Clavius, Christoph, Geometria practica

Table of contents

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[171.] DE AREA RECTANGVLORVM Capvt I.
[172.] DE AREA TRIANGVLORVM Capvt II.
[173.] DE AREA QVADRILATERORVM non rectangulorum. Capvt III.
[174.] DE AREA MVLTIL ATERARVM figurarum irregularium. Capvt IV.
[175.] DE AREA MVLTILATERA-rum figurarum regularium. Capvt V.
[176.] De dimenſione circuli ex Archimede. Capvt VI.
[177.] PROPOSITIO I.
[178.] SCHOLIVM.
[179.] PROPOSITIO II.
[180.] COROLLARIVM.
[181.] PROPOSITIO III.
[182.] DE AREA CIRCVLI, INVENTIONE-que circumferentiæ ex diametro, & diametri ex circumfetentia. Capvt VII.
[184.] II.
[185.] III.
[186.] IIII.
[187.] PROPOSITIO I.
[188.] PROPOSITIO II.
[189.] PROPOSITIO III.
[190.] I. EX diametro aream circuli vera maiorem inueſtigare.
[191.] II. EX diametro aream circuli vera minorem inueſtigare.
[192.] III. EX circumferentia aream circuli vera maiorem colligere.
[193.] IV. EX circumferentia aream circuli vera minorem concludere.
[194.] DE AREA SEGMENTORVM CIRCVLI. Capvt VIII.
[196.] II.
[197.] III.
[198.] IV.
[200.] VI.
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        <div xml:id="echoid-div418" type="section" level="1" n="172">
          <p>
            <s xml:id="echoid-s7001" xml:space="preserve">
              <pb o="169" file="199" n="199" rhead="LIBER QVARTVS."/>
            inquirendum erit fragmentum vltimæ particulæ (ſi quod ſuperfuerit) in parti-
              <lb/>
              <note position="right" xlink:label="note-199-01" xlink:href="note-199-01a" xml:space="preserve">Diuiſovno la-
                <lb/>
              tere figuræ in
                <lb/>
              quotuis part{es}
                <lb/>
              æquales, quo
                <lb/>
              pacto alia la-
                <lb/>
              ter ain eiſdem
                <lb/>
              partib{us} fiant
                <lb/>
              nota.</note>
            bus milleſimis, per ea, quæ Num. </s>
            <s xml:id="echoid-s7002" xml:space="preserve">14. </s>
            <s xml:id="echoid-s7003" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s7004" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7005" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s7006" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7007" xml:space="preserve">docuimus. </s>
            <s xml:id="echoid-s7008" xml:space="preserve">Ita enim in dimen-
              <lb/>
            ſionibus figurarum minus à vero aberrabimus.</s>
            <s xml:id="echoid-s7009" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7010" xml:space="preserve">9. </s>
            <s xml:id="echoid-s7011" xml:space="preserve">
              <emph style="sc">Neminem</emph>
            autẽ moueat, aut perturbet, quod rectas dixerimus metien-
              <lb/>
            das eſſe nonnunquam mechanice per catenulam aliquam ſerreã, aut per inſtru-
              <lb/>
            mentum partium. </s>
            <s xml:id="echoid-s7012" xml:space="preserve">Nam in hoc dimetiendi negotio, præſertimin campis, & </s>
            <s xml:id="echoid-s7013" xml:space="preserve">agris
              <lb/>
            admittenda omnino eſt huiuſmo dimechanica linearum dimenſio, tum quia a-
              <lb/>
            pud omues agrimenſores hic mos eſt: </s>
            <s xml:id="echoid-s7014" xml:space="preserve">tum quia non ſemper via Geometrica id
              <lb/>
            præſtare poteſt; </s>
            <s xml:id="echoid-s7015" xml:space="preserve">tum vero maximè, quia in dimenſi onibus agrorum, ſiue figu-
              <lb/>
              <note position="right" xlink:label="note-199-02" xlink:href="note-199-02a" xml:space="preserve">In negotio di-
                <lb/>
              menſionum
                <lb/>
              admittendam
                <lb/>
              eſſe in nonnul-
                <lb/>
              lis lineis &
                <lb/>
              angulis me-
                <lb/>
              chanicam
                <lb/>
              menſuratio-
                <lb/>
              nem.</note>
            rarum ſatis eſt rem prope verum attingere, dum modo notabilis error non cõ-
              <lb/>
            mitatur. </s>
            <s xml:id="echoid-s7016" xml:space="preserve">Quod ſi hæc dimenſio quarundem linearum alicuinõ probetur, is pro-
              <lb/>
            fecto è medio tollat, neceſſe eſt, omnem agrorum, figurarumue dimenſionem.
              <lb/>
            </s>
            <s xml:id="echoid-s7017" xml:space="preserve">Vnde enim conſtat, agrum propoſitum, vel figuram habere latera cognita, niſi
              <lb/>
            hæcipſa per menſuram aliquam materialem ſint explorata? </s>
            <s xml:id="echoid-s7018" xml:space="preserve">Siigitur laterum di-
              <lb/>
            menſio mechanica, tanquam à vero parum aberrans, ab omnibus vſurpatur,
              <lb/>
            cur eamin lineisintra figuras metiendis reij ciendam cenſeamus, nõ video. </s>
            <s xml:id="echoid-s7019" xml:space="preserve">Non
              <lb/>
            nego tamen, viam Geometricam, quando fieri poteſt, adhiben dam eſſe. </s>
            <s xml:id="echoid-s7020" xml:space="preserve">In fi-
              <lb/>
            guris quoque, vbilatera non ſunt nimis magna, vtendũ cenſeo doctrina, quam
              <lb/>
            in inſtrumento partium lib. </s>
            <s xml:id="echoid-s7021" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7022" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s7023" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7024" xml:space="preserve">ad finem Num. </s>
            <s xml:id="echoid-s7025" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7026" xml:space="preserve">tradidimus, non neglectis
              <lb/>
            etiamijs, quæ in eodem lib. </s>
            <s xml:id="echoid-s7027" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7028" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s7029" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7030" xml:space="preserve">Nume 14. </s>
            <s xml:id="echoid-s7031" xml:space="preserve">de quauis particula lineæ cogno-
              <lb/>
            ſcenda, in partibus ſaltem milleſimis, ſcripſimus, quod hac ratione vix à vero
              <lb/>
            quis aberrare poſsit.</s>
            <s xml:id="echoid-s7032" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7033" xml:space="preserve">
              <emph style="sc">Idem</emph>
            de mechanica angulorum dimenſione per quadrantem intelligen-
              <lb/>
            dum eſt: </s>
            <s xml:id="echoid-s7034" xml:space="preserve">præſertim ſi præter gradus inueſtigentur quo que minuta, vt lib. </s>
            <s xml:id="echoid-s7035" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7036" xml:space="preserve">cap.
              <lb/>
            </s>
            <s xml:id="echoid-s7037" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7038" xml:space="preserve">docuimus.</s>
            <s xml:id="echoid-s7039" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div455" type="section" level="1" n="173">
          <head xml:id="echoid-head176" xml:space="preserve">DE AREA QVADRILATERORVM
            <lb/>
          non rectangulorum.</head>
          <head xml:id="echoid-head177" xml:space="preserve">
            <emph style="sc">Capvt</emph>
          III.</head>
          <p>
            <s xml:id="echoid-s7040" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7041" xml:space="preserve">TRIA ſunt genera quadril aterarum figurarum, quæ vel nullum angu-
              <lb/>
              <note position="right" xlink:label="note-199-03" xlink:href="note-199-03a" xml:space="preserve">Rhombi &
                <lb/>
              Rhomboidis
                <lb/>
              area</note>
            lum rectum habent, vel certe non omnes rectos: </s>
            <s xml:id="echoid-s7042" xml:space="preserve">Rhombus, Rhom-
              <lb/>
            boides, & </s>
            <s xml:id="echoid-s7043" xml:space="preserve">Trapezium. </s>
            <s xml:id="echoid-s7044" xml:space="preserve">Primæ duæ figuræ nullum habent angulum re-
              <lb/>
            ctum: </s>
            <s xml:id="echoid-s7045" xml:space="preserve">poſterior autem poteſt habere vel vnum rectum, vel duos, veletiam
              <lb/>
            nullum: </s>
            <s xml:id="echoid-s7046" xml:space="preserve">Item duo latera oppoſita parallela, vel non parallela. </s>
            <s xml:id="echoid-s7047" xml:space="preserve">Rhom-
              <lb/>
            bi & </s>
            <s xml:id="echoid-s7048" xml:space="preserve">Rhomboidis, quorum latera nota ſint, area pro-
              <lb/>
              <figure xlink:label="fig-199-01" xlink:href="fig-199-01a" number="127">
                <image file="199-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/199-01"/>
              </figure>
            ducitur ex ductu perpendicularis in latus, in quod per-
              <lb/>
            pendicularis cadit. </s>
            <s xml:id="echoid-s7049" xml:space="preserve">Ita vt magnitudo perpendicularis accu-
              <lb/>
            rate ſit prius exploranda vel per inſtrumentum partium initio
              <lb/>
            huius operis conſtructi, vt paulo ante cap. </s>
            <s xml:id="echoid-s7050" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7051" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s7052" xml:space="preserve">8. </s>
            <s xml:id="echoid-s7053" xml:space="preserve">monui-
              <lb/>
            mus, vel alio modo, vt mox dicam. </s>
            <s xml:id="echoid-s7054" xml:space="preserve">Verbi gratia, in Rhombo
              <lb/>
            & </s>
            <s xml:id="echoid-s7055" xml:space="preserve">Rhomboide A B C D, producetur area ex multiplicatione
              <lb/>
            perpendicularis AE, in latus B C, Nam rectangulum A
              <note symbol="a" position="right" xlink:label="note-199-04" xlink:href="note-199-04a" xml:space="preserve">35. primi.</note>
            ſub A E, & </s>
            <s xml:id="echoid-s7056" xml:space="preserve">A D, comprehenſum æquale eſt parallelogram-
              <lb/>
            mo B D, quòd hæc duo parallelogramma ſint inter </s>
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