Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div244" type="section" level="1" n="107">
          <pb o="100" file="130" n="130" rhead="GEOMETR. PRACT."/>
          <p>
            <s xml:id="echoid-s3863" xml:space="preserve">7. </s>
            <s xml:id="echoid-s3864" xml:space="preserve">
              <emph style="sc">Iam</emph>
            verò abſq; </s>
            <s xml:id="echoid-s3865" xml:space="preserve">numer orum auxilio problema abſoluemus, ſi attentè ea
              <lb/>
            conſiderentur, quælib. </s>
            <s xml:id="echoid-s3866" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3867" xml:space="preserve">problem. </s>
            <s xml:id="echoid-s3868" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3869" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s3870" xml:space="preserve">7. </s>
            <s xml:id="echoid-s3871" xml:space="preserve">ſcripſimus. </s>
            <s xml:id="echoid-s3872" xml:space="preserve">Nam ſi fiat angulus
              <lb/>
            quicunque B A C, & </s>
            <s xml:id="echoid-s3873" xml:space="preserve">pro primo exemplo Num. </s>
            <s xml:id="echoid-s3874" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s3875" xml:space="preserve">
              <figure xlink:label="fig-130-01" xlink:href="fig-130-01a" number="57">
                <image file="130-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/130-01"/>
              </figure>
            huius problem. </s>
            <s xml:id="echoid-s3876" xml:space="preserve">ſumatur A D, æqualis lateri quadrati
              <lb/>
            AB, vel ſi eſſet nimis magnum, æqualis ſemiſsi, vel tertiæ
              <lb/>
            parti, aut quartæ, & </s>
            <s xml:id="echoid-s3877" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3878" xml:space="preserve">eiuſdem lateris. </s>
            <s xml:id="echoid-s3879" xml:space="preserve">Deinde D B, æ-
              <lb/>
            qualis vmbræ abſciſſę B E, (quæ ſumma cura per circi-
              <lb/>
            numin quadrato accipienda eſt) vel eius ſemiſsi, vel ter-
              <lb/>
            tiæ parti, aut quartæ & </s>
            <s xml:id="echoid-s3880" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3881" xml:space="preserve">vt nimirum A D, D B, ſintæquè
              <lb/>
            ſub-multiplices lateris AB, & </s>
            <s xml:id="echoid-s3882" xml:space="preserve">vmbræ BE, ſi eisæquales non ſunt. </s>
            <s xml:id="echoid-s3883" xml:space="preserve">Poſt hęc exin-
              <lb/>
            ſtrumento partium ſumatur AE, tot particularum, quotpalmi, aut pedes in al-
              <lb/>
            titudine AF, continentur. </s>
            <s xml:id="echoid-s3884" xml:space="preserve">Si enim iunctæ rectę DE, parallela agatur BC, conti-
              <lb/>
            nebit diſtantia F G, tot palmos, aut pedes, quotparticulę inſtrumenti partium
              <lb/>
            in interuallo EC, comprehenduntur. </s>
            <s xml:id="echoid-s3885" xml:space="preserve">Vt ſi altitudo AF, ſit pedum 5. </s>
            <s xml:id="echoid-s3886" xml:space="preserve">erit diſtan-
              <lb/>
            tia F G, pedum 3. </s>
            <s xml:id="echoid-s3887" xml:space="preserve">& </s>
            <s xml:id="echoid-s3888" xml:space="preserve">ſic de cęteris. </s>
            <s xml:id="echoid-s3889" xml:space="preserve">Atque hoc modo procedendum erit in aliis
              <lb/>
            exemplis omnibus, conſiderando videlicet attentè primas tres magnitudines
              <lb/>
            Regulætrium, & </s>
            <s xml:id="echoid-s3890" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3891" xml:space="preserve">quod ſemel monuiſſe ſatis eſt.</s>
            <s xml:id="echoid-s3892" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3893" xml:space="preserve">DISTANTIAM in plano per duas ſtationes in eodem plano factas
              <lb/>
            per Quadratum Geometricum metiri, quando in eius extremo erecta
              <lb/>
            eſt altitudo aliqua perpendicularis, etiamſi infimum eius extremum
              <lb/>
            non cernatur.</s>
            <s xml:id="echoid-s3894" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div247" type="section" level="1" n="108">
          <head xml:id="echoid-head111" xml:space="preserve">PROBLEMA III.</head>
          <p>
            <s xml:id="echoid-s3895" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3896" xml:space="preserve">
              <emph style="sc">Distantia</emph>
            inueſtiganda ſit A F. </s>
            <s xml:id="echoid-s3897" xml:space="preserve">Intelligatur planum Horizontis
              <lb/>
            KL; </s>
            <s xml:id="echoid-s3898" xml:space="preserve">erecta altitudo G L: </s>
            <s xml:id="echoid-s3899" xml:space="preserve">ſtatura menſoris AK, vel alia quædam menſura cog-
              <lb/>
            nita. </s>
            <s xml:id="echoid-s3900" xml:space="preserve">Supra aliquam baſem Horizonti æquidiſtantem collocetur quadratum
              <lb/>
            ſtabile, ita vt eius latus AD, cogitatione productum occurrat altitudini erectæ
              <lb/>
            in F, ad angulos rectos. </s>
            <s xml:id="echoid-s3901" xml:space="preserve">Inſpiciatur ſummitas G, per dioptram, ſecetque eius li-
              <lb/>
              <figure xlink:label="fig-130-02" xlink:href="fig-130-02a" number="58">
                <image file="130-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/130-02"/>
              </figure>
            nea fiduciæ vmbram verſam
              <lb/>
            CD, in E, quod ſemper con-
              <lb/>
            tinget, quando diſtantia A F,
              <lb/>
            maior eſt altitudine F G.
              <lb/>
            </s>
            <s xml:id="echoid-s3902" xml:space="preserve"> quod tunc angulus A,
              <note symbol="a" position="left" xlink:label="note-130-01" xlink:href="note-130-01a" xml:space="preserve">18. primi.</note>
            nor fiat angulo G, ac proin-
              <lb/>
            de ſemirecto minor, quem
              <lb/>
            cum AD, in A, faceret radius
              <lb/>
            per G, emiſſus. </s>
            <s xml:id="echoid-s3903" xml:space="preserve">Deindeacce-
              <lb/>
            de magis, vel recede per lon-
              <lb/>
            gitudinem notam Aa, & </s>
            <s xml:id="echoid-s3904" xml:space="preserve">col-
              <lb/>
            locato quadrato ſupra ean-
              <lb/>
            dem baſem, ſecetiterum dio-
              <lb/>
            ptra ad punctum G, directa
              <lb/>
            vmbram verſam c d, in H: </s>
            <s xml:id="echoid-s3905" xml:space="preserve">eritq; </s>
            <s xml:id="echoid-s3906" xml:space="preserve">vmbra verſa d H, in propinquioriſtatione ma-
              <lb/>
            ior, quam vmbra verſa D E, inſtatione remotiore, quod angulus a, maior
              <note symbol="b" position="left" xlink:label="note-130-02" xlink:href="note-130-02a" xml:space="preserve">16. ſexti.</note>
            angulo A. </s>
            <s xml:id="echoid-s3907" xml:space="preserve">Auferatur dI, ipſi D E, æqualis, vt HI, differentia ſit vmbrarum </s>
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