Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div219" type="section" level="1" n="99">
          <p>
            <s xml:id="echoid-s3264" xml:space="preserve">
              <pb o="85" file="115" n="115" rhead="LIBER TERTIVS."/>
            indein duab. </s>
            <s xml:id="echoid-s3265" xml:space="preserve">regulis BC, CD, ducantur tres parallelæ extremitatibus quadrati,
              <lb/>
              <note position="right" xlink:label="note-115-01" xlink:href="note-115-01a" xml:space="preserve">Vmbra recta,
                <lb/>
              & verſa in
                <lb/>
              quadrato quæ,
                <lb/>
              & in quot par
                <lb/>
              tes à Geome-
                <lb/>
              tris vtraque
                <lb/>
              ſecetur.</note>
            pro partibus & </s>
            <s xml:id="echoid-s3266" xml:space="preserve">numeris vtriuſque vmbræ deſignandis, vt in figura apparet. </s>
            <s xml:id="echoid-s3267" xml:space="preserve">La-
              <lb/>
            tus BC, vmbræ rectæ, & </s>
            <s xml:id="echoid-s3268" xml:space="preserve">CD, vmbræ verſæ deſtinatur à Geometris: </s>
            <s xml:id="echoid-s3269" xml:space="preserve">Vtrumque
              <lb/>
              <figure xlink:label="fig-115-01" xlink:href="fig-115-01a" number="50">
                <image file="115-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/115-01"/>
              </figure>
            autem in 12. </s>
            <s xml:id="echoid-s3270" xml:space="preserve">partes æquales partiri ſolent omnes, qui de vſu Quadrati Geome-
              <lb/>
              <note position="right" xlink:label="note-115-02" xlink:href="note-115-02a" xml:space="preserve">In quot part{es}
                <lb/>
              vtraque vm-
                <lb/>
              brain noſtro
                <lb/>
              quadrato di-
                <lb/>
              uidatur.
                <lb/>
              Scala altime-
                <lb/>
              tra quid.</note>
            triciſcrip ſerunt: </s>
            <s xml:id="echoid-s3271" xml:space="preserve">Et ſi capacitas inſtrumenti permittit, ſingulas partes in 60. </s>
            <s xml:id="echoid-s3272" xml:space="preserve">ſub-
              <lb/>
            diuidunt, vt tota vmbra partes 720. </s>
            <s xml:id="echoid-s3273" xml:space="preserve">complectatur, vel in 100. </s>
            <s xml:id="echoid-s3274" xml:space="preserve">vt partes 1200. </s>
            <s xml:id="echoid-s3275" xml:space="preserve">in
              <lb/>
            vtraque vmbra exiſtant. </s>
            <s xml:id="echoid-s3276" xml:space="preserve">Ego vtramque vmbram in 10. </s>
            <s xml:id="echoid-s3277" xml:space="preserve">partes duntaxat æqua-
              <lb/>
            les diuido, niſi inſtrumentum ſit tantæ magnitudinis, vt commode vtra que re-
              <lb/>
            cta BC, CD, in 100, aut 1000. </s>
            <s xml:id="echoid-s3278" xml:space="preserve">partes ſecari poſsit, ſub diuiſis videlicet ſingulis
              <lb/>
            decimis partibus in 10. </s>
            <s xml:id="echoid-s3279" xml:space="preserve">vel 100. </s>
            <s xml:id="echoid-s3280" xml:space="preserve">particulas. </s>
            <s xml:id="echoid-s3281" xml:space="preserve">Figura porro ex vtraque vmbra cõ-
              <lb/>
            ſtans dici ſolet à Geometris Scala altimetra.</s>
            <s xml:id="echoid-s3282" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3283" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3284" xml:space="preserve">
              <emph style="sc">Antepono</emph>
            autem diuiſioni conſuetæ in 12. </s>
            <s xml:id="echoid-s3285" xml:space="preserve">vel 720. </s>
            <s xml:id="echoid-s3286" xml:space="preserve">vel 1200. </s>
            <s xml:id="echoid-s3287" xml:space="preserve">partes
              <lb/>
              <note position="right" xlink:label="note-115-03" xlink:href="note-115-03a" xml:space="preserve">Quare noſtr
                <emph style="sub">a</emph>
                <lb/>
              diuiſio vmbr
                <emph style="sub">æ</emph>
                <lb/>
              præferatur a-
                <lb/>
              liorum diui-
                <lb/>
              ſioni.</note>
            diuiſionem noſtram in partes 10. </s>
            <s xml:id="echoid-s3288" xml:space="preserve">vel 100. </s>
            <s xml:id="echoid-s3289" xml:space="preserve">vel 1000. </s>
            <s xml:id="echoid-s3290" xml:space="preserve">æquales, propterea quòd, ſi
              <lb/>
            inſtrumentum propter paruitatem ſectum ſit tantummodo in 10. </s>
            <s xml:id="echoid-s3291" xml:space="preserve">partes, facili
              <lb/>
            admodum negotio cognoſcere poſſumus, quot centeſimæ, vel etiam milleſi-
              <lb/>
            mæ partes in qualibet particula cuiuſcunque partis decimæ rectarum B C, CD,
              <lb/>
            aſsignata comprehendantur: </s>
            <s xml:id="echoid-s3292" xml:space="preserve">non ſecus ac ſi vtra que recta in 100. </s>
            <s xml:id="echoid-s3293" xml:space="preserve">vel 1000.
              <lb/>
            </s>
            <s xml:id="echoid-s3294" xml:space="preserve">partes ſecta foret, vt Num. </s>
            <s xml:id="echoid-s3295" xml:space="preserve">14. </s>
            <s xml:id="echoid-s3296" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s3297" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3298" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3299" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3300" xml:space="preserve">copioſè expoſuimus. </s>
            <s xml:id="echoid-s3301" xml:space="preserve">Huc accedit,
              <lb/>
            quod in dimetiendis lineis per Quadratum Geometricum fieri ſemper debeat
              <lb/>
            multiplicatio, aut diuiſio per omnes partes lateris BC, vel CD: </s>
            <s xml:id="echoid-s3302" xml:space="preserve">Manifeſtum au-
              <lb/>
            tem eſt, faciliorem eſſe multiplicationẽ, diuiſionemue per 10. </s>
            <s xml:id="echoid-s3303" xml:space="preserve">aut 100. </s>
            <s xml:id="echoid-s3304" xml:space="preserve">vel 1000. </s>
            <s xml:id="echoid-s3305" xml:space="preserve">
              <lb/>
            quàm per 12. </s>
            <s xml:id="echoid-s3306" xml:space="preserve">aut 720. </s>
            <s xml:id="echoid-s3307" xml:space="preserve">vel 1200. </s>
            <s xml:id="echoid-s3308" xml:space="preserve">cum illa fiat per ſolam appoſitionem, vel
              <lb/>
            detractionem 0. </s>
            <s xml:id="echoid-s3309" xml:space="preserve">vel 00. </s>
            <s xml:id="echoid-s3310" xml:space="preserve">vel 000. </s>
            <s xml:id="echoid-s3311" xml:space="preserve">vtin noſtra Arithmetica practica declaraui-
              <lb/>
            mus.</s>
            <s xml:id="echoid-s3312" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3313" xml:space="preserve">
              <emph style="sc">Invenio</emph>
            quidem latus quadrati à do ctiſsimo
              <unsure/>
            10. </s>
            <s xml:id="echoid-s3314" xml:space="preserve">Antonio Magino diui-
              <lb/>
            ſum quo que eſſe, & </s>
            <s xml:id="echoid-s3315" xml:space="preserve">quidem optimo conſilio, in 100. </s>
            <s xml:id="echoid-s3316" xml:space="preserve">partes æquales; </s>
            <s xml:id="echoid-s3317" xml:space="preserve">quamuis
              <lb/>
            ab eo regula non tradatur, qua cognoſcendũ ſit, quot partes mill eſimæ in qua-
              <lb/>
            uis particula vnius centeſimæ comprehendantur, quod tamen omnino neceſ-
              <lb/>
            ſarium eſt, vt dimenſiones, ac ſtellarum altitudines exquiſitè obſeruentur: </s>
            <s xml:id="echoid-s3318" xml:space="preserve">præ-
              <lb/>
            ſertim ſi propter inſtrumenti paruitatem latus in 10. </s>
            <s xml:id="echoid-s3319" xml:space="preserve">partes duntaxat commode
              <lb/>
            poſsit diuidi. </s>
            <s xml:id="echoid-s3320" xml:space="preserve">Id quod per noſtram do ctrinam, vt diximus, ſine magno laborè
              <lb/>
            effici poteſt.</s>
            <s xml:id="echoid-s3321" xml:space="preserve"/>
          </p>
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