Clavius, Christoph, Geometria practica

Table of Notes

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              <pb o="56" file="086" n="86" rhead="GEOMETR. PRACT."/>
            ra earum aſſumptis deſcribantur verſ{us} alteram ad quodcunque idem interuallum ar-
              <lb/>
            c{us} H I, K L, M N, ex quib{us} arc{us} quadrante minor{es} abſcindantur in 1, L N, punctis,
              <lb/>
            per quæex centris rectæ egrediantur @ ſecant{es} C D, in O, P, Q. </s>
            <s xml:id="echoid-s2277" xml:space="preserve">Sumptis deinde in E I, pro-
              <lb/>
            ducta ipſi E O, tot partib{us} æqualib{us} vſque ad R, quot ſatis eſſe videbuntur, vt recta ex
              <lb/>
            R, verſ{us} concurſum ducta non valde oblique ipſ{as} rect{as} ſec{et}, accipiantur in F L, G N,
              <lb/>
              <handwritten xlink:label="hd-086-1" xlink:href="hd-086-1a" number="44"/>
              <handwritten xlink:label="hd-086-1" xlink:href="hd-086-1a" number="45"/>
            productis totidem part{es} ipſis F P, P Q, æqual{es} vſque ad S, T. </s>
            <s xml:id="echoid-s2278" xml:space="preserve">Dico tam rectam R S,
              <lb/>
            quam RT, & </s>
            <s xml:id="echoid-s2279" xml:space="preserve">quam ST, in punctum B, concurſ{us} cadere, ita vt puncta R, S, T, B, in vna
              <lb/>
            recta linea iaceant. </s>
            <s xml:id="echoid-s2280" xml:space="preserve"> Quoniam enim anguli E, F, G, æqual{es} ſunt, eruntrectæ E R, F
              <note symbol="a" position="left" xlink:label="note-086-01" xlink:href="note-086-01a" xml:space="preserve">27. Tertij.</note>
            GT, parallelæ. </s>
            <s xml:id="echoid-s2281" xml:space="preserve"> Cum ergo ER, FS, GT, eaſdem proportion{es} habeant, qu{as} EO, FE
              <unsure/>
            P, G
              <note symbol="b" position="left" xlink:label="note-086-02" xlink:href="note-086-02a" xml:space="preserve">28. Primi</note>
            hoc eſte EB, FB, GB, habent, cadentrectæ RS, RT, ST, in punctum B, quod eſt
              <note symbol="c" position="left" xlink:label="note-086-03" xlink:href="note-086-03a" xml:space="preserve">15. Quinti</note>
            ſitum.</s>
            <s xml:id="echoid-s2282" xml:space="preserve"/>
          </p>
          <note symbol="d" position="left" xml:space="preserve">4. Sexti &
            <lb/>
          permutãdo.</note>
          <p style="it">
            <s xml:id="echoid-s2283" xml:space="preserve">HOC ergo lemma ſi adhibeatur, ſatis exquiſitè in ſuperiore figura Num. </s>
            <s xml:id="echoid-s2284" xml:space="preserve">6. </s>
            <s xml:id="echoid-s2285" xml:space="preserve">punctum
              <lb/>
            concurſ{us} G, deprehendetur, proindeque menſura rectarum, qu{as} ſine numeris inuenire
              <lb/>
              <note symbol="e" position="left" xlink:label="note-086-05" xlink:href="note-086-05a" xml:space="preserve">ſchol. 4. ſex
                <lb/>
              ti.</note>
            docuim{us}, non multum à vero aberunt.</s>
            <s xml:id="echoid-s2286" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2287" xml:space="preserve">8. </s>
            <s xml:id="echoid-s2288" xml:space="preserve">VERVM commode obliquam illam ſectionem in concurſu G, vitabim{us}, ſi figu-
              <lb/>
              <note position="left" xlink:label="note-086-06" xlink:href="note-086-06a" xml:space="preserve">Quo pacto
                <lb/>
              infig. Num.
                <lb/>
              6. obliqua ſe-
                <lb/>
              ctio in pun-
                <lb/>
              cto concur-
                <lb/>
              ſus G, vite-
                <lb/>
              tur.</note>
            ram hoc alio modo conſtruem{us}, Fiat in figura Num. </s>
            <s xml:id="echoid-s2289" xml:space="preserve">6, angul{us} rect{us} EFG, & </s>
            <s xml:id="echoid-s2290" xml:space="preserve">in quoli-
              <lb/>
            b{et} puncto G, vbi concurſum eſſe volum{us}, conſtituantur anguli F G D, F G E, aqual{es}
              <lb/>
            complementis angulorum obſeruationum. </s>
            <s xml:id="echoid-s2291" xml:space="preserve">Ita enim DE, reſpondebit differentiæ ſtatio-
              <lb/>
            num, & </s>
            <s xml:id="echoid-s2292" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2293" xml:space="preserve">Quocirca ſi cogitetur DE, ſectain tot part{es} æqual{es}, quod palmi, vel ped{es}
              <unsure/>
            in
              <lb/>
            differentia ſtationum fuerunt aſſumpti, cognoſcem{us} per ea, quæ ad finem Num. </s>
            <s xml:id="echoid-s2294" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2295" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s2296" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s2297" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2298" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2299" xml:space="preserve">docuim{us}, quot ex ijs partib{us} in diſtantijs DF, EF, & </s>
            <s xml:id="echoid-s2300" xml:space="preserve">in altitudine F G, at que hy-
              <lb/>
            potenuſis GD, GE, comprehendantur. </s>
            <s xml:id="echoid-s2301" xml:space="preserve">Atque hoc modo punctum concurſ{us} G, dubium
              <lb/>
            aut incertum eſſe non poteſt, cum illud ante omnia elegerim{us}
              <unsure/>
            .</s>
            <s xml:id="echoid-s2302" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div117" type="section" level="1" n="50">
          <head xml:id="echoid-head53" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s2303" xml:space="preserve">Vt etiam pro tyronibus ſemel explicemus, quid per noſtrum loquendimo-
              <lb/>
              <handwritten xlink:label="hd-086-1" xlink:href="hd-086-1a" number="44"/>
              <handwritten xlink:label="hd-086-1" xlink:href="hd-086-1a" number="45"/>
            dum intelligamus, cum dicimus verbi gratia, Num. </s>
            <s xml:id="echoid-s2304" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2305" xml:space="preserve">huius problematis, Fiat.</s>
            <s xml:id="echoid-s2306" xml:space="preserve"/>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt O P, differentia inter \\ tangent{es} angulorum \\ obſeruationum # ad P N, vel H M, \\ Tangentem mino- \\ rem. # It a E D, diffe- \\ rentia ſtatio- \\ num # ad D F:
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s2307" xml:space="preserve">Sciendum eſt, nos hoc modo redigere opus ad termino s regulæ trium. </s>
            <s xml:id="echoid-s2308" xml:space="preserve">Qua
              <lb/>
            propter ſi iuxta tenorem regulæ numerus in tertio loco poſitus ducatur in eum,
              <lb/>
            qui ſecundum locum occupat, hoceſt, differentia ſtationum in propoſito e-
              <lb/>
            xemplo multip licetur per Tangentem minorem, productuſque numerus per
              <lb/>
            eum, qui in primo loco collocatur, id eſt, per differentiam Tangentium, diui-
              <lb/>
            datur: </s>
            <s xml:id="echoid-s2309" xml:space="preserve">(niſi quando primus numerus eſt ſinus totus Tunc enim diuiſio non fit,
              <lb/>
              <note position="left" xlink:label="note-086-08" xlink:href="note-086-08a" xml:space="preserve">Altitudinis
                <lb/>
              inuentio per
                <lb/>
              vnicam ſtatio
                <lb/>
              nem, quando
                <lb/>
              diſtantia nota
                <lb/>
              eſt.</note>
            ſed ex producto quinque figuræ abijciuntur, vel ſeptem, prout ſinus totus ſta-
              <lb/>
            tuitur 100.</s>
            <s xml:id="echoid-s2310" xml:space="preserve">000. </s>
            <s xml:id="echoid-s2311" xml:space="preserve">vel 10,000.</s>
            <s xml:id="echoid-s2312" xml:space="preserve">000.) </s>
            <s xml:id="echoid-s2313" xml:space="preserve">pro creabitur in quotiente quartus numerus,
              <lb/>
            qui quæritur, nimirum diſtantia D F. </s>
            <s xml:id="echoid-s2314" xml:space="preserve">Eademque eſt ratio de cæteris.</s>
            <s xml:id="echoid-s2315" xml:space="preserve"/>
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        <div xml:id="echoid-div120" type="section" level="1" n="51">
          <head xml:id="echoid-head54" xml:space="preserve">COROLLARIVM I.</head>
          <p>
            <s xml:id="echoid-s2316" xml:space="preserve">
              <emph style="sc">Itaqve</emph>
            quando diſtantia à loco menſoris vſque ad altitudinem ignotam
              <lb/>
            cognita eſt, inuenietur altitudo per vnicam ſtationem. </s>
            <s xml:id="echoid-s2317" xml:space="preserve"> Sifiat.</s>
            <s xml:id="echoid-s2318" xml:space="preserve"/>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſin{us} \\ tot{us} # ad Tangentem anguli \\ obſeruationis: # Ita diſtantia \\ nota # ad altitudinem.
            <lb/>
          </note>
          <note symbol="f" position="left" xml:space="preserve">4. Triang.
            <lb/>
          rectil.</note>
          <p>
            <s xml:id="echoid-s2319" xml:space="preserve">Hoc enim demonſtratum eſt Num. </s>
            <s xml:id="echoid-s2320" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2321" xml:space="preserve">huius problematis 1. </s>
            <s xml:id="echoid-s2322" xml:space="preserve">tam per angulum </s>
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