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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    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div15" type="section" level="1" n="12">
          <pb o="3" file="0019" n="19" rhead="Pars prima."/>
        </div>
        <div xml:id="echoid-div17" type="section" level="1" n="13">
          <head xml:id="echoid-head15" style="it" xml:space="preserve">Triangula æquiangula habere latera proportionalia. # Propoſ. 4.</head>
          <p>
            <s xml:id="echoid-s511" xml:space="preserve">SInt duo triangula A B C. </s>
            <s xml:id="echoid-s512" xml:space="preserve">D E F. </s>
            <s xml:id="echoid-s513" xml:space="preserve">æquiangula, ideſt angulus A. </s>
            <s xml:id="echoid-s514" xml:space="preserve">ſit æqualis angulo D. </s>
            <s xml:id="echoid-s515" xml:space="preserve">angulus B. </s>
            <s xml:id="echoid-s516" xml:space="preserve">angu-
              <lb/>
            lo E. </s>
            <s xml:id="echoid-s517" xml:space="preserve">angulus C. </s>
            <s xml:id="echoid-s518" xml:space="preserve">angulo F. </s>
            <s xml:id="echoid-s519" xml:space="preserve">dicentur hæc duo triangula ſimilia, eruntque latera vnius proportiona@ia la-
              <lb/>
            lateribus alterius, quæ ſunt circa æquales angulos, quæq; </s>
            <s xml:id="echoid-s520" xml:space="preserve">æqualibus angulis ſubtenduntur, v.</s>
            <s xml:id="echoid-s521" xml:space="preserve">g. </s>
            <s xml:id="echoid-s522" xml:space="preserve">qu@a anguli
              <lb/>
            A D. </s>
            <s xml:id="echoid-s523" xml:space="preserve">ſunt ęquales, erunt latera conſtituentia angulum A. </s>
            <s xml:id="echoid-s524" xml:space="preserve">analoga lateribus cõſtituentibus angulum D. </s>
            <s xml:id="echoid-s525" xml:space="preserve">ſi a-
              <lb/>
            men ordinatim ſumantur prout opponuutur angulis æqualibus, quare erit vt A B. </s>
            <s xml:id="echoid-s526" xml:space="preserve">ad A C. </s>
            <s xml:id="echoid-s527" xml:space="preserve">ita D E. </s>
            <s xml:id="echoid-s528" xml:space="preserve">ad D F.
              <lb/>
            </s>
            <s xml:id="echoid-s529" xml:space="preserve">ſunt enim priora duo circa angulum A. </s>
            <s xml:id="echoid-s530" xml:space="preserve">qui eſt æqualis angulo D. </s>
            <s xml:id="echoid-s531" xml:space="preserve">circa quem ſunt reliqua duo, & </s>
            <s xml:id="echoid-s532" xml:space="preserve">priora duo
              <lb/>
            opponuntur angulis C. </s>
            <s xml:id="echoid-s533" xml:space="preserve">& </s>
            <s xml:id="echoid-s534" xml:space="preserve">B. </s>
            <s xml:id="echoid-s535" xml:space="preserve">qui ſunt æquales angulis duobus F E. </s>
            <s xml:id="echoid-s536" xml:space="preserve">quibus eodem ordine reſpondent rel. </s>
            <s xml:id="echoid-s537" xml:space="preserve">qua
              <lb/>
            duo latera. </s>
            <s xml:id="echoid-s538" xml:space="preserve">Similiter erit vt A B. </s>
            <s xml:id="echoid-s539" xml:space="preserve">ad B C. </s>
            <s xml:id="echoid-s540" xml:space="preserve">ſic D E. </s>
            <s xml:id="echoid-s541" xml:space="preserve">ad E F. </s>
            <s xml:id="echoid-s542" xml:space="preserve">quę ſunt circa angulos pares B E. </s>
            <s xml:id="echoid-s543" xml:space="preserve">& </s>
            <s xml:id="echoid-s544" xml:space="preserve">ordinatim re-
              <lb/>
              <figure xlink:label="fig-0019-01" xlink:href="fig-0019-01a" number="6">
                <image file="0019-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0019-01"/>
              </figure>
            ſpondent angulis paribus C F. </s>
            <s xml:id="echoid-s545" xml:space="preserve">atque A. </s>
            <s xml:id="echoid-s546" xml:space="preserve">& </s>
            <s xml:id="echoid-s547" xml:space="preserve">D. </s>
            <s xml:id="echoid-s548" xml:space="preserve">tandem
              <lb/>
            erit vt B C. </s>
            <s xml:id="echoid-s549" xml:space="preserve">ad C A. </s>
            <s xml:id="echoid-s550" xml:space="preserve">ita E F. </s>
            <s xml:id="echoid-s551" xml:space="preserve">ad F D. </s>
            <s xml:id="echoid-s552" xml:space="preserve">quę angulos C F.
              <lb/>
            </s>
            <s xml:id="echoid-s553" xml:space="preserve">pares circunſiſtunt, paribuſque angulis ordinatim
              <lb/>
            ſubtenduntur. </s>
            <s xml:id="echoid-s554" xml:space="preserve">Hanc propoſitionem probat Geome-
              <lb/>
            tricè Euclides ad 4. </s>
            <s xml:id="echoid-s555" xml:space="preserve">ſexti. </s>
            <s xml:id="echoid-s556" xml:space="preserve">Tyro autem practicè idem
              <lb/>
            experiri poterit circino perfectè a cuminato: </s>
            <s xml:id="echoid-s557" xml:space="preserve">ſi enim
              <lb/>
            inuenerit latus A B. </s>
            <s xml:id="echoid-s558" xml:space="preserve">æqualilateri A C. </s>
            <s xml:id="echoid-s559" xml:space="preserve">inuenit etiam
              <lb/>
            D E. </s>
            <s xml:id="echoid-s560" xml:space="preserve">par lateri D F. </s>
            <s xml:id="echoid-s561" xml:space="preserve">Quod ſi idem A B. </s>
            <s xml:id="echoid-s562" xml:space="preserve">ſit duplum
              <lb/>
            lateris A C. </s>
            <s xml:id="echoid-s563" xml:space="preserve">pariter latus D E. </s>
            <s xml:id="echoid-s564" xml:space="preserve">duplũ erit lateris D F. </s>
            <s xml:id="echoid-s565" xml:space="preserve">
              <lb/>
            Et ſi A B. </s>
            <s xml:id="echoid-s566" xml:space="preserve">nouies, decieſuè contineatur in A C. </s>
            <s xml:id="echoid-s567" xml:space="preserve">toties
              <lb/>
            etiã D E. </s>
            <s xml:id="echoid-s568" xml:space="preserve">continebitur in D F. </s>
            <s xml:id="echoid-s569" xml:space="preserve">& </s>
            <s xml:id="echoid-s570" xml:space="preserve">ſic de alijs propor-
              <lb/>
            tionibus: </s>
            <s xml:id="echoid-s571" xml:space="preserve">vt tripla, dupla, &</s>
            <s xml:id="echoid-s572" xml:space="preserve">c. </s>
            <s xml:id="echoid-s573" xml:space="preserve">Similiter reperiet eaſ-
              <lb/>
            dẽ habere analogias reliqua latera A B. </s>
            <s xml:id="echoid-s574" xml:space="preserve">ad B C. </s>
            <s xml:id="echoid-s575" xml:space="preserve">quas
              <lb/>
            D E. </s>
            <s xml:id="echoid-s576" xml:space="preserve">ad E F. </s>
            <s xml:id="echoid-s577" xml:space="preserve">necnon B C. </s>
            <s xml:id="echoid-s578" xml:space="preserve">ad C A. </s>
            <s xml:id="echoid-s579" xml:space="preserve">quas E F. </s>
            <s xml:id="echoid-s580" xml:space="preserve">ad F D. </s>
            <s xml:id="echoid-s581" xml:space="preserve">
              <lb/>
            atque in varijs triangulorum æquiangulorum formis, ſemper vera comperiet.</s>
            <s xml:id="echoid-s582" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div19" type="section" level="1" n="14">
          <head xml:id="echoid-head16" style="it" xml:space="preserve">Datis duobus angulis vnius trianguli, alterum triangulum constituere, quod illi ſit ſimile,
            <lb/>
          quod habe at latera analoga lateribus illius. # Propoſ. 5.</head>
          <p>
            <s xml:id="echoid-s583" xml:space="preserve">AD problema iſtud conficiendum excogitauimus huiuſmodi fi-
              <lb/>
              <figure xlink:label="fig-0019-02" xlink:href="fig-0019-02a" number="7">
                <image file="0019-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0019-02"/>
              </figure>
            guram ſeu inſtrumentum. </s>
            <s xml:id="echoid-s584" xml:space="preserve">In plana quapiam ſuperficie ſatis
              <lb/>
            magna, ducatur linea A B. </s>
            <s xml:id="echoid-s585" xml:space="preserve">quantumuis longa; </s>
            <s xml:id="echoid-s586" xml:space="preserve">in qua facto ini-
              <lb/>
            tio ab A. </s>
            <s xml:id="echoid-s587" xml:space="preserve">ſumantur ope circini particulæ decem æquales, & </s>
            <s xml:id="echoid-s588" xml:space="preserve">con-
              <lb/>
            tinuæ, ſicque habebitur pars vna huius lineæ conſtans 10. </s>
            <s xml:id="echoid-s589" xml:space="preserve">æquis
              <lb/>
            particulis. </s>
            <s xml:id="echoid-s590" xml:space="preserve">hæc eadem ſumatur decies continenter, ita vt tota A C.
              <lb/>
            </s>
            <s xml:id="echoid-s591" xml:space="preserve">contineat 100. </s>
            <s xml:id="echoid-s592" xml:space="preserve">particulas; </s>
            <s xml:id="echoid-s593" xml:space="preserve">numerique ſingulis ſui adſcribantur, vti
              <lb/>
            vides in figura. </s>
            <s xml:id="echoid-s594" xml:space="preserve">Poſtea centro C. </s>
            <s xml:id="echoid-s595" xml:space="preserve">& </s>
            <s xml:id="echoid-s596" xml:space="preserve">interuallo C E. </s>
            <s xml:id="echoid-s597" xml:space="preserve">deſcribatur ſe-
              <lb/>
            micirculus B D E. </s>
            <s xml:id="echoid-s598" xml:space="preserve">ac centro interuallo A E. </s>
            <s xml:id="echoid-s599" xml:space="preserve">ducatur quadrans E F. </s>
            <s xml:id="echoid-s600" xml:space="preserve">
              <lb/>
            Facto deinde initio ab E. </s>
            <s xml:id="echoid-s601" xml:space="preserve">diuidatur per primam Propoſ. </s>
            <s xml:id="echoid-s602" xml:space="preserve">huius, ſemi-
              <lb/>
            circulus in 180. </s>
            <s xml:id="echoid-s603" xml:space="preserve">gradus: </s>
            <s xml:id="echoid-s604" xml:space="preserve">Quadrans vero in 90. </s>
            <s xml:id="echoid-s605" xml:space="preserve">& </s>
            <s xml:id="echoid-s606" xml:space="preserve">quiliber eorum gra-
              <lb/>
            dus ru@ſum ſecetur ſaltem in 5. </s>
            <s xml:id="echoid-s607" xml:space="preserve">particulas, quarũ ſingulæ contineant
              <lb/>
            minuta 12. </s>
            <s xml:id="echoid-s608" xml:space="preserve">numerique gr. </s>
            <s xml:id="echoid-s609" xml:space="preserve">ſuis locis apponantur: </s>
            <s xml:id="echoid-s610" xml:space="preserve">licet nos pręſenti fi-
              <lb/>
            guræ, quæ parua eſt, confuſionis vitandæ cauſa, tãtummodo gradus,
              <lb/>
            eoſq; </s>
            <s xml:id="echoid-s611" xml:space="preserve">tantum per quindenos annotauerimus. </s>
            <s xml:id="echoid-s612" xml:space="preserve">ſit iam aliquod Trian-
              <lb/>
            gulum vbicumque illud fuerit, cuius tamen duos angulos notos ha-
              <lb/>
            beamus, vnus, v.</s>
            <s xml:id="echoid-s613" xml:space="preserve">g. </s>
            <s xml:id="echoid-s614" xml:space="preserve">ſit rectus, ideſt gr. </s>
            <s xml:id="echoid-s615" xml:space="preserve">90. </s>
            <s xml:id="echoid-s616" xml:space="preserve">alter vero acutus gr. </s>
            <s xml:id="echoid-s617" xml:space="preserve">v.</s>
            <s xml:id="echoid-s618" xml:space="preserve">g. </s>
            <s xml:id="echoid-s619" xml:space="preserve">15. </s>
            <s xml:id="echoid-s620" xml:space="preserve">
              <lb/>
            erit reliquus neceſſario gr. </s>
            <s xml:id="echoid-s621" xml:space="preserve">75. </s>
            <s xml:id="echoid-s622" xml:space="preserve">cum omnes tres anguli cuiuſuis trian-
              <lb/>
            guli contineant, per tertiam Propoſ. </s>
            <s xml:id="echoid-s623" xml:space="preserve">huius gr. </s>
            <s xml:id="echoid-s624" xml:space="preserve">180. </s>
            <s xml:id="echoid-s625" xml:space="preserve">huiuſmodi trian-
              <lb/>
            gulo ſic conſtitues triangulumſimile inexpoſito inſtrumento. </s>
            <s xml:id="echoid-s626" xml:space="preserve">Ex
              <lb/>
            centro C. </s>
            <s xml:id="echoid-s627" xml:space="preserve">ſemicirculi duc lineam C D. </s>
            <s xml:id="echoid-s628" xml:space="preserve">ad gr. </s>
            <s xml:id="echoid-s629" xml:space="preserve">90. </s>
            <s xml:id="echoid-s630" xml:space="preserve">quæ faciet angulos
              <lb/>
            rectos cum diametro ad C. </s>
            <s xml:id="echoid-s631" xml:space="preserve">poſtea ex A centro quadrantis per gr. </s>
            <s xml:id="echoid-s632" xml:space="preserve">15. </s>
            <s xml:id="echoid-s633" xml:space="preserve">
              <lb/>
            duc lineam A G. </s>
            <s xml:id="echoid-s634" xml:space="preserve">occurrentẽ ipſi C D. </s>
            <s xml:id="echoid-s635" xml:space="preserve">in G. </s>
            <s xml:id="echoid-s636" xml:space="preserve">eritque triangulũ A C G. </s>
            <s xml:id="echoid-s637" xml:space="preserve">
              <lb/>
            conſtructum ſimile, & </s>
            <s xml:id="echoid-s638" xml:space="preserve">analogum illitriangulo; </s>
            <s xml:id="echoid-s639" xml:space="preserve">cum enim habeat
              <lb/>
            angulum ad C. </s>
            <s xml:id="echoid-s640" xml:space="preserve">rectum continentem ſcilicet gr. </s>
            <s xml:id="echoid-s641" xml:space="preserve">90. </s>
            <s xml:id="echoid-s642" xml:space="preserve">& </s>
            <s xml:id="echoid-s643" xml:space="preserve">angulum ad A. </s>
            <s xml:id="echoid-s644" xml:space="preserve">
              <lb/>
            gr. </s>
            <s xml:id="echoid-s645" xml:space="preserve">15. </s>
            <s xml:id="echoid-s646" xml:space="preserve">ex ſecũda Propoſitione huius, erit conſequenter reliquus an-
              <lb/>
            gulus ad G. </s>
            <s xml:id="echoid-s647" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s648" xml:space="preserve">75. </s>
            <s xml:id="echoid-s649" xml:space="preserve">quare erit propoſito triangulo æquiangulum, & </s>
            <s xml:id="echoid-s650" xml:space="preserve">
              <lb/>
            ſimile, & </s>
            <s xml:id="echoid-s651" xml:space="preserve">proinde per quartam huius, habebit latera lateribus illius
              <lb/>
            analoga, ſeu proportionalia. </s>
            <s xml:id="echoid-s652" xml:space="preserve">ſit alterum triangulum ambligonium,
              <lb/>
            cuius angulus obtuſus ſit, v.</s>
            <s xml:id="echoid-s653" xml:space="preserve">g. </s>
            <s xml:id="echoid-s654" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s655" xml:space="preserve">120. </s>
            <s xml:id="echoid-s656" xml:space="preserve">alter vero ſit gr. </s>
            <s xml:id="echoid-s657" xml:space="preserve">15. </s>
            <s xml:id="echoid-s658" xml:space="preserve">tertius erit
              <lb/>
            45. </s>
            <s xml:id="echoid-s659" xml:space="preserve">huic triangulũ ſimile in parata figura ſic efficies; </s>
            <s xml:id="echoid-s660" xml:space="preserve">duc lineam C H. </s>
            <s xml:id="echoid-s661" xml:space="preserve">
              <lb/>
            in ſemicirculo per gr. </s>
            <s xml:id="echoid-s662" xml:space="preserve">120. </s>
            <s xml:id="echoid-s663" xml:space="preserve">itidẽ lineam A H. </s>
            <s xml:id="echoid-s664" xml:space="preserve">in quadrante per gr. </s>
            <s xml:id="echoid-s665" xml:space="preserve">15. </s>
            <s xml:id="echoid-s666" xml:space="preserve">
              <lb/>
            occurrentem alteri in H. </s>
            <s xml:id="echoid-s667" xml:space="preserve">erit triangulũ A C H. </s>
            <s xml:id="echoid-s668" xml:space="preserve">ſimile prædicto </s>
          </p>
        </div>
      </text>
    </echo>
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