vt rectangulum S Z, quadra-
              <lb/>
            to rectæ X, vel rectilineo C H, foret æquale: </s>
            <s xml:id="echoid-s11373" xml:space="preserve">ducenda eſſet ex proximo an-
              <lb/>
            gulo D, alia parallela D a, & </s>
            <s xml:id="echoid-s11374" xml:space="preserve">rectilineo D H, conſtituendum quadratum æ-
              <lb/>
            quale; </s>
            <s xml:id="echoid-s11375" xml:space="preserve">at que rectæ K N, & </s>
            <s xml:id="echoid-s11376" xml:space="preserve">lateri poſtremi huius quadrati inuenti adiungen-
              <lb/>
            da tertia proportionalis, & </s>
            <s xml:id="echoid-s11377" xml:space="preserve">ei abſcindenda æqualis Y b. </s>
            <s xml:id="echoid-s11378" xml:space="preserve">Et ſi Y B, foret minor,
              <lb/>
            quam Y N, ducenda adhuc eſſet ex proximo angulo G, parallela lateri B I, & </s>
            <s xml:id="echoid-s11379" xml:space="preserve">
              <lb/>
            rectilineo inter hanc parallelam, & </s>
            <s xml:id="echoid-s11380" xml:space="preserve">D a, comprehenſo effi ciendum quadratum
              <lb/>
            æquale: </s>
            <s xml:id="echoid-s11381" xml:space="preserve">ac rectæ K N, & </s>
            <s xml:id="echoid-s11382" xml:space="preserve">lateri huius quadrati adiungenda tertia proportiona-
              <lb/>
            lis, &</s>
            <s xml:id="echoid-s11383" xml:space="preserve">c. </s>
            <s xml:id="echoid-s11384" xml:space="preserve">Atque ita progrediendum deinceps, donec inuenta ſit tertia </s>
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