Clavius, Christoph, Geometria practica

Table of handwritten notes

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            <s xml:id="echoid-s4946" xml:space="preserve">
              <pb o="127" file="157" n="157" rhead="LIBER TERTIVS."/>
            nacidiorum conſpiciatur) vertatur dioptra, donec per eam punctum quo que
              <lb/>
            C, appareat, & </s>
            <s xml:id="echoid-s4947" xml:space="preserve">vmbra abſciſſa notetur, per quam ex problem. </s>
            <s xml:id="echoid-s4948" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4949" xml:space="preserve">anguli C G D,
              <lb/>
            magnitudo addiſcatur. </s>
            <s xml:id="echoid-s4950" xml:space="preserve">Quod ſi alterum latus quadrati vltra rectam G C, exi-
              <lb/>
            ſtat, erit angulus CGD, acutus: </s>
            <s xml:id="echoid-s4951" xml:space="preserve">ſi verò citra rectam GC, extiterit, dictus angu-
              <lb/>
            lus erit obtuſus: </s>
            <s xml:id="echoid-s4952" xml:space="preserve">quem cognoſcemus, ſi ad rectum adiiciemus reliquum angu-
              <lb/>
            lum, inter alterum illud latus, & </s>
            <s xml:id="echoid-s4953" xml:space="preserve">rectam GC; </s>
            <s xml:id="echoid-s4954" xml:space="preserve">quem quidem inueſtigabimus, vt
              <lb/>
              <figure xlink:label="fig-157-01" xlink:href="fig-157-01a" number="85">
                <image file="157-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/157-01"/>
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            de acuto C G D, diximus, ſi nimirum in recta CD, mente notemus punctum, in
              <lb/>
            quod alterum illud latus productum incideret. </s>
            <s xml:id="echoid-s4955" xml:space="preserve">Nam ſi tunc latus illud rectæ
              <lb/>
            G C, congruat, & </s>
            <s xml:id="echoid-s4956" xml:space="preserve">dioptra ad punctum notatum vergat, indicabit vmbra inter
              <lb/>
            latus illud, & </s>
            <s xml:id="echoid-s4957" xml:space="preserve">lineam fiduciæ angulum prædictum reliquum, vt in problemate 1.
              <lb/>
            </s>
            <s xml:id="echoid-s4958" xml:space="preserve">dictum eſt. </s>
            <s xml:id="echoid-s4959" xml:space="preserve">Si denique alterum illud latus præcisè rectæ GC, congruat, angulus
              <lb/>
            CGD, rectus erit. </s>
            <s xml:id="echoid-s4960" xml:space="preserve">His peractis, quia in triangulo CGD, latera GC, GD, nota
              <lb/>
            continent angulum G, etiam cognitum; </s>
            <s xml:id="echoid-s4961" xml:space="preserve"> cognoſcetur quoque tertium
              <note symbol="a" position="right" xlink:label="note-157-01" xlink:href="note-157-01a" xml:space="preserve">12. triang.
                <lb/>
              rectil.</note>
            CD, quod quæritur.</s>
            <s xml:id="echoid-s4962" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4963" xml:space="preserve">2. </s>
            <s xml:id="echoid-s4964" xml:space="preserve">
              <emph style="sc">Vervm</emph>
            inuentis diſtantiis GC, G D, in aliqua menſura, vna cum an-
              <lb/>
            gulo G, fa cilius, licet non tam certò, interuallum CD, co
              <unsure/>
            gnoſcemus hoc pacto.
              <lb/>
            </s>
            <s xml:id="echoid-s4965" xml:space="preserve">Deſcripto angulo G, ſeorſum ſumatur in GC, portio quotlibet partium late-
              <lb/>
            ris quadrati, verbi gratia 500. </s>
            <s xml:id="echoid-s4966" xml:space="preserve">id eſt, ſemiſsis lateris. </s>
            <s xml:id="echoid-s4967" xml:space="preserve">Et fiat, vt diſtantia inuen-
              <lb/>
            ta G C, ad diſtantiam inuentam G D, ita partes acceptæ 500. </s>
            <s xml:id="echoid-s4968" xml:space="preserve">ad aliud. </s>
            <s xml:id="echoid-s4969" xml:space="preserve">Nam
              <lb/>
            Quotiens dabit numerum quartum proportionalem earundem partium la-
              <lb/>
            teris quadrati; </s>
            <s xml:id="echoid-s4970" xml:space="preserve">quibus ſi capiatur in G D, portio æqualis, erit
              <note symbol="b" position="right" xlink:label="note-157-02" xlink:href="note-157-02a" xml:space="preserve">2. ſexti.</note>
            inter extrema puncta dictarum portionum, æquidiſtans interuallo CD; </s>
            <s xml:id="echoid-s4971" xml:space="preserve">vt con-
              <lb/>
            ſtat, ſi illæ portiones in rectas GC, GD, in figura transferrentur; </s>
            <s xml:id="echoid-s4972" xml:space="preserve">propterea ꝙ in
              <lb/>
            illis extremis punctis rectæ GC, GD, ſectæ eſſent proportionaliter. </s>
            <s xml:id="echoid-s4973" xml:space="preserve">Quare ſi il-
              <lb/>
            lud interuallum circino menſuretur in eiſdem partibus lateris quadrati, con-
              <lb/>
            tinebit interuallum C D, totidem particulas rectæ G C, in 500. </s>
            <s xml:id="echoid-s4974" xml:space="preserve">partes æqua-
              <lb/>
            les diuiſæ, quot in illo interuallo comprehen duntur ex particulis lateris qua-
              <lb/>
            drati: </s>
            <s xml:id="echoid-s4975" xml:space="preserve">cum ſit vt portio particularum 500. </s>
            <s xml:id="echoid-s4976" xml:space="preserve">ad interuallum illud, ita G C, di-
              <lb/>
            uiſa in partes æquales 500. </s>
            <s xml:id="echoid-s4977" xml:space="preserve">ad CD. </s>
            <s xml:id="echoid-s4978" xml:space="preserve">Quæ particulæ reducentur ad menſuram, in
              <lb/>
            qua inuentæ ſunt GC, GD: </s>
            <s xml:id="echoid-s4979" xml:space="preserve">ſi fiat, vt GC, quatenus 500. </s>
            <s xml:id="echoid-s4980" xml:space="preserve">ad menſuras in G C,
              <lb/>
            inuentas, ita C D, inuenta in particulis rectæ GC, in 500. </s>
            <s xml:id="echoid-s4981" xml:space="preserve">partes diuiſæ, ad
              <lb/>
            aliud.</s>
            <s xml:id="echoid-s4982" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4983" xml:space="preserve">
              <emph style="sc">Qvia</emph>
            verò vix per circinum accurate reperiri poteſt interuallum illud inter
              <lb/>
            extremitates proportionalium, magis ex quiſitè, licet laborioſius, interuallum
              <lb/>
            propoſitum cognoſcetur per 12. </s>
            <s xml:id="echoid-s4984" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s4985" xml:space="preserve">rectilineorum.</s>
            <s xml:id="echoid-s4986" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4987" xml:space="preserve">INTERVALLVM tranſuerſum in Horizonte, cuius vtrumque ex-
              <lb/>
            tremum videri poteſt, per quadratum metiri.</s>
            <s xml:id="echoid-s4988" xml:space="preserve"/>
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