Blancanus, Josephus, Sphaera mvndi, sev cosmographia demonstratiua , ac facile methodo tradita : in qua totius Mundi fabrica, vna cum nouis, Tychonis, Kepleri, Galilaei, aliorumq' ; Astronomorum adinuentis continentur ; Accessere I. Breuis introductio ad geographiam. II. Apparatus ad mathematicarum studium. III. Echometria, idest Geometrica tractatio de Echo. IV. Nouum instrumentum ad Horologia

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        <div xml:id="echoid-div19" type="section" level="1" n="14">
          <p>
            <s xml:id="echoid-s668" xml:space="preserve">
              <pb o="4" file="0020" n="20" rhead="Apparatus ad Sphœram."/>
            ginario trigono: </s>
            <s xml:id="echoid-s669" xml:space="preserve">per ſecundam enim huius angulus A C H. </s>
            <s xml:id="echoid-s670" xml:space="preserve">eſt gr. </s>
            <s xml:id="echoid-s671" xml:space="preserve">120. </s>
            <s xml:id="echoid-s672" xml:space="preserve">angulus vero C A H. </s>
            <s xml:id="echoid-s673" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s674" xml:space="preserve">15. </s>
            <s xml:id="echoid-s675" xml:space="preserve">ergo neceſ-
              <lb/>
            ſario reliquus angulus ad H. </s>
            <s xml:id="echoid-s676" xml:space="preserve">æqualis erit reliquo angulo dati trianguli, quare per quartã huius, erunt latera
              <lb/>
            huius trianguli analoga lateribus illius, eo modo, ac ordine, quem ibi diximus. </s>
            <s xml:id="echoid-s677" xml:space="preserve">Sit tandem datum triãgulum
              <lb/>
            Oxigoniũ, cuius duo anguli ſint cogniti, vnus quidem gr. </s>
            <s xml:id="echoid-s678" xml:space="preserve">30. </s>
            <s xml:id="echoid-s679" xml:space="preserve">alter gr. </s>
            <s xml:id="echoid-s680" xml:space="preserve">35. </s>
            <s xml:id="echoid-s681" xml:space="preserve">ducantur lineæ C I. </s>
            <s xml:id="echoid-s682" xml:space="preserve">quidem per gr.
              <lb/>
            </s>
            <s xml:id="echoid-s683" xml:space="preserve">75. </s>
            <s xml:id="echoid-s684" xml:space="preserve">in ſemicirculo. </s>
            <s xml:id="echoid-s685" xml:space="preserve">A I. </s>
            <s xml:id="echoid-s686" xml:space="preserve">vero per 30. </s>
            <s xml:id="echoid-s687" xml:space="preserve">in quadrante, factumq; </s>
            <s xml:id="echoid-s688" xml:space="preserve">erit trigonum C A I. </s>
            <s xml:id="echoid-s689" xml:space="preserve">illi ſimile, atque analogum,
              <lb/>
            vt ex nuper citatis propoſit. </s>
            <s xml:id="echoid-s690" xml:space="preserve">patet. </s>
            <s xml:id="echoid-s691" xml:space="preserve">Si occurrant anguli continentes gradus, & </s>
            <s xml:id="echoid-s692" xml:space="preserve">minuta, ſimiliter in figura
              <lb/>
            accipienda ſunt minuta vltra gradus. </s>
            <s xml:id="echoid-s693" xml:space="preserve">Linea A C. </s>
            <s xml:id="echoid-s694" xml:space="preserve">conſtans particulis 100. </s>
            <s xml:id="echoid-s695" xml:space="preserve">latinis modulus appellatur; </s>
            <s xml:id="echoid-s696" xml:space="preserve">recen-
              <lb/>
            tioribus vero ſcala, quoniam reliquorum laterum eſt modulus, ideſt, menſura.</s>
            <s xml:id="echoid-s697" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div21" type="section" level="1" n="15">
          <head xml:id="echoid-head17" style="it" xml:space="preserve">Cognitis duobus angulis, & vno latere ſecundum aliquam menſuram, alicuius dati trianguli@
            <lb/>
          reliquorum quoque laterum quantitatem inuenire. # Propoſ. 6.</head>
          <p>
            <s xml:id="echoid-s698" xml:space="preserve">ESt autem propoſitio hæc, Tyroni magni facienda, ac diligenter addiſcenda, eſt enim Aſtronomicarum
              <lb/>
            demonſtrationum baſis, ac fundamentum. </s>
            <s xml:id="echoid-s699" xml:space="preserve">Sit v. </s>
            <s xml:id="echoid-s700" xml:space="preserve">g. </s>
            <s xml:id="echoid-s701" xml:space="preserve">propoſitum trigonum imaginarium huiuſmodi:
              <lb/>
            </s>
            <s xml:id="echoid-s702" xml:space="preserve">intelligatur primo linea ducta à centro terræ vſque ad Lunam: </s>
            <s xml:id="echoid-s703" xml:space="preserve">altera à Luna, vſq; </s>
            <s xml:id="echoid-s704" xml:space="preserve">ad habitatorẽ noſtri Ho-
              <lb/>
            rizontis; </s>
            <s xml:id="echoid-s705" xml:space="preserve">tertia ab eodem habitare, ideſt, ſuperficie terræ, quam nos incolimus ad centrum terræ deſcendat: </s>
            <s xml:id="echoid-s706" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0020-01" xlink:href="fig-0020-01a" number="8">
                <image file="0020-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0020-01"/>
              </figure>
            quod triangulum OCL.
              <lb/>
            </s>
            <s xml:id="echoid-s707" xml:space="preserve">aliquo modo cõtemplari
              <lb/>
            poteris in adiecta figura; </s>
            <s xml:id="echoid-s708" xml:space="preserve">
              <lb/>
            Angulus enim O C L. </s>
            <s xml:id="echoid-s709" xml:space="preserve">ad
              <lb/>
            centrum terræ cognitus
              <lb/>
            ſit, v. </s>
            <s xml:id="echoid-s710" xml:space="preserve">g. </s>
            <s xml:id="echoid-s711" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s712" xml:space="preserve">45. </s>
            <s xml:id="echoid-s713" xml:space="preserve">alter an-
              <lb/>
            gulus, C O L. </s>
            <s xml:id="echoid-s714" xml:space="preserve">ad oculum
              <lb/>
            habitatoris notus, ſit gr. </s>
            <s xml:id="echoid-s715" xml:space="preserve">
              <lb/>
            133. </s>
            <s xml:id="echoid-s716" xml:space="preserve">latus præterea O C. </s>
            <s xml:id="echoid-s717" xml:space="preserve">
              <lb/>
            cognitũ, ſit linea ab ocu-
              <lb/>
            lo ad centrũ mundi, quæ
              <lb/>
            eſt ſemidiameter, cogni-
              <lb/>
            tain milliarijs, eſt enim
              <lb/>
            fere milliariorum 3436. </s>
            <s xml:id="echoid-s718" xml:space="preserve">
              <lb/>
            Iam propoſitum ſit inue
              <lb/>
            ſtigare quantitatẽ lateris
              <lb/>
            pertinentis à centro ter-
              <lb/>
            ræ ad vſq; </s>
            <s xml:id="echoid-s719" xml:space="preserve">Lunam, ideſt
              <lb/>
            diſtantiam Lunæ à terræ
              <lb/>
            cẽtro; </s>
            <s xml:id="echoid-s720" xml:space="preserve">fiat igitur per quin
              <lb/>
            tam præcedẽtem propo-
              <lb/>
            ſitionem, triangulum ſi-
              <lb/>
            mile huic imaginario, ac
              <lb/>
            magno triangulo prædi-
              <lb/>
            cto, hac tamen conditio-
              <lb/>
            ne vt angulus factus in quadrante inſtrumenti ad A. </s>
            <s xml:id="echoid-s721" xml:space="preserve">ſit æqualis angulo ad centrum terræ; </s>
            <s xml:id="echoid-s722" xml:space="preserve">angulus vero qui
              <lb/>
            fiet ad C. </s>
            <s xml:id="echoid-s723" xml:space="preserve">centrum ſemicirculi par ſit angulo facto in ſuperficie terrę apud habitatoris oculum. </s>
            <s xml:id="echoid-s724" xml:space="preserve">ſic enim latus
              <lb/>
            inſtrumenti A C. </s>
            <s xml:id="echoid-s725" xml:space="preserve">qui reliquorum modulus, ac menſura eſſe debet, quod cognitum ſit, reſpondebit ſemidia-
              <lb/>
            metro terræ, quę pariter nota eſt. </s>
            <s xml:id="echoid-s726" xml:space="preserve">Quia ergo triangulum hoc in inſtrumento factũ, eſt ſimile triangulo ma-
              <lb/>
            gno acimaginario, cuius latera quòd inacc@ſſibilia ſint, menſurare nequimus: </s>
            <s xml:id="echoid-s727" xml:space="preserve">habetq; </s>
            <s xml:id="echoid-s728" xml:space="preserve">latera circa angulum
              <lb/>
            A. </s>
            <s xml:id="echoid-s729" xml:space="preserve">analoga lateribus illius circa centrum terræ poſitis; </s>
            <s xml:id="echoid-s730" xml:space="preserve">ſi@gitur triangulum in ſtrumenti A C H. </s>
            <s xml:id="echoid-s731" xml:space="preserve">habuerit an-
              <lb/>
            gulos prædictos, ſeu ęquales angulis trianguli magni O C L. </s>
            <s xml:id="echoid-s732" xml:space="preserve">eritvt latus A C. </s>
            <s xml:id="echoid-s733" xml:space="preserve">ad latus v.</s>
            <s xml:id="echoid-s734" xml:space="preserve">g. </s>
            <s xml:id="echoid-s735" xml:space="preserve">A H. </s>
            <s xml:id="echoid-s736" xml:space="preserve">ita ſemidia-
              <lb/>
            meter terræ oc, ad diſtantiam c l, Lunæ à terra. </s>
            <s xml:id="echoid-s737" xml:space="preserve">quare quoties latus A C. </s>
            <s xml:id="echoid-s738" xml:space="preserve">quod eſt 100. </s>
            <s xml:id="echoid-s739" xml:space="preserve">continebitur in alte-
              <lb/>
            ro latere V G. </s>
            <s xml:id="echoid-s740" xml:space="preserve">A H. </s>
            <s xml:id="echoid-s741" xml:space="preserve">toties etiam ſemidiameter terrę continebitur in diſtantia Lunæ à terra. </s>
            <s xml:id="echoid-s742" xml:space="preserve">experire igitur
              <lb/>
            per circinum quoties latus A C. </s>
            <s xml:id="echoid-s743" xml:space="preserve">ingrediatur in latus A H. </s>
            <s xml:id="echoid-s744" xml:space="preserve">& </s>
            <s xml:id="echoid-s745" xml:space="preserve">ſi opus fuerit producere latus A H. </s>
            <s xml:id="echoid-s746" xml:space="preserve">extra inſtru-
              <lb/>
            mentum, appoſita al@qua plana ſuperficie, v.</s>
            <s xml:id="echoid-s747" xml:space="preserve">g. </s>
            <s xml:id="echoid-s748" xml:space="preserve">Magna tabula, id fiat. </s>
            <s xml:id="echoid-s749" xml:space="preserve">quoties igitur latus A C. </s>
            <s xml:id="echoid-s750" xml:space="preserve">ingredietur
              <lb/>
            in latus A H. </s>
            <s xml:id="echoid-s751" xml:space="preserve">toties ſemidiameter terræ nota neceſſario ingredietur in diſtantiam Luna à terra, hoc eſt, to-
              <lb/>
            ties in ea continebuntur milliaria 3436. </s>
            <s xml:id="echoid-s752" xml:space="preserve">vnde cognita atque perſpecta erit Lunaris illa altitudo, quæ latus
              <lb/>
            vnumæ quidem inacceſſum trianguli dati magni efficiebat.</s>
            <s xml:id="echoid-s753" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s754" xml:space="preserve">Quod ſi accidat iatus A C. </s>
            <s xml:id="echoid-s755" xml:space="preserve">nec ſemel, nec bis, teruè pręcisè contineri in latere A H. </s>
            <s xml:id="echoid-s756" xml:space="preserve">tunc per circinum ac-
              <lb/>
            cipiendum eſt ipſum A C. </s>
            <s xml:id="echoid-s757" xml:space="preserve">applicandumque lateri A H. </s>
            <s xml:id="echoid-s758" xml:space="preserve">quoties fieri poteſt, & </s>
            <s xml:id="echoid-s759" xml:space="preserve">poſtea pars, quæ ſupereſt de
              <lb/>
            latere A H. </s>
            <s xml:id="echoid-s760" xml:space="preserve">accipienda eſt circini interuallo, viciſſimq; </s>
            <s xml:id="echoid-s761" xml:space="preserve">applicando ipſi A C. </s>
            <s xml:id="echoid-s762" xml:space="preserve">incipiendo ab A. </s>
            <s xml:id="echoid-s763" xml:space="preserve">vt appareat
              <lb/>
            quantæ parti ipſius adęquetur, v.</s>
            <s xml:id="echoid-s764" xml:space="preserve">g. </s>
            <s xml:id="echoid-s765" xml:space="preserve">quia latus A C. </s>
            <s xml:id="echoid-s766" xml:space="preserve">ſemel tantum integrè continetur in latere A H. </s>
            <s xml:id="echoid-s767" xml:space="preserve">triangu-
              <lb/>
            li conſtructi in inſtrumento, adæquaturque parti ipſius A L. </s>
            <s xml:id="echoid-s768" xml:space="preserve">quæ propterea eſſe 100. </s>
            <s xml:id="echoid-s769" xml:space="preserve">apparet: </s>
            <s xml:id="echoid-s770" xml:space="preserve">vt reliquam
              <lb/>
            quoque partem L H. </s>
            <s xml:id="echoid-s771" xml:space="preserve">cognoſcamus, eam interuallo circini acceptam vicifſim adaptabimus lateri A C. </s>
            <s xml:id="echoid-s772" xml:space="preserve">inci-
              <lb/>
            pientes ab A. </s>
            <s xml:id="echoid-s773" xml:space="preserve">congruetque, v.</s>
            <s xml:id="echoid-s774" xml:space="preserve">g. </s>
            <s xml:id="echoid-s775" xml:space="preserve">parti eius A 30. </s>
            <s xml:id="echoid-s776" xml:space="preserve">quę eſt 30. </s>
            <s xml:id="echoid-s777" xml:space="preserve">particularum: </s>
            <s xml:id="echoid-s778" xml:space="preserve">quare tota A H. </s>
            <s xml:id="echoid-s779" xml:space="preserve">erit 130. </s>
            <s xml:id="echoid-s780" xml:space="preserve">partium,
              <lb/>
            qualium A C. </s>
            <s xml:id="echoid-s781" xml:space="preserve">eſt 100. </s>
            <s xml:id="echoid-s782" xml:space="preserve">proportio igitur earum nota: </s>
            <s xml:id="echoid-s783" xml:space="preserve">latuſque A H. </s>
            <s xml:id="echoid-s784" xml:space="preserve">notum, quod intendebamus.</s>
            <s xml:id="echoid-s785" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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