Clavius, Christoph, Geometria practica

Table of contents

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[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.
[141.] PROBLEMA XXIV.
[142.] PROBLEMA XXV.
[143.] SCHOLIVM.
[144.] PROBLEMA XXVI.
[145.] PROBLEMA XXVII.
[146.] PROBLEMA XXVIII.
[147.] PROBLEMA XXIX.
[148.] PROBLEMA XXX.
[149.] PROBLEMA XXXI.
[150.] PROBLEMA XXXII.
[151.] PROBLEMA XXXIII.
[152.] PROBLEMA XXXIV.
[153.] PROBLEMA XXXV.
[154.] PROBLEMA XXXVI.
[155.] PROBLEMA XXXVII.
[156.] PROBLEMA XXXVIII.
[157.] PROBLEMA XXXIX.
[158.] ALITER.
[159.] ALITER.
[160.] PROBLEMA XL.
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          <pb o="106" file="136" n="136" rhead="GEOMETR. PRACT."/>
          <p>
            <s xml:id="echoid-s4115" xml:space="preserve">procreabitur diſtantia quæſita AF, in partibus differentiæ ſtationum Aa,</s>
          </p>
          <p>
            <s xml:id="echoid-s4116" xml:space="preserve">4. </s>
            <s xml:id="echoid-s4117" xml:space="preserve">
              <emph style="sc">Hic</emph>
            etiam ſi forte in vna ſtatione linea fiduciæ, aut filum perpendiculi,
              <lb/>
            tranſierit per punctum, C, aſſumendum erit vellatus vmbræ rectæ, vel verſæ, vt
              <lb/>
            Num. </s>
            <s xml:id="echoid-s4118" xml:space="preserve">6. </s>
            <s xml:id="echoid-s4119" xml:space="preserve">præcedentis problematis dictum eſt.</s>
            <s xml:id="echoid-s4120" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4121" xml:space="preserve">ALTITVDINEM cuiuslibet rei erectæ per eius diſtantiam ab ocu-
              <lb/>
            lo menſoris, beneficio quadrati coniicere.</s>
            <s xml:id="echoid-s4122" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div265" type="section" level="1" n="115">
          <head xml:id="echoid-head118" xml:space="preserve">PROBLEMA V.</head>
          <figure number="64">
            <image file="136-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/136-01"/>
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            <s xml:id="echoid-s4123" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4124" xml:space="preserve">
              <emph style="sc">Sit</emph>
            altitudo conijcienda GL, vel ML, vel IL, ad Horizontem perpen-
              <lb/>
            dicularis. </s>
            <s xml:id="echoid-s4125" xml:space="preserve">Statura menſoris, vel aliqua alia menſura nota ſit F L, vel A K, pare-
              <lb/>
            turque planum Horizonti parallelum A F, in quo quadratum erigatur, cuius la-
              <lb/>
            tus A D, intelligatur productum occurrens altitudini in F. </s>
            <s xml:id="echoid-s4126" xml:space="preserve">Inſpecto cacumine
              <lb/>
            I, ſecet primum dioptra vel filum perpendiculi latus C D, vmbræ verſæ in E.
              <lb/>
            </s>
            <s xml:id="echoid-s4127" xml:space="preserve">quod accidet, quando diſtantia A F, maior eſt, altitudine F I, vt problemate @. </s>
            <s xml:id="echoid-s4128" xml:space="preserve">
              <lb/>
            Num. </s>
            <s xml:id="echoid-s4129" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4130" xml:space="preserve">oſtendimus. </s>
            <s xml:id="echoid-s4131" xml:space="preserve">Quoniam igitur triangulum ADE, triangulo AFI, æqui-
              <lb/>
            angulum eſt, vtibidem monſtratum eſt;</s>
            <s xml:id="echoid-s4132" xml:space="preserve"> erit vt AD, ad DE, ita AF, ad FI. </s>
            <s xml:id="echoid-s4133" xml:space="preserve">
              <note symbol="a" position="left" xlink:label="note-136-01" xlink:href="note-136-01a" xml:space="preserve">4. ſexti.</note>
            obrem ſi fiat,</s>
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          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt lat{us} qua- \\ drati 1000. # Ad vmbram \\ verſam DE: # Ita diſtantia A F, vel data, vel \\ inuenta per probl. 3. aut 4. # AD F I
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s4134" xml:space="preserve">patefacta erit altitudo F I, in partibus diſtantiæ A F, quæ ſi data non eſt, exqui-
              <lb/>
            renda erit vel per problema 3. </s>
            <s xml:id="echoid-s4135" xml:space="preserve">vel 4. </s>
            <s xml:id="echoid-s4136" xml:space="preserve">Et ſi ad F I, adijcietur menſura, vel ſtatura
              <lb/>
            menſoris F L, tota altitudo propoſita IL, nota fiet,</s>
          </p>
          <p>
            <s xml:id="echoid-s4137" xml:space="preserve">2. </s>
            <s xml:id="echoid-s4138" xml:space="preserve">
              <emph style="sc">Deinde</emph>
            linea fiduciæ tranſeat per punctum C. </s>
            <s xml:id="echoid-s4139" xml:space="preserve">quod fiet, quando di-
              <lb/>
              <note symbol="b" position="left" xlink:label="note-136-03" xlink:href="note-136-03a" xml:space="preserve">ſchol. 34.
                <lb/>
              primi.</note>
            ſtantia AF, altitudini FM, æqualis eſt;</s>
            <s xml:id="echoid-s4140" xml:space="preserve"> quod tunc angulus CAD, ſemirectus ſit, ac proinde & </s>
            <s xml:id="echoid-s4141" xml:space="preserve">reliquus M, in triangulo F A M. </s>
            <s xml:id="echoid-s4142" xml:space="preserve"> Ideoque latera AF, FM,
              <note symbol="c" position="left" xlink:label="note-136-04" xlink:href="note-136-04a" xml:space="preserve">6. primi.</note>
            lia ſint. </s>
            <s xml:id="echoid-s4143" xml:space="preserve">Quanta ergo eſt diſtantia AF, quæ vel data eſt, velinuenienda per pro-
              <lb/>
            blema 3. </s>
            <s xml:id="echoid-s4144" xml:space="preserve">vel 4. </s>
            <s xml:id="echoid-s4145" xml:space="preserve">tanta erit altitudo F M, cui addita F L, nota patefaciet totam al-
              <lb/>
            titudinem M L.</s>
            <s xml:id="echoid-s4146" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4147" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4148" xml:space="preserve">
              <emph style="sc">Postremo</emph>
            interſeceturvmbræ rectæ latus in H. </s>
            <s xml:id="echoid-s4149" xml:space="preserve">quod eueniet, </s>
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