Clavius, Christoph, Geometria practica

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            <s xml:id="echoid-s15044" xml:space="preserve">
              <pb o="321" file="351" n="351" rhead="LIBER SEPTIMVS."/>
            ribus AD, BC, angulos rectos effi ciat, ſecabunt ſe mutuò continuè ſemidiame-
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            ter in circumferentia D B, circumacta, & </s>
            <s xml:id="echoid-s15045" xml:space="preserve">recta D C, deorſum lata, in punctis,
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            quæ lineam Quadratricem deſcribent: </s>
            <s xml:id="echoid-s15046" xml:space="preserve">hoc eſt, per quæ linea Quadratrix
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            tranſibit, cuiuſmodi eſt linea inflexa DE. </s>
            <s xml:id="echoid-s15047" xml:space="preserve">Sed quia duo iſti motus vniformes,
              <lb/>
            quorum vnus per circumferentiam D B, fit, & </s>
            <s xml:id="echoid-s15048" xml:space="preserve">alter per lineas rectas D A, C B,
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            effici non poſſunt, niſi proportio habeatur cir-
              <lb/>
              <figure xlink:label="fig-351-01" xlink:href="fig-351-01a" number="241">
                <image file="351-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/351-01"/>
              </figure>
            cularis lineæ ad rectam, meritò à Pappo deſcri-
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            ptio hæc repræhenditur: </s>
            <s xml:id="echoid-s15049" xml:space="preserve">quippe cum ignota
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            adhuc ſit ea proportio, & </s>
            <s xml:id="echoid-s15050" xml:space="preserve">quæ per hanc lineam
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            inueſtiganda proponatur. </s>
            <s xml:id="echoid-s15051" xml:space="preserve">Quare nos Geome-
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            tricè eandem lineam Quadratricem deſcribe-
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            mus hoc modo. </s>
            <s xml:id="echoid-s15052" xml:space="preserve">Arcus B D, in quotuis partes
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            æquales diuidatur, & </s>
            <s xml:id="echoid-s15053" xml:space="preserve">latus vtrumque AD, BC,
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            in totidem æquales partes. </s>
            <s xml:id="echoid-s15054" xml:space="preserve">Facillima diuiſio
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            erit, ſi & </s>
            <s xml:id="echoid-s15055" xml:space="preserve">arcus D B, & </s>
            <s xml:id="echoid-s15056" xml:space="preserve">vtrumque latus AD, BC,
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            ſecetur primum bifariam, deinde vtraque ſe-
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            miſsis iterum bifariam, atq; </s>
            <s xml:id="echoid-s15057" xml:space="preserve">ita deinceps, quan-
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            tum libuerit. </s>
            <s xml:id="echoid-s15058" xml:space="preserve">Quo autem plures extiterint diuiſiones, eo accuratius Quadratrix
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            linea deſcribetur. </s>
            <s xml:id="echoid-s15059" xml:space="preserve">Nos ad confuſionem vitandam ſecuimus tam arcum D B,
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            quam duo latera AD, BC, in octo tantum partes æquales.</s>
            <s xml:id="echoid-s15060" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s15061" xml:space="preserve">
              <emph style="sc">Deinde</emph>
            bina puncta laterum AD, BC, æqualiter diſtantia à latere DC, vel
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            AB, coniungantur lineis rectis occultis, atque ex centro A, aliæ rectæ occultæ ad
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            ſingula diuiſionũ puncta Quadrantis DB, extendantur. </s>
            <s xml:id="echoid-s15062" xml:space="preserve">Vbi enim hærectæ prio-
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            res rectas interſecabunt, prima primam, ſecunda ſecundam, &</s>
            <s xml:id="echoid-s15063" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15064" xml:space="preserve">perea puncta
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            Quadratrix linea congruenter ducenda eſt, ita vtnon ſit ſinuoſa, ſed æquabili-
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            liter ſemper progrediatur nullum effi ciens gibbum, autangulum alicubi: </s>
            <s xml:id="echoid-s15065" xml:space="preserve">qua-
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            lis eſt linea inflexa D E, ſecans ſemidiametrum AB, in E.</s>
            <s xml:id="echoid-s15066" xml:space="preserve"/>
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            <s xml:id="echoid-s15067" xml:space="preserve">6. </s>
            <s xml:id="echoid-s15068" xml:space="preserve">
              <emph style="sc">Sed</emph>
            quia punctum E, in latere A B, inuenire Geometricè non poteſt,
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            cum ibi omnis ſectio rectarum ceſſet: </s>
            <s xml:id="echoid-s15069" xml:space="preserve">vt illud ſine notabili errore, quiſcilicet
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            ſub ſenſum cadat, reperiamus: </s>
            <s xml:id="echoid-s15070" xml:space="preserve">vtemur hoc artificio: </s>
            <s xml:id="echoid-s15071" xml:space="preserve">Infimam partem A F, la-
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            teris AD, ſi ſatis exigua non ſit, ſecabimus bifariam continuè, donec infima par-
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            ticula ſit perexigua: </s>
            <s xml:id="echoid-s15072" xml:space="preserve">Eodemque modo infimam partem B I, arcus D B, bifariam
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            continuè ſecabimus, donectot fiant ſub diuiſiones, quot in parte A F, factæ ſunt,
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            vt pa
              <unsure/>
            rticula B K, talis pars ſit totius arcus D B, qualis pars eſt A G, totius lateris
              <lb/>
            AD. </s>
            <s xml:id="echoid-s15073" xml:space="preserve">Particulæ deinde A G, æquales abſcindemus BL, BN, AM, ducemuſque
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            rectas occultas GL, MN. </s>
            <s xml:id="echoid-s15074" xml:space="preserve">Ducta verò ex A, centro recta occulta AK, quæ ſecet
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            GL, in H, puncto, quod accuratiſsimè notetur (adhibito videlicet Lemmate
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            Probl. </s>
            <s xml:id="echoid-s15075" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15076" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s15077" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15078" xml:space="preserve">vt concurſus H, quam ex quiſitiſsimè reperiatur) ſumemus ipſi
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            GH, æqualem M P. </s>
            <s xml:id="echoid-s15079" xml:space="preserve">Si enim Quadratricem vſque ad H, deſcriptam continua-
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            bimus æquabili, atque vniformi extenſione vſq; </s>
            <s xml:id="echoid-s15080" xml:space="preserve">ad P, ſecabit Quadratrix li-
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            nea latus AB, in E, puncto, quod quæritur. </s>
            <s xml:id="echoid-s15081" xml:space="preserve">Nam propter paruam rectarum GH,
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            A E, M P, inter ſe diſtantiam efficitur, vt fermè ſint æquales, licet Geometri-
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            cèloquendo recta A E, ſemper maior ſit aliquanto, quantumuis parum eæ re-
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            ctæ inter ſe diſtent: </s>
            <s xml:id="echoid-s15082" xml:space="preserve">ſed exceſlus ille circino deprehendi non poteſt: </s>
            <s xml:id="echoid-s15083" xml:space="preserve">adeò vt
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            arcus circuli ex A, per H, P, deſcriptus verum punctum E, quod ad ſenſum at-
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            tinet, indicare videatur. </s>
            <s xml:id="echoid-s15084" xml:space="preserve">Id quod etiam in circumferentia circuli contingit.</s>
            <s xml:id="echoid-s15085" xml:space="preserve"/>
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