Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div219" type="section" level="1" n="99">
          <p>
            <s xml:id="echoid-s3376" xml:space="preserve">
              <pb o="87" file="117" n="117" rhead="LIBER TERTIVS."/>
            latus CD: </s>
            <s xml:id="echoid-s3377" xml:space="preserve">Tunc enim neceſſario latus BC, produci debet, vt ſecaripoſsit. </s>
            <s xml:id="echoid-s3378" xml:space="preserve">Item
              <lb/>
            ſæpe numero vmbra verſa ſuperat latus C D, quando videlicet filum perpendi-
              <lb/>
            culi, aut linea fiduciæ interſecat latus B C: </s>
            <s xml:id="echoid-s3379" xml:space="preserve">Tunc enim neceſſario latus D C,
              <lb/>
            productum verſus C, ſecabitur, vt perſpicuum eſt. </s>
            <s xml:id="echoid-s3380" xml:space="preserve">Ne ergo cogamur vel la-
              <lb/>
            tus B C, vel C D, producere, aſſumenda eſt vmbra quidem verſa, quando recta
              <lb/>
            latus BC, excedit: </s>
            <s xml:id="echoid-s3381" xml:space="preserve">recta autem, quando verſa ſuo latere C D, maior eſt.</s>
            <s xml:id="echoid-s3382" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3383" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3384" xml:space="preserve">
              <emph style="sc">Est</emph>
            autem perpetuo latus qua-
              <lb/>
              <figure xlink:label="fig-117-01" xlink:href="fig-117-01a" number="51">
                <image file="117-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/117-01"/>
              </figure>
              <note position="right" xlink:label="note-117-01" xlink:href="note-117-01a" xml:space="preserve">Gnomon me-
                <lb/>
              dio loco pro-
                <lb/>
              portionalis eſt
                <lb/>
              inter vmbrã
                <lb/>
              rectam, &
                <lb/>
              verſam.
                <lb/>
                <lb/>
              </note>
            drati, quod Gnomonem appellant, me-
              <lb/>
            dio loco proportionale inter vmbrã re-
              <lb/>
            ctam ac verſam. </s>
            <s xml:id="echoid-s3385" xml:space="preserve">Secet namque in qua-
              <lb/>
            drato pendulo filum perpendiculi, vel in
              <lb/>
            ſtabili linea fiduciæ, latus vmbræ BC, in E,
              <lb/>
            & </s>
            <s xml:id="echoid-s3386" xml:space="preserve">latus vmbræ DC, productũ in F. </s>
            <s xml:id="echoid-s3387" xml:space="preserve">Erunt
              <lb/>
            igitur triangula ABE, ADF, æquiangula,
              <lb/>
              <note symbol="a" position="right" xlink:label="note-117-02" xlink:href="note-117-02a" xml:space="preserve">29. primi.</note>
            cum anguli B, D. </s>
            <s xml:id="echoid-s3388" xml:space="preserve">recti ſint, & </s>
            <s xml:id="echoid-s3389" xml:space="preserve">tam
              <note symbol="b" position="right" xlink:label="note-117-03" xlink:href="note-117-03a" xml:space="preserve">4. ſexti.</note>
            BAE, DFA, quam BEA, DAF, æquales.</s>
            <s xml:id="echoid-s3390" xml:space="preserve"> Quamobrem erit vt B E, vmbra abſciſſa
              <lb/>
            ad gnomonem B A, ita gnomon A D, ad vmbram abſciſſam D F: </s>
            <s xml:id="echoid-s3391" xml:space="preserve">hoc eſt gno-
              <lb/>
            mon B A, vel A D, medio loco eſt proportionalis inter duas vmbras B E, D F,
              <lb/>
            quarum vna recta eſt, & </s>
            <s xml:id="echoid-s3392" xml:space="preserve">altera verſa.
              <lb/>
            </s>
            <s xml:id="echoid-s3393" xml:space="preserve">
              <note position="right" xlink:label="note-117-04" xlink:href="note-117-04a" xml:space="preserve">Redactio vm-
                <lb/>
              bræ rectæ ad
                <lb/>
              verſam, &
                <lb/>
              contra.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s3394" xml:space="preserve">7. </s>
            <s xml:id="echoid-s3395" xml:space="preserve">
              <emph style="sc">Hinc</emph>
            facilis eſt reductio vnius vmbræ ad aliam, quod non raro vſu ve-
              <lb/>
            nit. </s>
            <s xml:id="echoid-s3396" xml:space="preserve">Nam ſi gnomon complectens partes 1000. </s>
            <s xml:id="echoid-s3397" xml:space="preserve">(in tot namq; </s>
            <s xml:id="echoid-s3398" xml:space="preserve">partes latus qua-
              <lb/>
            drati diuiſum concipere lubet) in ſe mu@tiplicetur, & </s>
            <s xml:id="echoid-s3399" xml:space="preserve">productus numerus qua-
              <lb/>
            dratus 1000000. </s>
            <s xml:id="echoid-s3400" xml:space="preserve">lateris AB, per alterutram vmbram diuidatur, indicabit Quo-
              <lb/>
            tiens partes alterius vmbræ: </s>
            <s xml:id="echoid-s3401" xml:space="preserve">hoc eſt, ſi fiat,</s>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt alterutra vmbra # ad gnomonem # itagnomon # ad alteram vmbram:
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s3402" xml:space="preserve">hoc eſt, ſi quadratus numerus lateris quadrati, vel gnomonis, videlicet
              <lb/>
            1000000. </s>
            <s xml:id="echoid-s3403" xml:space="preserve">per alterutram vmbram diuidatur. </s>
            <s xml:id="echoid-s3404" xml:space="preserve">Verbi gratia ſi ponatur B E, vm-
              <lb/>
            bra recta partium 700. </s>
            <s xml:id="echoid-s3405" xml:space="preserve">diuidatur que numerus quadratus 1000000. </s>
            <s xml:id="echoid-s3406" xml:space="preserve">lateris A B,
              <lb/>
            per 700. </s>
            <s xml:id="echoid-s3407" xml:space="preserve">producetur vmbra verſa DF, partium 1428 {2/3}. </s>
            <s xml:id="echoid-s3408" xml:space="preserve">Sic etiam, ſi BE, ſtatua-
              <lb/>
            tur vmbra verſa partium 700. </s>
            <s xml:id="echoid-s3409" xml:space="preserve">reperietur vmbra recta DF, partium 1428 {2/3}. </s>
            <s xml:id="echoid-s3410" xml:space="preserve">Quod
              <lb/>
            ſi vna vmbra ſit 400. </s>
            <s xml:id="echoid-s3411" xml:space="preserve">erit altera 2500. </s>
            <s xml:id="echoid-s3412" xml:space="preserve">& </s>
            <s xml:id="echoid-s3413" xml:space="preserve">ſic de cæteris. </s>
            <s xml:id="echoid-s3414" xml:space="preserve">Sediam ad vſum vtri-
              <lb/>
            uſque quadrati accedamus.</s>
            <s xml:id="echoid-s3415" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3416" xml:space="preserve">ALTITVDINEM Solis, vel ſtellę cuiuſuis per quadratum Geome-
              <lb/>
              <handwritten xlink:label="hd-117-2" xlink:href="hd-117-2a" number="47"/>
            tricum obſeruare.</s>
            <s xml:id="echoid-s3417" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div227" type="section" level="1" n="100">
          <head xml:id="echoid-head103" xml:space="preserve">PROBLEMA I.</head>
          <p>
            <s xml:id="echoid-s3418" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3419" xml:space="preserve">
              <emph style="sc">Præparetvr</emph>
            baſis plana Horizontiæ quidiſtans, vt ſupra illam Qua-
              <lb/>
              <note position="right" xlink:label="note-117-06" xlink:href="note-117-06a" xml:space="preserve">Altitudo So-
                <lb/>
              lis, velſtellæ,
                <lb/>
              quo pacto per
                <lb/>
              quadratum
                <lb/>
              cognoſcatur.</note>
            dratum ſtabile erectum, ſit ad Horizontem perpendiculare. </s>
            <s xml:id="echoid-s3420" xml:space="preserve">Eleuetur deinde
              <lb/>
            pendulum qua dratum, centro A, ad Solem, vel ſtellam verſo, ita vt eius pla-
              <lb/>
            num per centrum Solis, aut ſtellæ tranſeat, donec radius Solis per duo fo-
              <lb/>
            ramina pinnacidiorum tranſire deprehendatur: </s>
            <s xml:id="echoid-s3421" xml:space="preserve">vel radius viſualis per </s>
          </p>
        </div>
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