Clavius, Christoph, Geometria practica

Table of contents

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[161.] ALITER.
[162.] PROBLEMA XLI.
[163.] PROBLEMA XLII.
[164.] PROBLEMA XLIII.
[165.] PROBLEMA XLIV.
[166.] SCHOLIVM.
[167.] PROBLEMA XLV.
[168.] FINIS LIBRI TERTII.
[169.] GEOMETRIÆ PRACTICÆ LIBER QVARTVS.
[170.] AREAS
[171.] DE AREA RECTANGVLORVM Capvt I.
[172.] DE AREA TRIANGVLORVM Capvt II.
[173.] DE AREA QVADRILATERORVM non rectangulorum. Capvt III.
[174.] DE AREA MVLTIL ATERARVM figurarum irregularium. Capvt IV.
[175.] DE AREA MVLTILATERA-rum figurarum regularium. Capvt V.
[176.] De dimenſione circuli ex Archimede. Capvt VI.
[177.] PROPOSITIO I.
[178.] SCHOLIVM.
[179.] PROPOSITIO II.
[180.] COROLLARIVM.
[181.] PROPOSITIO III.
[182.] DE AREA CIRCVLI, INVENTIONE-que circumferentiæ ex diametro, & diametri ex circumfetentia. Capvt VII.
[184.] II.
[185.] III.
[186.] IIII.
[187.] PROPOSITIO I.
[188.] PROPOSITIO II.
[189.] PROPOSITIO III.
[190.] I. EX diametro aream circuli vera maiorem inueſtigare.
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          <head xml:id="echoid-head149" xml:space="preserve">PROBLEMA XXVIII.</head>
          <p>
            <s xml:id="echoid-s5304" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5305" xml:space="preserve">Hoc etiam aliud nihil eſt, niſi altitu dinem quampiam ex eius ſummo fa-
              <lb/>
            ſtigio per duas ſtationes in haſta aliqua erecta dimetiri, vt in problem. </s>
            <s xml:id="echoid-s5306" xml:space="preserve">9. </s>
            <s xml:id="echoid-s5307" xml:space="preserve">factum
              <lb/>
            eſt, & </s>
            <s xml:id="echoid-s5308" xml:space="preserve">in præcedenti problemate repetitum. </s>
            <s xml:id="echoid-s5309" xml:space="preserve">Sit enim vallis inter duos montes
              <lb/>
            AB, NG, poſita, & </s>
            <s xml:id="echoid-s5310" xml:space="preserve">terminus ipſius C, ex monte A B, conſpici poſsit, Erecta ha-
              <lb/>
              <figure xlink:label="fig-166-01" xlink:href="fig-166-01a" number="97">
                <image file="166-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/166-01"/>
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            ſta A E, in qua duæ ſtationes oculimenſoris fieri poſsint in D, E, ſi reliqua con-
              <lb/>
            ſtruantur, vt in problemate 24. </s>
            <s xml:id="echoid-s5311" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5312" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5313" xml:space="preserve">cuius hic figuram iterauimus; </s>
            <s xml:id="echoid-s5314" xml:space="preserve">inueſtigabi-
              <lb/>
            tur recta EB, vtin 1. </s>
            <s xml:id="echoid-s5315" xml:space="preserve">figura præcedentis probl. </s>
            <s xml:id="echoid-s5316" xml:space="preserve">recta EB, fuit inuenta. </s>
            <s xml:id="echoid-s5317" xml:space="preserve">Etſi dema-
              <lb/>
            tur portio haſtæ A E, altitudo montis A B, vel profunditas vallis H C, reliqua
              <lb/>
            fiet nota.</s>
            <s xml:id="echoid-s5318" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5319" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5320" xml:space="preserve">
              <emph style="sc">Descensvs</emph>
            autem obliquus IC, ita colligetur. </s>
            <s xml:id="echoid-s5321" xml:space="preserve">Per vmbram à dioptra
              <lb/>
            ad C, directa abſciſſam eliciatur angulus BDC, ex 1. </s>
            <s xml:id="echoid-s5322" xml:space="preserve">problemate, hoc eſt, angu-
              <lb/>
            lus CIM, qui ei æqualis eſt, externus interno; </s>
            <s xml:id="echoid-s5323" xml:space="preserve">eritque proinde reliquus
              <note symbol="a" position="left" xlink:label="note-166-01" xlink:href="note-166-01a" xml:space="preserve">29. primi.</note>
            lus I C M, notus, vtpote illius complementum. </s>
            <s xml:id="echoid-s5324" xml:space="preserve">Quocirca cum in triangulo
              <lb/>
            C I M, anguli acuti cogniti ſint, vna cum latere I M, nuper inuento; </s>
            <s xml:id="echoid-s5325" xml:space="preserve"> baſis I
              <note symbol="b" position="left" xlink:label="note-166-02" xlink:href="note-166-02a" xml:space="preserve">5. triang. re-
                <lb/>
              ctil.</note>
            ignorari non poterit.</s>
            <s xml:id="echoid-s5326" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5327" xml:space="preserve">
              <emph style="sc">Sed</emph>
            hæc omnia facilius per vnicam ſtationem inueſtigabuntur, ſi in D, pun-
              <lb/>
            cto haſtæ quadratum bis applicetur, vt in præcedenti problemate Num. </s>
            <s xml:id="echoid-s5328" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5329" xml:space="preserve">& </s>
            <s xml:id="echoid-s5330" xml:space="preserve">in
              <lb/>
            ſcholio problem. </s>
            <s xml:id="echoid-s5331" xml:space="preserve">9. </s>
            <s xml:id="echoid-s5332" xml:space="preserve">factum eſt in puncto A, &</s>
            <s xml:id="echoid-s5333" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5334" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5335" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5336" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi terminus C, non cernatur, eligatur aliquod ſignum K, in valle,
              <lb/>
            quod ex ſtationibus D, & </s>
            <s xml:id="echoid-s5337" xml:space="preserve">E, appareat. </s>
            <s xml:id="echoid-s5338" xml:space="preserve">Ita enim per problema 9. </s>
            <s xml:id="echoid-s5339" xml:space="preserve">vel potius per
              <lb/>
            eius ſcholium, eadem altitudo I M, vel H C, inuenietur.</s>
            <s xml:id="echoid-s5340" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s5341" xml:space="preserve">
              <emph style="sc">Immo</emph>
            ſi in plano vallis duæ ſtationes commode fieri poſsint, percipietur
              <lb/>
            ex illis eadem altitudo I M, per problema 6. </s>
            <s xml:id="echoid-s5342" xml:space="preserve">vel per ſcholium problem. </s>
            <s xml:id="echoid-s5343" xml:space="preserve">7. </s>
            <s xml:id="echoid-s5344" xml:space="preserve">De-
              <lb/>
            ſcenſus verò obliquus IC, tanquam interuallũ inter duo ſigna I, & </s>
            <s xml:id="echoid-s5345" xml:space="preserve">C, per pro-
              <lb/>
            blema 16. </s>
            <s xml:id="echoid-s5346" xml:space="preserve">indagandus erit.</s>
            <s xml:id="echoid-s5347" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5348" xml:space="preserve">4. </s>
            <s xml:id="echoid-s5349" xml:space="preserve">
              <emph style="sc">Eandem</emph>
            denique profunditatem C H, venarilicebit ex altiore monte
              <lb/>
            N G, ſi modo terminus C, minoris montis, vel aliquod ſignum in valle appare-
              <lb/>
            at ex cacumine N: </s>
            <s xml:id="echoid-s5350" xml:space="preserve">non aliter, quam in problemate 22. </s>
            <s xml:id="echoid-s5351" xml:space="preserve">vel 23. </s>
            <s xml:id="echoid-s5352" xml:space="preserve">minorem </s>
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