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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          <pb o="147" file="177" n="177" rhead="LIBER TERTIVS."/>
          <p>
            <s xml:id="echoid-s5658" xml:space="preserve">ALTITVDINEM monti impoſitam, ſi modo altitudinis baſis poſſit
              <lb/>
            conſpici, vel portionem ſuperiorem alicuius turris, beneficio ſpeculi
              <lb/>
            plani efficere notam.</s>
            <s xml:id="echoid-s5659" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div388" type="section" level="1" n="162">
          <head xml:id="echoid-head165" xml:space="preserve">PROBLEMA XLI.</head>
          <p>
            <s xml:id="echoid-s5660" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5661" xml:space="preserve">
              <emph style="sc">Qvando</emph>
            ad turrim patet acceſſus, vt eius à menſore diſtantia cogno-
              <lb/>
            ſcipoſsit; </s>
            <s xml:id="echoid-s5662" xml:space="preserve">ſi per probl. </s>
            <s xml:id="echoid-s5663" xml:space="preserve">39. </s>
            <s xml:id="echoid-s5664" xml:space="preserve">inueſtigetur tam altitudo à ſummitate portionis pro-
              <lb/>
            poſitæ, vſque ad baſem turris, quam altitudo ab infima parte eiuſdem portio-
              <lb/>
            nis, vſque ad eandem turris baſem: </s>
            <s xml:id="echoid-s5665" xml:space="preserve">& </s>
            <s xml:id="echoid-s5666" xml:space="preserve">minor hæc altitudo ab illa maiore de-
              <lb/>
            matur, reliqua fiet portio, quæ inquiritur.</s>
            <s xml:id="echoid-s5667" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5668" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5669" xml:space="preserve">
              <emph style="sc">At</emph>
            verò, quando altitudo monti eſt impoſita, & </s>
            <s xml:id="echoid-s5670" xml:space="preserve">baſis altitudinis appa-
              <lb/>
            ret, aut ad turrim nonpatet acceſſ
              <unsure/>
            us: </s>
            <s xml:id="echoid-s5671" xml:space="preserve">exquirenda erit per præcedens problema
              <lb/>
            vtraquealtitudo prædicta. </s>
            <s xml:id="echoid-s5672" xml:space="preserve">Namrurſus minor detracta exmaiore, reliquam fa-
              <lb/>
            ciet altitudinem, vel portionem, quæ deſideratur.</s>
            <s xml:id="echoid-s5673" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5674" xml:space="preserve">SITVM cuiuslibet campi, aut atrii, vel templi, vel etiam vrbis, aut re-
              <lb/>
            g@onis cuiuſuis in plano deſcribere, ſi è duobus locis intra ipſum ſi-
              <lb/>
            tum aſſumptis baculi ex omnibus campi angulis erecti, vel certè
              <lb/>
            ipſi anguli in ædificio, aut vrbe, vel loca regionis videri poſſint: </s>
            <s xml:id="echoid-s5675" xml:space="preserve">ſi-
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            mulque longitudines laterum campi, vel ædificii, nec non diſtan-
              <lb/>
            tias inter angulos, & </s>
            <s xml:id="echoid-s5676" xml:space="preserve">vtrumuis locorum aſſumptorum in data men-
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            ſura cognoſcere. </s>
            <s xml:id="echoid-s5677" xml:space="preserve">Quod ſi talia duo loca intra ſitum eliginequeant,
              <lb/>
            idem efficere, dummodo ſitum poſſimus circumire.</s>
            <s xml:id="echoid-s5678" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div389" type="section" level="1" n="163">
          <head xml:id="echoid-head166" xml:space="preserve">PROBLEMA XLII.</head>
          <p>
            <s xml:id="echoid-s5679" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5680" xml:space="preserve">
              <emph style="sc">Etsi</emph>
            problema hocvel Geographicum eſt, vel Architectonicum; </s>
            <s xml:id="echoid-s5681" xml:space="preserve">ta-
              <lb/>
              <note position="right" xlink:label="note-177-01" xlink:href="note-177-01a" xml:space="preserve">Sit{us} camp@
                <lb/>
              cuiuſuis, quo
                <unsure/>
                <lb/>
              pacto ex duo-
                <lb/>
              b{us} locis in-
                <lb/>
              tra ipſum aſ-
                <lb/>
              ſumptis deli-
                <lb/>
              neetur.</note>
            men quia ſine dimenſione linearum abſolui non poteſt, lubet illud hocloco
              <lb/>
            paucis explicare. </s>
            <s xml:id="echoid-s5682" xml:space="preserve">Sit ergo campus quinque lateribus AB, BC, CD, DE, EA,
              <lb/>
            cinctus. </s>
            <s xml:id="echoid-s5683" xml:space="preserve">Figantur in quinque angulis A, B, C, D, E, quinque baculi ad angu-
              <lb/>
            losrectos cum Horizonte, paretur que circa medium areæ planum aliquantu-
              <lb/>
            lum altum Horizonti æquidiſtans, in quo duo puncta F, G, quantumlibetin-
              <lb/>
            ter ſe diſtantia, verbigratia 100. </s>
            <s xml:id="echoid-s5684" xml:space="preserve">pedibus, è quibus omnes quinque baculi cerni
              <lb/>
            poſsint. </s>
            <s xml:id="echoid-s5685" xml:space="preserve">Per F, G, ducatur recta F G, ad vtraſque partes; </s>
            <s xml:id="echoid-s5686" xml:space="preserve">continebitque ſe-
              <lb/>
            gmentum F G, 100. </s>
            <s xml:id="echoid-s5687" xml:space="preserve">pedes ex hypotheſi. </s>
            <s xml:id="echoid-s5688" xml:space="preserve">Affixa deinde dioptra volubili cum
              <lb/>
            pinna cidiis in vtroq; </s>
            <s xml:id="echoid-s5689" xml:space="preserve">puncto F, & </s>
            <s xml:id="echoid-s5690" xml:space="preserve">G, deſcriptiſque circulis duobus ex F, & </s>
            <s xml:id="echoid-s5691" xml:space="preserve">G, vt
              <lb/>
            per eorum circumferentias angulorum magnitudines, qui in F, G, conſtituẽtur,
              <lb/>
            cognoſcipo ſsint, inſpiciantur ex F, & </s>
            <s xml:id="echoid-s5692" xml:space="preserve">G, perforamina pinnacidiorum (circum-
              <lb/>
            ducta dioptra) baculi ex angulis A, B, C, D, E, erecti, & </s>
            <s xml:id="echoid-s5693" xml:space="preserve">anguli, quos linea fiducię
              <lb/>
            cũ recta HI, facit, aut quos rectæ à linea fiduciæ deſignatę inter ſefaciunt, tranſ-
              <lb/>
            ferantur ordine ad puncta K, L, quomodocunq; </s>
            <s xml:id="echoid-s5694" xml:space="preserve">inter ſe diſtantia in recta, </s>
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