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

Table of figures

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[81. Figure (Variables: p q r d t ſ e)]
[82. Figure (Variables: a c d @)]
[83. Figure (Variables: H B D L M K G F C E N A)]
[84. Figure: Pr@ma. (Variables: C A B D)]
[85. Figure: Secun da. (Variables: E)]
[86. Figure: Tertia (Variables: F)]
[87. Figure: Tertia. (Variables: G)]
[88. Figure: MERIDIES. Aequinoctij circulus. Orizon ſeu Fin@tor uiſus, ſeu Limen uiſus. Orizon ORIENS. OCCIDENS circulus Poſitionis. circulus Poſitionis. SEPTEN TRIO. (Variables: 3 6 9 12 15 18 21 24 27 30 33 36 39 42 43 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 96 99 102 105 108 111 114 117 120 123 126 129 132 135 138 141 144 147 150 153 156 159 162 165 168 171 174 177 180 183 186 189 192 195 198 201 204 207 210 213 216 219 222 300 303 306 309 312 315 318 321 324 327 330 333 336 339 342 345 348 351 354 357 360)]
[89. Figure (Variables: A B 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1)]
[90. Figure (Variables: 10 20 30 40 50 60 65)]
[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]
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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>