Clavius, Christoph, Geometria practica

Table of contents

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[111.] PROBLEMA IV.
[112.] ALITER
[113.] ALITER.
[114.] ALITER.
[115.] PROBLEMA V.
[116.] PROBLEMA VI.
[117.] ALITER.
[118.] ALITER
[119.] ALITER.
[120.] ALITER.
[121.] PROBLEMA VII.
[122.] SCHOLIVM.
[123.] Vel
[124.] PROBLEMA VIII.
[125.] PROBLEMA IX.
[126.] SCHOLIVM.
[127.] PROBLEMA X.
[128.] PROBLEMA XI.
[129.] PROBLEMA XII.
[130.] PROBLEMA XIII.
[131.] PROBLEMA XIV.
[132.] PROBLEMA XV.
[133.] PROBLEMA XVI.
[134.] PROBLEMA XVII.
[135.] PROBLEMA XVIII.
[136.] PROBLEMA XIX.
[137.] PROBLEMA XX.
[138.] PROBLEMA XXI.
[139.] PROBLEMA XXII.
[140.] PROBLEMA XXIII.
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            ſtiganda ſunt ſegmenta BD, CD, inter perpendicularem, perea, quæ lib. </s>
            <s xml:id="echoid-s6378" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6379" xml:space="preserve">cap.
              <lb/>
            </s>
            <s xml:id="echoid-s6380" xml:space="preserve">
              <note position="left" xlink:label="note-192-01" xlink:href="note-192-01a" xml:space="preserve">Segmenta ba-
                <lb/>
              ſis, quæ à per-
                <lb/>
              pendiculari
                <lb/>
              abſcinduntur,
                <lb/>
              quo pacto cog-
                <lb/>
              noſcatur.</note>
            3. </s>
            <s xml:id="echoid-s6381" xml:space="preserve">Nũ. </s>
            <s xml:id="echoid-s6382" xml:space="preserve">9. </s>
            <s xml:id="echoid-s6383" xml:space="preserve">ſcrip ſimus, hac ratione. </s>
            <s xml:id="echoid-s6384" xml:space="preserve">Fiat vt latus BC, in quod cadit perpendicularis
              <lb/>
            AD, (Semper autem eſſet demittenda perpendi-
              <lb/>
              <figure xlink:label="fig-192-01" xlink:href="fig-192-01a" number="122">
                <image file="192-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/192-01"/>
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            cularis in maximumlatus, vtintra triangulum ca-
              <lb/>
            deret) ad ſummam aliorum duorum laterum A B,
              <lb/>
            AC, nimirum vt 21. </s>
            <s xml:id="echoid-s6385" xml:space="preserve">ad 27. </s>
            <s xml:id="echoid-s6386" xml:space="preserve">ita differentia eorundem
              <lb/>
              <handwritten xlink:label="hd-192-2" xlink:href="hd-192-2a" number="59"/>
            laterum, videlicet 7. </s>
            <s xml:id="echoid-s6387" xml:space="preserve">ad aliud. </s>
            <s xml:id="echoid-s6388" xml:space="preserve">Producetur enim
              <lb/>
            numerus 9. </s>
            <s xml:id="echoid-s6389" xml:space="preserve">(qui quoniam minor eſt latere BC, ar-
              <lb/>
            gumento eſt, perpendicularem intra triangulum
              <lb/>
            cadere. </s>
            <s xml:id="echoid-s6390" xml:space="preserve">Si enim maior eſſet, caderet extra, vt prop oſ. </s>
            <s xml:id="echoid-s6391" xml:space="preserve">9. </s>
            <s xml:id="echoid-s6392" xml:space="preserve">noſtrorum triangulo-
              <lb/>
            rumrectil. </s>
            <s xml:id="echoid-s6393" xml:space="preserve">oſtendimus) qui ablatus ex latere BC, id eſt, ex 21. </s>
            <s xml:id="echoid-s6394" xml:space="preserve">relinquit 12. </s>
            <s xml:id="echoid-s6395" xml:space="preserve">cuius
              <lb/>
            ſemiſsis 6. </s>
            <s xml:id="echoid-s6396" xml:space="preserve">dabit minus ſegmentum B D, prope minus latus AB, quę eadem ſe-
              <lb/>
            miſsis ex latere BC, ſubtracta reliquum faciet maius ſegmentum C D, nimirum
              <lb/>
            15. </s>
            <s xml:id="echoid-s6397" xml:space="preserve">iuxta maius latus AC.</s>
            <s xml:id="echoid-s6398" xml:space="preserve"/>
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          <handwritten number="60"/>
          <p>
            <s xml:id="echoid-s6399" xml:space="preserve">
              <emph style="sc">Sit</emph>
            rurſus triangulum ABD, cuius latus AB, 12. </s>
            <s xml:id="echoid-s6400" xml:space="preserve">AD, 11. </s>
            <s xml:id="echoid-s6401" xml:space="preserve">& </s>
            <s xml:id="echoid-s6402" xml:space="preserve">B D, 20. </s>
            <s xml:id="echoid-s6403" xml:space="preserve">demit-
              <lb/>
            tenda autem ſit perpendicularis ex D, ad AB. </s>
            <s xml:id="echoid-s6404" xml:space="preserve">Fiat, vtlatus AB, 12. </s>
            <s xml:id="echoid-s6405" xml:space="preserve">ad ſummam
              <lb/>
            aliorum duorum 31. </s>
            <s xml:id="echoid-s6406" xml:space="preserve">ita differentia eorundem, ni-
              <lb/>
              <figure xlink:label="fig-192-02" xlink:href="fig-192-02a" number="123">
                <image file="192-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/192-02"/>
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            mirum 9. </s>
            <s xml:id="echoid-s6407" xml:space="preserve">ad aliud. </s>
            <s xml:id="echoid-s6408" xml:space="preserve">Producetur enim numerus
              <lb/>
            23 {1/4}. </s>
            <s xml:id="echoid-s6409" xml:space="preserve">(qui quo niam maior eſt latere AB, argumen-
              <lb/>
            to eſt, perpendicularem cadere extra triangulum,
              <lb/>
            angulumque A, eſſe obtuſum,) ex quo latus A B,
              <lb/>
            12. </s>
            <s xml:id="echoid-s6410" xml:space="preserve">ſubtractum, relinquit, 11 {1/4}. </s>
            <s xml:id="echoid-s6411" xml:space="preserve">Huius autem nu-
              <lb/>
            meri ſemiſsis 5 {5/8}. </s>
            <s xml:id="echoid-s6412" xml:space="preserve">dabit ſegmentum exterius A C,
              <lb/>
            inter perpendicularem, & </s>
            <s xml:id="echoid-s6413" xml:space="preserve">angulum obtuſum: </s>
            <s xml:id="echoid-s6414" xml:space="preserve">eademque ſemiſsis addita lateri
              <lb/>
            AB, efficiet aliud ſegmentum BC, inter perpendicularem, & </s>
            <s xml:id="echoid-s6415" xml:space="preserve">angulum acutum
              <lb/>
            17 {5/8}. </s>
            <s xml:id="echoid-s6416" xml:space="preserve">Atque hæc ratio expeditiſsima eſt.</s>
            <s xml:id="echoid-s6417" xml:space="preserve"/>
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          <handwritten number="61"/>
          <p>
            <s xml:id="echoid-s6418" xml:space="preserve">A
              <emph style="sc">LITER.</emph>
            Sit ducenda perpendicularis ad maximum latus B C, in priori
              <lb/>
            triangulo ABC, quæ neceſſario cadet intra triangulum; </s>
            <s xml:id="echoid-s6419" xml:space="preserve"> propterea, quod
              <note symbol="a" position="left" xlink:label="note-192-02" xlink:href="note-192-02a" xml:space="preserve">18. primi.</note>
            gulus A, maior eſt vtrolibet BC; </s>
            <s xml:id="echoid-s6420" xml:space="preserve">ac proindevterque horum acutus eſt. </s>
            <s xml:id="echoid-s6421" xml:space="preserve">
              <note symbol="b" position="left" xlink:label="note-192-03" xlink:href="note-192-03a" xml:space="preserve">13. ſecundi.</note>
            niam autem quadratum rectę A B, minus eſt quadratis rectarum A C, BC, re-
              <lb/>
              <handwritten xlink:label="hd-192-3" xlink:href="hd-192-3a" number="62"/>
              <handwritten xlink:label="hd-192-3" xlink:href="hd-192-3a" number="63"/>
            ctangulo bis comprehenſo ſub BC, & </s>
            <s xml:id="echoid-s6422" xml:space="preserve">ſegmento CD, inter C, & </s>
            <s xml:id="echoid-s6423" xml:space="preserve">perpendicula-
              <lb/>
            rem: </s>
            <s xml:id="echoid-s6424" xml:space="preserve">ſi quadratum rectę AB, 100. </s>
            <s xml:id="echoid-s6425" xml:space="preserve">detrahatur ex ſumma quadratorum rectarum
              <lb/>
            A C, B C, id eſt ex 730. </s>
            <s xml:id="echoid-s6426" xml:space="preserve">reliquum fiet rectangulum 630. </s>
            <s xml:id="echoid-s6427" xml:space="preserve">bis comprehenſum
              <lb/>
            ſub B C, & </s>
            <s xml:id="echoid-s6428" xml:space="preserve">ſegmento CD, inter C, & </s>
            <s xml:id="echoid-s6429" xml:space="preserve">perpendicularem. </s>
            <s xml:id="echoid-s6430" xml:space="preserve">Quare eius ſemiſ-
              <lb/>
            ſis 315. </s>
            <s xml:id="echoid-s6431" xml:space="preserve">æqualis erit rectangulo illi ſemel ſumpto: </s>
            <s xml:id="echoid-s6432" xml:space="preserve">ac proinde hoc rectangu-
              <lb/>
            lo 315. </s>
            <s xml:id="echoid-s6433" xml:space="preserve">diuiſo per latus B C, 21. </s>
            <s xml:id="echoid-s6434" xml:space="preserve">dabit Quotiens 15. </s>
            <s xml:id="echoid-s6435" xml:space="preserve">ſegmentum C D, prope
              <lb/>
            angulum acutum C, cui opponitur latus A B, cuius quadratum ex ſumma
              <lb/>
            reliquorum quadratorum detractum fuit. </s>
            <s xml:id="echoid-s6436" xml:space="preserve">Ablato autem ſegmento C D, 15.
              <lb/>
            </s>
            <s xml:id="echoid-s6437" xml:space="preserve">ex latere B C, 21. </s>
            <s xml:id="echoid-s6438" xml:space="preserve">remanebit alterum ſegmentum B D, 6. </s>
            <s xml:id="echoid-s6439" xml:space="preserve">Eodem pacto,
              <note symbol="c" position="left" xlink:label="note-192-04" xlink:href="note-192-04a" xml:space="preserve">13. ſecundi.</note>
            quadratum rectę A C, minus eſt quadratis rectarum A B, B C, rectangulo
              <lb/>
              <handwritten xlink:label="hd-192-3" xlink:href="hd-192-3a" number="62"/>
              <handwritten xlink:label="hd-192-3" xlink:href="hd-192-3a" number="63"/>
            bis comprehenſo ſub CB, & </s>
            <s xml:id="echoid-s6440" xml:space="preserve">ſegmento B D, inter B, & </s>
            <s xml:id="echoid-s6441" xml:space="preserve">perpendicularem: </s>
            <s xml:id="echoid-s6442" xml:space="preserve">ſi
              <lb/>
            quadratum rectę A C, 289. </s>
            <s xml:id="echoid-s6443" xml:space="preserve">ſubducatur ex ſumma 541. </s>
            <s xml:id="echoid-s6444" xml:space="preserve">quadratorum recta-
              <lb/>
            rum A B, B C, reliquum fiet rectangulum 252. </s>
            <s xml:id="echoid-s6445" xml:space="preserve">comprehenſum bis ſub C B,
              <lb/>
            & </s>
            <s xml:id="echoid-s6446" xml:space="preserve">ſegmento B D, inter B, & </s>
            <s xml:id="echoid-s6447" xml:space="preserve">perpendicularem. </s>
            <s xml:id="echoid-s6448" xml:space="preserve">Quare eius ſemiſsis 126. </s>
            <s xml:id="echoid-s6449" xml:space="preserve">æ-
              <lb/>
            qualis erit illi rectangulo ſemel ſumpto: </s>
            <s xml:id="echoid-s6450" xml:space="preserve">ac proinde hoc rectangulo 126. </s>
            <s xml:id="echoid-s6451" xml:space="preserve">di-
              <lb/>
            uiſo per latus CB, 21. </s>
            <s xml:id="echoid-s6452" xml:space="preserve">dabit Quotiens 6. </s>
            <s xml:id="echoid-s6453" xml:space="preserve">ſegmentum BD, iuxta acutum angu-
              <lb/>
            lum B, cui latus A C, quadrati ex duobus aliis quadratis detracti opponitur.</s>
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