Clavius, Christoph, Geometria practica

Table of Notes

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            <s xml:id="echoid-s5967" xml:space="preserve">
              <pb o="154" file="184" n="184" rhead="GEOMETR. PRACT."/>
            tentur. </s>
            <s xml:id="echoid-s5968" xml:space="preserve">Si nam que ex A; </s>
            <s xml:id="echoid-s5969" xml:space="preserve">filum cum perpendiculo egrediatur, & </s>
            <s xml:id="echoid-s5970" xml:space="preserve">omnes partes
              <lb/>
            excindantur, relictis ſolum cruribus inſtrumenti AB, AC, vna cum perip heria ſe-
              <lb/>
            micirculi IDK, cõſtru ctum erit inſtrumentum ad liberationes per opportunum.</s>
            <s xml:id="echoid-s5971" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s5972" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5973" xml:space="preserve">
              <emph style="sc">Nam</emph>
            in campo aliquo, vel horto, poſitis punctis B, C, in terra, ſi filum
              <lb/>
              <note position="left" xlink:label="note-184-01" xlink:href="note-184-01a" xml:space="preserve">Spatium in æ-
                <lb/>
              quale quo pa-
                <lb/>
              cto libretur.</note>
            perpendiculi tranſit per D, erunt puncta B, C, in terra eiuſdem altitu dinis, ita vt ſi
              <lb/>
            ſpatium in teriectum B C, complanetur, ſpatium illud horti, vel campi ſit libratũ,
              <lb/>
            hoc eſt, Horizonti parallelum.</s>
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            <s xml:id="echoid-s5975" xml:space="preserve">
              <emph style="sc">Sivero</emph>
            filum perpendiculi AH, abſcindet ex quadrante DI, aliquot partes,
              <lb/>
            nimirum 3. </s>
            <s xml:id="echoid-s5976" xml:space="preserve">erit punctum C, tribus palmis altius puncto B, atque ita fo diendum
              <lb/>
            ibi erit ad altitudinem trium palmorum, vt complanatum ſpatium inter B & </s>
            <s xml:id="echoid-s5977" xml:space="preserve">in-
              <lb/>
            fimum punctum eff oſſum Horizonti ſit parallelum. </s>
            <s xml:id="echoid-s5978" xml:space="preserve">Quod ſi filum perpendi-
              <lb/>
            culi abſcin deret ex alio quadrante DK, quotcunq; </s>
            <s xml:id="echoid-s5979" xml:space="preserve">partes nimirum 5. </s>
            <s xml:id="echoid-s5980" xml:space="preserve">eſlet pun-
              <lb/>
            ctum C, depreſsius quinque palmis puncto B. </s>
            <s xml:id="echoid-s5981" xml:space="preserve">Quare tunc ſuperimp onenda,
              <lb/>
            foret puncto C, terra ad altitudinem 5. </s>
            <s xml:id="echoid-s5982" xml:space="preserve">palmorum, vt ſpatium inter B, & </s>
            <s xml:id="echoid-s5983" xml:space="preserve">ſupre-
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            mum punctum terræ ſuperimp oſitæ complanatum Horizonti æquidiſter. </s>
            <s xml:id="echoid-s5984" xml:space="preserve">Com-
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            planato ſpatio inter B, & </s>
            <s xml:id="echoid-s5985" xml:space="preserve">aliud punctum prope C, ſiue effo ſſum, ſiue eleuatum,
              <lb/>
            iteranda erit eadem operatio, poſito crure A B, in puncto inuento, &</s>
            <s xml:id="echoid-s5986" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5987" xml:space="preserve">Atque
              <lb/>
            ita deinceps procedendum eſt vſque ad vltimum ſignum in horto, vel campo
              <lb/>
            propoſitum. </s>
            <s xml:id="echoid-s5988" xml:space="preserve">Hoc ita demonſtratur. </s>
            <s xml:id="echoid-s5989" xml:space="preserve">Concipiatur ducta recta BC, & </s>
            <s xml:id="echoid-s5990" xml:space="preserve">recta CF,
              <lb/>
            filo perpendiculi AH, duci parallela, quæ ad Horizontem erit perpendicularis,
              <lb/>
            ac proinde ducta BF, ad CF, perpendicularis Horizonti æquidiſtabit. </s>
            <s xml:id="echoid-s5991" xml:space="preserve">Et quo-
              <lb/>
            niam in triangulis A G H, B F C, recti anguli E, F, æquales ſunt, nec non & </s>
            <s xml:id="echoid-s5992" xml:space="preserve">
              <note symbol="a" position="left" xlink:label="note-184-02" xlink:href="note-184-02a" xml:space="preserve">29. primi.</note>
            terni C, H, æquiangula erunt triangula; </s>
            <s xml:id="echoid-s5993" xml:space="preserve">Eſt autem A G H, triangulo A D
              <note symbol="b" position="left" xlink:label="note-184-03" xlink:href="note-184-03a" xml:space="preserve">32. primi.</note>
            æquiangulum, quod & </s>
            <s xml:id="echoid-s5994" xml:space="preserve">recti G, E, æquales ſint, & </s>
            <s xml:id="echoid-s5995" xml:space="preserve">A, communis. </s>
            <s xml:id="echoid-s5996" xml:space="preserve">Igitur tri-
              <lb/>
            angula quoque A D E, B C F, æquiangula erunt. </s>
            <s xml:id="echoid-s5997" xml:space="preserve"> Ideo que erit vt A D, 10.</s>
            <s xml:id="echoid-s5998" xml:space="preserve">
              <note symbol="c" position="left" xlink:label="note-184-04" xlink:href="note-184-04a" xml:space="preserve">4. ſexti.</note>
            partium ad D E, 3. </s>
            <s xml:id="echoid-s5999" xml:space="preserve">partium, ita B C, 10. </s>
            <s xml:id="echoid-s6000" xml:space="preserve">palmorum, ad C E, ac proinde C F, 3.
              <lb/>
            </s>
            <s xml:id="echoid-s6001" xml:space="preserve">palmos continebit, tot nimirum, quot partes filum perpen diculi abſcindit ex
              <lb/>
            ſemicirculo I D K. </s>
            <s xml:id="echoid-s6002" xml:space="preserve">Quod ſi quadratum C F, nimirum in dato exemplo 9. </s>
            <s xml:id="echoid-s6003" xml:space="preserve">pal-
              <lb/>
            mi (cum latus C F, ſit 3. </s>
            <s xml:id="echoid-s6004" xml:space="preserve">palmorum) dematur ex 100. </s>
            <s xml:id="echoid-s6005" xml:space="preserve">id eſt, ex quadrato BC. </s>
            <s xml:id="echoid-s6006" xml:space="preserve">10. </s>
            <s xml:id="echoid-s6007" xml:space="preserve">
              <lb/>
            palmorum, reliquum fiet quadratum 91. </s>
            <s xml:id="echoid-s6008" xml:space="preserve">lineæ horizontalis BF, cuius quadrata
              <lb/>
            radix 9 {10/19}. </s>
            <s xml:id="echoid-s6009" xml:space="preserve">dabit horizontalem diſtantiam B F, à puncto B, vſque ad perpendi-
              <lb/>
            cularem CF.</s>
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            <s xml:id="echoid-s6011" xml:space="preserve">
              <emph style="sc">Hæc</emph>
            eadem diſtantia horizontalis B F, cogno ſcetur quo que ſine nume-
              <lb/>
            rorum ſupputatione, hoc modo. </s>
            <s xml:id="echoid-s6012" xml:space="preserve">Ex A, deſcribatur alius ſemicirculus, & </s>
            <s xml:id="echoid-s6013" xml:space="preserve">in ſe-
              <lb/>
            micir culum AED, transferantur omnia interualla inter A, & </s>
            <s xml:id="echoid-s6014" xml:space="preserve">punctarectæ AD, ac
              <lb/>
            tandem ex A, rectis occultis emiſsis per puncta in ſemicirculo notata, obſeruẽ-
              <lb/>
            tur earum interſectiones cum ſemicir culo ex A, deſcripto, transferantur que in
              <lb/>
            alterum quadrantem verſus K. </s>
            <s xml:id="echoid-s6015" xml:space="preserve">Nam quot partes filum perpen diculi AH, ex vl-
              <lb/>
            timo hoc ſemicirculo ex A, deſcripto abſcindet, tot palmos continebit hori-
              <lb/>
            zontalis longitudo BF: </s>
            <s xml:id="echoid-s6016" xml:space="preserve"> propterea quod eadem eſt pro portio DA, ad AE,
              <note symbol="d" position="left" xlink:label="note-184-05" xlink:href="note-184-05a" xml:space="preserve">4. ſexti.</note>
            CB, ad BF, quippe cum triangula D A E, CBF, oſtenſa ſint ſimilia. </s>
            <s xml:id="echoid-s6017" xml:space="preserve">Cum ergo ex
              <lb/>
            conſtructione, recta AE, complectatur tot partes rectę A D, quot ex A, in ſemi-
              <lb/>
            circulum AED, vſque ad filum perpendiculiſunt translatæ, (vt in noſtro exem-
              <lb/>
            plo partes propemodum 9 {1/2}.) </s>
            <s xml:id="echoid-s6018" xml:space="preserve">comprehendentur totidem palmirectæ CB, in re-
              <lb/>
            cta BF. </s>
            <s xml:id="echoid-s6019" xml:space="preserve">Eſt autem conſideratione dignum, partes poſterioris ſemicirculi contra-
              <lb/>
            rio ordine ſimiles eſſe partibus prioris ſemicir culi IDK. </s>
            <s xml:id="echoid-s6020" xml:space="preserve">Nam ſi verbi gratia rectæ
              <lb/>
            D E, quæ æqualis eſt tribus partibus rectæ D A, initium ſumentibus à D, </s>
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