Clavius, Christoph, Geometria practica

List of thumbnails

< >
31
31 		32
32
33
33 (3) 		34
34 (4)
35
35 (5) 		36
36 (6)
37
37 (7) 		38
38 (8)
39
39 (9) 		40
40 (10)
< >
page |< < (10) of 450 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div17" type="section" level="1" n="17">
          <pb o="10" file="040" n="40" rhead="GEOMETR. PRACT."/>
          <p>
            <s xml:id="echoid-s720" xml:space="preserve">16. </s>
            <s xml:id="echoid-s721" xml:space="preserve">
              <emph style="sc">In</emph>
            altera facie inſtrumenti, in quam chordę arcuum quadrantis
              <lb/>
              <note position="left" xlink:label="note-040-01" xlink:href="note-040-01a" xml:space="preserve">Quo pacto a-
                <lb/>
              liter ex circu-
                <lb/>
              lo abſcindan-
                <lb/>
              tur arc{us} da-
                <lb/>
              torum gr. &
                <lb/>
              min.</note>
            ſunt translatę, facilius arcum quotcunque graduum accipiemus, hoc mo-
              <lb/>
            do. </s>
            <s xml:id="echoid-s722" xml:space="preserve">Chordæ quadrantis propoſiti ſumatur ęquale interuallum F G: </s>
            <s xml:id="echoid-s723" xml:space="preserve">Vel
              <lb/>
            etiam ſemidiametro Quadrantis, chordę nimirum grad. </s>
            <s xml:id="echoid-s724" xml:space="preserve">60. </s>
            <s xml:id="echoid-s725" xml:space="preserve">capiatur inter-
              <lb/>
            uallum 60. </s>
            <s xml:id="echoid-s726" xml:space="preserve">60. </s>
            <s xml:id="echoid-s727" xml:space="preserve">ęquale. </s>
            <s xml:id="echoid-s728" xml:space="preserve">Siigitur verbigratia deſideret quis arcum Grad. </s>
            <s xml:id="echoid-s729" xml:space="preserve">56.
              <lb/>
            </s>
            <s xml:id="echoid-s730" xml:space="preserve">ſumendum erit per circinum interuallum inter puncta 56. </s>
            <s xml:id="echoid-s731" xml:space="preserve">& </s>
            <s xml:id="echoid-s732" xml:space="preserve">56. </s>
            <s xml:id="echoid-s733" xml:space="preserve">Huic enim
              <lb/>
            ęqualis eſt chorda grad. </s>
            <s xml:id="echoid-s734" xml:space="preserve">56, Si præter gradus accipienda ſint etiam minuta,
              <lb/>
            oportebit per ęſtimationem in ſequentiparticula accipere talem partem ipſi-
              <lb/>
            us, qualem minuta propoſita partem vnius gradus conſtituunt, Vt ſi cupiat
              <lb/>
            quis min. </s>
            <s xml:id="echoid-s735" xml:space="preserve">30. </s>
            <s xml:id="echoid-s736" xml:space="preserve">ſumenda eſt ſemiſsis, ſi 20. </s>
            <s xml:id="echoid-s737" xml:space="preserve">tertia pars, &</s>
            <s xml:id="echoid-s738" xml:space="preserve">c. </s>
            <s xml:id="echoid-s739" xml:space="preserve">Interuallum enim
              <lb/>
            inter partem regulę A F, & </s>
            <s xml:id="echoid-s740" xml:space="preserve">partemregulę A G, acceptum dabit chordam
              <lb/>
              <note position="left" xlink:label="note-040-02" xlink:href="note-040-02a" xml:space="preserve">Quo pacto a-
                <lb/>
              liter cogno-
                <lb/>
              ſcatur, quot
                <lb/>
              grad. & min.
                <lb/>
              in dato arcu
                <lb/>
              comprehen-
                <lb/>
              dantur.</note>
            quęſiti arcus.</s>
            <s xml:id="echoid-s741" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s742" xml:space="preserve">
              <emph style="sc">Vicissim</emph>
            ſi cognoſcere velimus, quot gradus, ac minuta in dato arcu
              <lb/>
            exiſtant, inueſtiganda erit eius chorda inter rectas A F, A G, ita vt puncta eius
              <lb/>
            cadant vel in duas partes eaſdem, vel ęqualiter à duabus eiſdẽ diſtent. </s>
            <s xml:id="echoid-s743" xml:space="preserve">Nam
              <lb/>
            tot gradus continebuntur in dato arcu, quotgradus cõtinentur in recta A F,
              <lb/>
            à centro A, vſque ad punctum, è quo chorda datiarcus in rectam A G, trãs-
              <lb/>
            lata eſt: </s>
            <s xml:id="echoid-s744" xml:space="preserve">ita vt ſi dati arcus chorda extiterit inter grad. </s>
            <s xml:id="echoid-s745" xml:space="preserve">70. </s>
            <s xml:id="echoid-s746" xml:space="preserve">& </s>
            <s xml:id="echoid-s747" xml:space="preserve">70. </s>
            <s xml:id="echoid-s748" xml:space="preserve">propoſitus ar-
              <lb/>
            cus complectatur gr. </s>
            <s xml:id="echoid-s749" xml:space="preserve">70. </s>
            <s xml:id="echoid-s750" xml:space="preserve">&</s>
            <s xml:id="echoid-s751" xml:space="preserve">c.</s>
            <s xml:id="echoid-s752" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Quaratione
            <lb/>
          ex datarecta
            <lb/>
          pars imperata
            <lb/>
          abſcindatur.</note>
          <handwritten number="10"/>
          <p>
            <s xml:id="echoid-s753" xml:space="preserve">17. </s>
            <s xml:id="echoid-s754" xml:space="preserve">
              <emph style="sc">Iam</emph>
            vero nemo neſcit, ſi ex linea aliqua abſcindenda ſit {1/2}. </s>
            <s xml:id="echoid-s755" xml:space="preserve">vel {1/3}. </s>
            <s xml:id="echoid-s756" xml:space="preserve">vel
              <lb/>
            {1/17}. </s>
            <s xml:id="echoid-s757" xml:space="preserve">vel denique quęcunq; </s>
            <s xml:id="echoid-s758" xml:space="preserve">pars, cuius denominator maior non ſit quam 100.
              <lb/>
            </s>
            <s xml:id="echoid-s759" xml:space="preserve">quo pactoid fieri debeat. </s>
            <s xml:id="echoid-s760" xml:space="preserve">Sinamque interuallum F G, in priori facie inſtru-
              <lb/>
            menti ęquale fuerit datę rectę, dabit interuallum inter 50. </s>
            <s xml:id="echoid-s761" xml:space="preserve">& </s>
            <s xml:id="echoid-s762" xml:space="preserve">50. </s>
            <s xml:id="echoid-s763" xml:space="preserve">partem {1/2}. </s>
            <s xml:id="echoid-s764" xml:space="preserve">
              <lb/>
            Interuallum autem inter 25. </s>
            <s xml:id="echoid-s765" xml:space="preserve">& </s>
            <s xml:id="echoid-s766" xml:space="preserve">25. </s>
            <s xml:id="echoid-s767" xml:space="preserve">partem. </s>
            <s xml:id="echoid-s768" xml:space="preserve">{1/4}. </s>
            <s xml:id="echoid-s769" xml:space="preserve">Interuallum vero inter 20. </s>
            <s xml:id="echoid-s770" xml:space="preserve">& </s>
            <s xml:id="echoid-s771" xml:space="preserve">
              <lb/>
            20. </s>
            <s xml:id="echoid-s772" xml:space="preserve">partem {1/5}. </s>
            <s xml:id="echoid-s773" xml:space="preserve">Item ſi interuallum inter 90. </s>
            <s xml:id="echoid-s774" xml:space="preserve">& </s>
            <s xml:id="echoid-s775" xml:space="preserve">90. </s>
            <s xml:id="echoid-s776" xml:space="preserve">vel inter 60. </s>
            <s xml:id="echoid-s777" xml:space="preserve">& </s>
            <s xml:id="echoid-s778" xml:space="preserve">60. </s>
            <s xml:id="echoid-s779" xml:space="preserve">vel in-
              <lb/>
            ter 30. </s>
            <s xml:id="echoid-s780" xml:space="preserve">& </s>
            <s xml:id="echoid-s781" xml:space="preserve">30. </s>
            <s xml:id="echoid-s782" xml:space="preserve">fiat datę rectę ęquale, dabitinteruallum inter 30. </s>
            <s xml:id="echoid-s783" xml:space="preserve">& </s>
            <s xml:id="echoid-s784" xml:space="preserve">30. </s>
            <s xml:id="echoid-s785" xml:space="preserve">vel in-
              <lb/>
            ter 20. </s>
            <s xml:id="echoid-s786" xml:space="preserve">& </s>
            <s xml:id="echoid-s787" xml:space="preserve">20. </s>
            <s xml:id="echoid-s788" xml:space="preserve">vel inter 10. </s>
            <s xml:id="echoid-s789" xml:space="preserve">& </s>
            <s xml:id="echoid-s790" xml:space="preserve">0. </s>
            <s xml:id="echoid-s791" xml:space="preserve">partem {1/3}. </s>
            <s xml:id="echoid-s792" xml:space="preserve">Rurſus ſi interuallum inter 17. </s>
            <s xml:id="echoid-s793" xml:space="preserve">& </s>
            <s xml:id="echoid-s794" xml:space="preserve">17. </s>
            <s xml:id="echoid-s795" xml:space="preserve">
              <lb/>
            vel inter 34. </s>
            <s xml:id="echoid-s796" xml:space="preserve">& </s>
            <s xml:id="echoid-s797" xml:space="preserve">34. </s>
            <s xml:id="echoid-s798" xml:space="preserve">datæ rectę ſumatur ęquale, dabit interuallum inter 1. </s>
            <s xml:id="echoid-s799" xml:space="preserve">& </s>
            <s xml:id="echoid-s800" xml:space="preserve">1. </s>
            <s xml:id="echoid-s801" xml:space="preserve">
              <lb/>
            vel inter 2. </s>
            <s xml:id="echoid-s802" xml:space="preserve">& </s>
            <s xml:id="echoid-s803" xml:space="preserve">2. </s>
            <s xml:id="echoid-s804" xml:space="preserve">partem {1/1@}. </s>
            <s xml:id="echoid-s805" xml:space="preserve">Atinteruallum inter 5. </s>
            <s xml:id="echoid-s806" xml:space="preserve">& </s>
            <s xml:id="echoid-s807" xml:space="preserve">5. </s>
            <s xml:id="echoid-s808" xml:space="preserve">velinter 10. </s>
            <s xml:id="echoid-s809" xml:space="preserve">& </s>
            <s xml:id="echoid-s810" xml:space="preserve">10. </s>
            <s xml:id="echoid-s811" xml:space="preserve">da-
              <lb/>
            bit {5/17}. </s>
            <s xml:id="echoid-s812" xml:space="preserve">&</s>
            <s xml:id="echoid-s813" xml:space="preserve">c. </s>
            <s xml:id="echoid-s814" xml:space="preserve">Ex hiſceporro exemplis adductis facileintelliges, quo modo te
              <lb/>
            in aliis partibus imperatis gerere debeas.</s>
            <s xml:id="echoid-s815" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Quaratione
            <lb/>
          ex dato circu-
            <lb/>
          lo lat{us} poly-
            <lb/>
          goni propoſiti
            <lb/>
          inueniatur.</note>
          <p>
            <s xml:id="echoid-s816" xml:space="preserve">18. </s>
            <s xml:id="echoid-s817" xml:space="preserve">
              <emph style="sc">Non</emph>
            aliter in poſteriori facie inſtrumenti Iatera polygonorũ in quo-
              <lb/>
            uis circulo reperiemus. </s>
            <s xml:id="echoid-s818" xml:space="preserve">Nam gradus 120. </s>
            <s xml:id="echoid-s819" xml:space="preserve">(quifacile accipientur, ſi quadran-
              <lb/>
            ti graduum 90. </s>
            <s xml:id="echoid-s820" xml:space="preserve">adij ciantur gradus 30.) </s>
            <s xml:id="echoid-s821" xml:space="preserve">dabuntlatus trianguli ęquilateri. </s>
            <s xml:id="echoid-s822" xml:space="preserve">Gra-
              <lb/>
            dus 90. </s>
            <s xml:id="echoid-s823" xml:space="preserve">latus quadrati. </s>
            <s xml:id="echoid-s824" xml:space="preserve">Gradus 72. </s>
            <s xml:id="echoid-s825" xml:space="preserve">latus pentagoni. </s>
            <s xml:id="echoid-s826" xml:space="preserve">Gradus 51 {3/7}. </s>
            <s xml:id="echoid-s827" xml:space="preserve">hoc eſt,
              <lb/>
            gradus 51. </s>
            <s xml:id="echoid-s828" xml:space="preserve">min. </s>
            <s xml:id="echoid-s829" xml:space="preserve">26. </s>
            <s xml:id="echoid-s830" xml:space="preserve">paulo minus, latus heptagoni. </s>
            <s xml:id="echoid-s831" xml:space="preserve">&</s>
            <s xml:id="echoid-s832" xml:space="preserve">c. </s>
            <s xml:id="echoid-s833" xml:space="preserve">qui quidem gradus
              <lb/>
            habebuntur, ſi gradus 360. </s>
            <s xml:id="echoid-s834" xml:space="preserve">totius circuli per numerum laterum polygoni
              <lb/>
            propoſiti diuidantur.</s>
            <s xml:id="echoid-s835" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s836" xml:space="preserve">19. </s>
            <s xml:id="echoid-s837" xml:space="preserve">
              <emph style="sc">Qvando</emph>
            in dato quadrante cognoſcere lubet, (quod non raro v-
              <lb/>
              <note position="left" xlink:label="note-040-05" xlink:href="note-040-05a" xml:space="preserve">Quopacto co-
                <lb/>
              gnoſcatur, in
                <lb/>
              quodpunctũ
                <lb/>
              ſemidiametri
                <lb/>
              cadat perpen-
                <lb/>
              dicularis ex
                <lb/>
              quolibet gra-
                <lb/>
              du quadran-
                <lb/>
              tisdemiſſa.</note>
            ſu venit) in quodnam punctum ſemidiametriperpendicularis ex quouis gra-
              <lb/>
            du ab altera ſemidiametro numerato demiſſa cadat, ita agendum erit. </s>
            <s xml:id="echoid-s838" xml:space="preserve">Sit
              <lb/>
            verbi gratia ſemidiameter alicuius quadrantis F G, quærendumq; </s>
            <s xml:id="echoid-s839" xml:space="preserve">ſit punctũ,
              <lb/>
            in quod cadat perpendicularis ex grad. </s>
            <s xml:id="echoid-s840" xml:space="preserve">26. </s>
            <s xml:id="echoid-s841" xml:space="preserve">min. </s>
            <s xml:id="echoid-s842" xml:space="preserve">45. </s>
            <s xml:id="echoid-s843" xml:space="preserve">demiſſa. </s>
            <s xml:id="echoid-s844" xml:space="preserve">Sinus grad. </s>
            <s xml:id="echoid-s845" xml:space="preserve">26.
              <lb/>
            </s>
            <s xml:id="echoid-s846" xml:space="preserve">min. </s>
            <s xml:id="echoid-s847" xml:space="preserve">45. </s>
            <s xml:id="echoid-s848" xml:space="preserve">eſt 45. </s>
            <s xml:id="echoid-s849" xml:space="preserve">poſito ſinutoto 100. </s>
            <s xml:id="echoid-s850" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s851" xml:space="preserve">recta interpartes 45. </s>
            <s xml:id="echoid-s852" xml:space="preserve">& </s>
            <s xml:id="echoid-s853" xml:space="preserve">45. </s>
            <s xml:id="echoid-s854" xml:space="preserve">erit
              <lb/>
            ſinus grad. </s>
            <s xml:id="echoid-s855" xml:space="preserve">26. </s>
            <s xml:id="echoid-s856" xml:space="preserve">min. </s>
            <s xml:id="echoid-s857" xml:space="preserve">45. </s>
            <s xml:id="echoid-s858" xml:space="preserve">reſpectu ſinus totius F G, vt Num. </s>
            <s xml:id="echoid-s859" xml:space="preserve">12. </s>
            <s xml:id="echoid-s860" xml:space="preserve">oſtenſum eſt. </s>
            <s xml:id="echoid-s861" xml:space="preserve">
              <lb/>
            Quocirca recta 45. </s>
            <s xml:id="echoid-s862" xml:space="preserve">45. </s>
            <s xml:id="echoid-s863" xml:space="preserve">in ſemidiametrum dati quadrantis ex centro translata
              <lb/>
            indicabit punctum quæſitum.</s>
            <s xml:id="echoid-s864" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum