Cardano, Geronimo, Offenbarung der Natur und natürlicher dingen auch mancherley subtiler würckungen

Table of figures

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[91. Figure]
[92. Figure: Frigula. Habitabilis Borea@is. Ecliptica Tor ri da Habitabilis Auſhalis. Frigida. (Variables: 23{1/2} c 23{1/2} g 43 m 23{1/2} b 23{1/2} n 43 f 23{1/2} d 23{1/2} h 43 l 23{1/2} a 23{1/2} k 43 47 47)]
[93. Figure (Variables: a d e f g c b)]
[94. Figure (Variables: c a b e f d)]
[95. Figure (Variables: A E C D G H M N L B F)]
[96. Figure (Variables: A B C V E D)]
[97. Figure]
[98. Figure (Variables: a d c b e)]
[99. Figure: Arcticus Orient. Occides. Antarcti. (Variables: c a b d)]
[100. Figure (Variables: @ e f d g c a)]
[101. Figure]
[102. Figure]
[103. Figure (Variables: c d b a)]
[104. Figure (Variables: a c b d g l e l f)]
[105. Figure (Variables: a b c d e f k g h o)]
[106. Figure (Variables: d e a b c)]
[107. Figure (Variables: b a e d c)]
[108. Figure: Tetra cedron.]
[109. Figure: Exace dron.]
[110. Figure: Octo cedron]
[111. Figure: Icoſa he dron.]
[112. Figure]
[113. Figure]
[114. Figure: Gn@m@.]
[115. Figure (Variables: a g h b e m n f c k l d 1)]
[116. Figure (Variables: g h b e m n f c k l d 2)]
[117. Figure (Variables: a k l m b e q r g f ſ t h c n o p d 3)]
[118. Figure (Variables: a g h b e m n f c k l d 4)]
[119. Figure (Variables: a k b e m g f n h c l d 5)]
[120. Figure (Variables: a b c d 1)]
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page |< < (dxi) of 997 > >|
ſachen/ Das zwölfft bůch.
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      <text xml:lang="de" type="free">
        <div type="section" level="1" n="68">
          <p>
            <s xml:space="preserve">
              <pb o="dxi" file="0567" n="567" rhead="ſachen/ Das zwölfft bůch."/>
            quadrant/ vnd die ſeiten D geſtrackt/ zeigt ſie an daß alle
              <lb/>
              <anchor type="figure" xlink:label="fig-0567-01a" xlink:href="fig-0567-01"/>
            ſeyten bekant/ vnnd diſes auß den propoſitionen ſo vorhin
              <lb/>
            fürgehalten/ vnd auß den vier ſchlußreden ſo ich bald her
              <lb/>
            nach will ſetzen. </s>
            <s xml:space="preserve">Deßhalben fürt ſie die ſeitẽ C D biß zů A/
              <lb/>
            damit C A ein quadrant ſeye/ das iſt neüntzig grad. </s>
            <s xml:space="preserve">vnnd
              <lb/>
            zeücht A B ſchnůr ſchlecht auff A C. </s>
            <s xml:space="preserve">Alſo iſt durch die
              <lb/>
            fünffte propoſition das C des A B Polus. </s>
            <s xml:space="preserve">wann nun A B
              <lb/>
            neüntzig grad iſt/ wirt das B Polus durch die ſelbigen zů A C gezogen/ deß
              <lb/>
            halben C F biß zů E/ ſo wirt C E ſchnůrſchlecht auff A B ſthen/ nach der
              <lb/>
            ſechßten propoſitiõ. </s>
            <s xml:space="preserve">Weil auch das C des A B Polus iſt/ wirt C B nach der
              <lb/>
            vierdtẽ p ropoſition des C B quadrãt/ vnd eigentlich auff dem A B ſthen.
              <lb/>
            </s>
            <s xml:space="preserve">Alſo haſt du in diſer figur fünff quadrantẽ A C/ C B/ A B/ D B/ vñ C E. </s>
            <s xml:space="preserve">
              <lb/>
            ſie ſthond auch alle ſchnůr ſchlecht auff den ſeyten ſo gegen einanderẽ ſeind/
              <lb/>
            damit die eck ſeyend A/ C/ B/ D/ E. </s>
            <s xml:space="preserve">vnd ſeind alle ſieben gerad. </s>
            <s xml:space="preserve">Diſes iſt
              <lb/>
            die figur welche er zůerſt ſtellet. </s>
            <s xml:space="preserve">Demnach ſetzet er vier ſchlußreden/ vnder
              <lb/>
            welchen die erſt. </s>
            <s xml:space="preserve">Wañ man ein geſtrackt eck D ſetzet/ ſo wirt die proportz des
              <lb/>
            gantzen Sinus oder ſchoß ſein/ das iſt des quadranten gegen der ſchoß der
              <lb/>
            überigen ſeyten/ ſo die rechte begreifft/ nammlich A D. </s>
            <s xml:space="preserve">als des eck ſchoß/
              <lb/>
            wann die geſtrackte die ſeyten begreifft/ nammlich A E zů dem ſinu oder
              <lb/>
            ſchoß des übrigen eck/ ſo gegen der ſelbigen ſeyten ſicht/ welches das F iſt. </s>
            <s xml:space="preserve">di
              <lb/>
            ſes lernet er inn der achzehenden propoſition des vierdten bůchs von den
              <lb/>
            trianglen. </s>
            <s xml:space="preserve">Für welches man wiſſen ſoll/ daß des eck ſchoß genẽnet wirt/ der
              <lb/>
            bogen am außgeſtreckten circkel gegen dem eck ſo an dem Polo deſſelbigen
              <lb/>
            circkel ſteth. </s>
            <s xml:space="preserve">als des eck ſchoß A B D/ iſt ein ſchoß des bogen A D/ vñ wirt
              <lb/>
            die ſchoß C D/ ein ſchoß des übrigẽ eck A B D geneñet. </s>
            <s xml:space="preserve">vnd iſt des eck ſchoß
              <lb/>
            A C E ein ſchoß des bogen A E/ vnnd des übrigen bogen E B. </s>
            <s xml:space="preserve">Man ſoll
              <lb/>
            auch wüſſen daß man in allen propoſitionen ſolliches enderen vnd vmbke-
              <lb/>
            ren mag. </s>
            <s xml:space="preserve">als wir jetz zůmal ſagen/ der gantzen ſchoß proportz ſeye gegen der
              <lb/>
            eck ſchoß C/ wie die ſchoß der übrigen ſeytten C D gegen der ſchoß des über-
              <lb/>
            blibenen eck F.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="7">
            <note position="left" xlink:label="note-0566-01" xlink:href="note-0566-01a" xml:space="preserve">Aſtronomi
              <lb/>
            ſchetaflen.</note>
            <figure xlink:label="fig-0567-01" xlink:href="fig-0567-01a">
              <variables xml:space="preserve">a d e f g c b</variables>
            </figure>
          </div>
          <p>
            <s xml:space="preserve">Die ander propoſition iſt die neünzehend deſſelbigen vierdten bůch. </s>
            <s xml:space="preserve">vnd
              <lb/>
            iſt. </s>
            <s xml:space="preserve">Wann man ein triangel mitt rechten ecken ſetzet C D F/ welches D ge-
              <lb/>
            ſtrackt iſt/ iſt der gantzen ſchoß proportz zů der ſchoß F B/ vnd das übrig an
              <lb/>
            der ſeyten D F. </s>
            <s xml:space="preserve">gleich wie die ſchoß zů der übrigen ſeytẽ C D gegen der ſchoß
              <lb/>
            F E ſo an der ſeytten C F überbiben/ nach der außgeſtreckten geraden lini-
              <lb/>
            en. </s>
            <s xml:space="preserve">Alſo bedenckt er in diſer propoſition das übrig an dreyen ſeitten des tri-
              <lb/>
            angels/ damit die proportz der gantzen ſchoß gegen der ſchoß ſeye/ ſo das ü-
              <lb/>
            berig begreifft/ wie das überig an der anderen ſeite/ ſo do begreifft beyder
              <lb/>
            ſchoß der übrigen entgegen geſetzten ſeiten am rechten eck.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">Die dritt propoſition iſt allen trianglen geleich/ ſie habend geleiche eck o-
              <lb/>
            der nit/ vnd iſt die ſiebẽzehend deſſelben vierdten bůchs/ inn welcher er an-
              <lb/>
            zeigt/ daß inn einem jeden triangel der größeren circklen die proportz an der
              <lb/>
            eck en ſchoß vnder jnen ſelbs iſt/ wie auch der ſchoß ſeiten ſo einander anſe-
              <lb/>
            ben. </s>
            <s xml:space="preserve">Deßhalben wañ man diſe regel vmb keeret/ iſt der ſchoßen eck proportz
              <lb/>
            gegen den ſchoßen ſo der ſeyten eck anſchauwẽ/ ein ding. </s>
            <s xml:space="preserve">diſes bedarff auch
              <lb/>
            keines exempel.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">Die vierdte propoſition iſt/ daß inn einem yeden triangel der größeren
              <lb/>
            circklenn/ er ſeye vonn geleichen graden linienn oder nitt/ die proportz</s>
          </p>
        </div>
      </text>
    </echo>