Clavius, Christoph, Geometria practica

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          <p>
            <s xml:id="echoid-s5453" xml:space="preserve">
              <pb o="140" file="170" n="170" rhead="GEOMETR. PRACT."/>
            modetur virgula C D, ita vt circa B, deprimi aut eleuari poſsit, donec radius vi-
              <lb/>
            ſualis per CD, tranſiens occurrat extremo E, diſtantiæ A E, metiendæ. </s>
            <s xml:id="echoid-s5454" xml:space="preserve">Deinde
              <lb/>
            virgula C D, manente immobili, ne angulus D B A, mutetur, vertatur baculus
              <lb/>
            AC, ad rectos ſemper angulos Horizonti inſiſtens, donec radius viſualis per e-
              <lb/>
            andem virgulam CD, incedens occurrat plano alicui prope flumen, aut ſtagnũ,
              <lb/>
            in quo nimirum menſor exiſtit, & </s>
            <s xml:id="echoid-s5455" xml:space="preserve">quod menſuraripoſsit, in puncto F. </s>
            <s xml:id="echoid-s5456" xml:space="preserve">Quoniam
              <lb/>
            ergo duo anguli A, B, trianguli ABE, duobus angulis A, B, trianguli ABF, æqua-
              <lb/>
            les ſunt, & </s>
            <s xml:id="echoid-s5457" xml:space="preserve">latus AB, commune: </s>
            <s xml:id="echoid-s5458" xml:space="preserve"> erunt latera AE, AF, æqualia: </s>
            <s xml:id="echoid-s5459" xml:space="preserve">atque
              <note symbol="a" position="left" xlink:label="note-170-01" xlink:href="note-170-01a" xml:space="preserve">26. primi.</note>
            ſi AF, in plano per aliquam menſuram efficiatur nota; </s>
            <s xml:id="echoid-s5460" xml:space="preserve">diſtantia quo que AE, co-
              <lb/>
            gnita erit.</s>
            <s xml:id="echoid-s5461" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s5462" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5463" xml:space="preserve">
              <emph style="sc">Alii</emph>
            hoc ipſum efficiunt ſine baculo, hac ratione. </s>
            <s xml:id="echoid-s5464" xml:space="preserve">Erigunt ſe ad angu-
              <lb/>
            losrectos cum Horizonte: </s>
            <s xml:id="echoid-s5465" xml:space="preserve">Deinde deprimunt pileum, qui ſit aliquantulũ la-
              <lb/>
            tus, donecradius viſualis per extremitatem pilei excurrens in cidat in terminum
              <lb/>
            E, diſtantiæ AE, metiendæ: </s>
            <s xml:id="echoid-s5466" xml:space="preserve">Pileo vero immobili manente, vertunt ſe verſus pla-
              <lb/>
            num aliquod menſurabile, notantque in eo punctum F, in quo radius viſualis
              <lb/>
            ipſi plano occurrit. </s>
            <s xml:id="echoid-s5467" xml:space="preserve">Nam rurſus longitudo AF, quæ per menſuram aliquam co-
              <lb/>
            gnoſcenda eſt, diſtantiæ A E, propoſitæ æqualis eſt: </s>
            <s xml:id="echoid-s5468" xml:space="preserve">propterea quod ſtatura
              <lb/>
            menſoris fungitur tunc munere baculi AB, & </s>
            <s xml:id="echoid-s5469" xml:space="preserve">pileus depreſſus vices gerit virgu-
              <lb/>
            læ C D, vt conſtat.</s>
            <s xml:id="echoid-s5470" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5471" xml:space="preserve">ALTITVDINEM cuiuſque rei erectæ ex eius vmbra, quam Sole lu-
              <lb/>
            cente proiicit, ſi nota fuerit, per quadratum deprehendere.</s>
            <s xml:id="echoid-s5472" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div365" type="section" level="1" n="152">
          <head xml:id="echoid-head155" xml:space="preserve">PROBLEMA XXXIV.</head>
          <p>
            <s xml:id="echoid-s5473" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5474" xml:space="preserve">Hoc problema à quinto non differt, niſi quòd hic vtimur radio Solis
              <lb/>
            pro radio viſuali, & </s>
            <s xml:id="echoid-s5475" xml:space="preserve">longitudine vmbræ, quam altitudo, Sole lucente, proiicit,
              <lb/>
            pro diſtantia à menſore ad altitu dinem vſque. </s>
            <s xml:id="echoid-s5476" xml:space="preserve">Sit ergo altitudo FG, vel FI, vel
              <lb/>
            FM, eiuſque vmbra proiecta FA. </s>
            <s xml:id="echoid-s5477" xml:space="preserve">Dirigatur qua dratum verſus Solem (licet hoc
              <lb/>
            non fiat è directo altitudinis) & </s>
            <s xml:id="echoid-s5478" xml:space="preserve">tranſeunte radio Solis per foramina pinnaci-
              <lb/>
            diorum, notetur quanta vmbra ſiue recta, ſiue verſa à dioptra, vel filo perpen-
              <lb/>
            diculi in quadrato abſcindatur. </s>
            <s xml:id="echoid-s5479" xml:space="preserve">Nam ita ſeſe ha-
              <lb/>
              <figure xlink:label="fig-170-01" xlink:href="fig-170-01a" number="102">
                <image file="170-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/170-01"/>
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            bebit vmbra recta H B, in quadrato ad latus A B,
              <lb/>
            vt vmbra proiecta AF, ad altitudinem F G. </s>
            <s xml:id="echoid-s5480" xml:space="preserve">Item
              <lb/>
            ea eſt proportio lateris A D, ad vmbram verſam
              <lb/>
            DE, in quadrato, quæ vmbræ proiectæ AF, ad alti-
              <lb/>
            tudinem FI. </s>
            <s xml:id="echoid-s5481" xml:space="preserve">Denique dio ptra, vel filo perpendi-
              <lb/>
            culi per punctum C, incedente, tanta erit vmbra
              <lb/>
            proiecta A F, quanta eſt altitudo F M. </s>
            <s xml:id="echoid-s5482" xml:space="preserve">quæ omnia
              <lb/>
            in problemate 5. </s>
            <s xml:id="echoid-s5483" xml:space="preserve">demonſtrata ſunt. </s>
            <s xml:id="echoid-s5484" xml:space="preserve">Igitur ſi fiat.</s>
            <s xml:id="echoid-s5485" xml:space="preserve"/>
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