Clavius, Christoph, Geometria practica

Table of handwritten notes

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          <pb o="39" file="069" n="69" rhead="LIBER PRIMVS."/>
          <p>
            <s xml:id="echoid-s1420" xml:space="preserve">10. </s>
            <s xml:id="echoid-s1421" xml:space="preserve">
              <emph style="sc">Qvando</emph>
            intra Quadrantem non deſcripti ſunt plures quadrantes,
              <lb/>
              <note position="right" xlink:label="note-069-01" xlink:href="note-069-01a" xml:space="preserve">Quo pact@
                <lb/>
              per circinum
                <lb/>
              deprehendan-
                <lb/>
              tur Minuta,
                <lb/>
              ac ſecunda in
                <lb/>
              quauis propo-
                <lb/>
              ſita grad{us}
                <lb/>
              particula.
                <lb/>
                <lb/>
              </note>
            ſed vnicus tantum adeſt in 90. </s>
            <s xml:id="echoid-s1422" xml:space="preserve">gradus exquiſitè diſtributus, cognoſcemus ſo-
              <lb/>
            lo circinibeneſicio, quot Minuta, ac ſecunda in quauis gradus particula conti-
              <lb/>
            neantur: </s>
            <s xml:id="echoid-s1423" xml:space="preserve">id quod etiam in libello de vſu, & </s>
            <s xml:id="echoid-s1424" xml:space="preserve">fabrica inſtrumenti horologiorũ,
              <lb/>
            & </s>
            <s xml:id="echoid-s1425" xml:space="preserve">in Aſtrolabio fecimus, hoc ſcilicet modo. </s>
            <s xml:id="echoid-s1426" xml:space="preserve">Sit data verbigratia particulatu,
              <lb/>
            in gradu 20. </s>
            <s xml:id="echoid-s1427" xml:space="preserve">ſuperioris Quadrantis BC. </s>
            <s xml:id="echoid-s1428" xml:space="preserve">Sumatur ea diligentiſsimè beneſicio
              <lb/>
            circini, & </s>
            <s xml:id="echoid-s1429" xml:space="preserve">à principio Quadrantis, id eſt, à puncto C, incipiendo, eadem aper-
              <lb/>
            tura circini accipiantur 60. </s>
            <s xml:id="echoid-s1430" xml:space="preserve">æquales particulæ vſque ad punctum X, ita vt arcus
              <lb/>
            CX, ſexagecuplus ſit arcus t u: </s>
            <s xml:id="echoid-s1431" xml:space="preserve">Quot. </s>
            <s xml:id="echoid-s1432" xml:space="preserve">n. </s>
            <s xml:id="echoid-s1433" xml:space="preserve">gradus integri in hoc arcu ſexagecu-
              <lb/>
            plo comprehenduntur, tot minuta complectetur particula data tu. </s>
            <s xml:id="echoid-s1434" xml:space="preserve">Et ſi vl-
              <lb/>
            tra gradus integros in arcu CX, ſuperſit aliqua particula, accipiatur ea ſexagies
              <lb/>
            quoque, initio facto à puncto C. </s>
            <s xml:id="echoid-s1435" xml:space="preserve">Nam quot gradus integri in hoc arcu ſexa-
              <lb/>
            gecuplo continentur, tot ſecunda vltra Minuta inuenta continebuntur in da-
              <lb/>
              <handwritten xlink:label="hd-069-1" xlink:href="hd-069-1a" number="24"/>
              <handwritten xlink:label="hd-069-1" xlink:href="hd-069-1a" number="25"/>
              <handwritten xlink:label="hd-069-1" xlink:href="hd-069-1a" number="26"/>
              <handwritten xlink:label="hd-069-1" xlink:href="hd-069-1a" number="27"/>
              <handwritten xlink:label="hd-069-1" xlink:href="hd-069-1a" number="28"/>
              <handwritten xlink:label="hd-069-1" xlink:href="hd-069-1a" number="29"/>
            ta particula t u. </s>
            <s xml:id="echoid-s1436" xml:space="preserve">Quod ſi adhuc aliquid ſuperſit, reperientur eodem modo Ter-
              <lb/>
            tia, &</s>
            <s xml:id="echoid-s1437" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1438" xml:space="preserve">Ita que cumin arcu CX, quiſexagecuplus eſt particulæ t u, continean-
              <lb/>
            tur 40. </s>
            <s xml:id="echoid-s1439" xml:space="preserve">gradus integri, comprehendet particula t u, quadraginta Minuta, & </s>
            <s xml:id="echoid-s1440" xml:space="preserve">in-
              <lb/>
            ſuper tot ſecunda, quot gradus continenturin arcu, qui ſexagecuplus ſit par-
              <lb/>
            ticulæ vltra 40. </s>
            <s xml:id="echoid-s1441" xml:space="preserve">gradus in arcu CX, contentæ, &</s>
            <s xml:id="echoid-s1442" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1443" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1444" xml:space="preserve">
              <emph style="sc">Hoc</emph>
            autem ita demonſtro. </s>
            <s xml:id="echoid-s1445" xml:space="preserve">Quã proportionem habet arcus 60. </s>
            <s xml:id="echoid-s1446" xml:space="preserve">graduum
              <lb/>
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              <handwritten xlink:label="hd-069-1" xlink:href="hd-069-1a" number="25"/>
              <handwritten xlink:label="hd-069-1" xlink:href="hd-069-1a" number="26"/>
              <handwritten xlink:label="hd-069-1" xlink:href="hd-069-1a" number="27"/>
              <handwritten xlink:label="hd-069-1" xlink:href="hd-069-1a" number="28"/>
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            ad 1. </s>
            <s xml:id="echoid-s1447" xml:space="preserve">gradum, eam habetarcus CX. </s>
            <s xml:id="echoid-s1448" xml:space="preserve">ad particulam tu, cum vtrobique propor-
              <lb/>
            tio ſit ſexagecupla. </s>
            <s xml:id="echoid-s1449" xml:space="preserve">Igitur permutando erit, vt arcus 60. </s>
            <s xml:id="echoid-s1450" xml:space="preserve">graduum ad arcum
              <lb/>
            CX, ita 1. </s>
            <s xml:id="echoid-s1451" xml:space="preserve">gradus ad particulam t u: </s>
            <s xml:id="echoid-s1452" xml:space="preserve">Ac proinde quot partes ſexageſimæ arcus
              <lb/>
            60. </s>
            <s xml:id="echoid-s1453" xml:space="preserve">graduum, hoc eſt, quot gradus in arcu C X, continentur, tot ſexageſimæ
              <lb/>
            partes vnius gradus, id eſt, tot minuta in particula tu, exiſtent. </s>
            <s xml:id="echoid-s1454" xml:space="preserve">Item quam
              <lb/>
            proportionem haber arcus 60. </s>
            <s xml:id="echoid-s1455" xml:space="preserve">Minutorum adi. </s>
            <s xml:id="echoid-s1456" xml:space="preserve">Minutum eam habet arcus ſe-
              <lb/>
            xagecuplus particulæ, quæ vltra gradus integros vſque ad X, ſupereſt ad hanc
              <lb/>
            ipſam particulam. </s>
            <s xml:id="echoid-s1457" xml:space="preserve">Permutando igitur erit, vt arcus 60. </s>
            <s xml:id="echoid-s1458" xml:space="preserve">Minutorum ad arcum
              <lb/>
            ſexagecuplum dictæ particulæ reliquæ, ita 1. </s>
            <s xml:id="echoid-s1459" xml:space="preserve">Minutum ad dictam particulam re-
              <lb/>
            liquam. </s>
            <s xml:id="echoid-s1460" xml:space="preserve">Quare quot partes ſexageſimæ arcus 60. </s>
            <s xml:id="echoid-s1461" xml:space="preserve">Minutorum, hoc eſt, quot
              <lb/>
            minuta in arcu dictæ particulæ ſexagecuplo (ſumendo nunc gradus Quadran-
              <lb/>
            tis BC, pro Minutis) continentur, tot partes ſexageſimæ vnius Minuti, id eſt, tot
              <lb/>
            Secunda, in reliqua illa particula includentur, & </s>
            <s xml:id="echoid-s1462" xml:space="preserve">ſic deinceps, ſi opus ſit, de
              <lb/>
            Tertijs, Quartis, &</s>
            <s xml:id="echoid-s1463" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1464" xml:space="preserve">intelligatur. </s>
            <s xml:id="echoid-s1465" xml:space="preserve">Sed ſatis eſt, meo iudicio, ſi minuta diligen-
              <lb/>
            ter inquirantur. </s>
            <s xml:id="echoid-s1466" xml:space="preserve">Etſi quidem particula remanens maior fuerit ſemiſſe gradus,
              <lb/>
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            pro illa Minutum aſſumatur, Minutiſque inuentis adij ciatur, quod tunc in illa
              <lb/>
            particula contineantur plura Secunda quam 30. </s>
            <s xml:id="echoid-s1467" xml:space="preserve">Si verò eadem particula ſe-
              <lb/>
            miſſe gradus fuerit minor, nihil Minutis inuẽtis adijciatur, quod tuncin illa par-
              <lb/>
            ticula pauciora Secũ da includantur, ꝗ̃ 30. </s>
            <s xml:id="echoid-s1468" xml:space="preserve">Si deniq; </s>
            <s xml:id="echoid-s1469" xml:space="preserve">dicta particula ſemiſsi grad.
              <lb/>
            </s>
            <s xml:id="echoid-s1470" xml:space="preserve">fuerit æqualis, liberũ ſit addere Minutis inuẽtis vnum Minutũ, vel non addere.</s>
            <s xml:id="echoid-s1471" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1472" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1473" xml:space="preserve">
              <emph style="sc">Qvia</emph>
            verò fa cilè error committi poteſt, ſi circino particulam dictam
              <lb/>
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              <handwritten xlink:label="hd-069-1" xlink:href="hd-069-1a" number="27"/>
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            gradus, vel minuti ſexagies ordine ſumere velimus, rectius feceris, quando
              <lb/>
            particula data ſemiſſe gradus minor eſt, ſi eam vna cum præcedente graduacce-
              <lb/>
            ptam primo loco quintuples, deinde hunc arcum quintuplũ duples, tertio hũc
              <lb/>
              <handwritten xlink:label="hd-069-1" xlink:href="hd-069-1a" number="24"/>
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            arcum duplum triples, ac tandem quarto hunc arcum triplum iterum duples.
              <lb/>
            </s>
            <s xml:id="echoid-s1474" xml:space="preserve">Vltimus enim hic arcus erit datæ particulæ vna cum gradu accepto ſexagecu-
              <lb/>
            plus. </s>
            <s xml:id="echoid-s1475" xml:space="preserve">Quareſi ex eo demãtur 60. </s>
            <s xml:id="echoid-s1476" xml:space="preserve">gradus, in dicabuntreliqui gradus numerũ mi-
              <lb/>
            nutorumin data particula contentorum. </s>
            <s xml:id="echoid-s1477" xml:space="preserve">Qnod ſi per æſtimationẽ cognoueris,
              <lb/>
              <handwritten xlink:label="hd-069-1" xlink:href="hd-069-1a" number="24"/>
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            </s>
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