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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Von mancherlei wunderbaren
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          <p>
            <s xml:space="preserve">
              <pb o="dxij" file="0568" n="568" rhead="Von mancherlei wunderbaren"/>
            der viereckechten geraden gantzen ſchooß gegẽ dem außgefürtẽ der ſchooſ-
              <lb/>
            ſen ſeiten am triangel vndereinãder/ iſt wie die ſchooß am vmbkerten eck/
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            ſo von beiden ſeitten begriffenn/ gegen der vmbkerten ſchooß der dritten
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            ſeitten/ vnnd der vmbkerten ſchoß vnderſcheid an den zwo erſten ſeittenn.
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            </s>
            <s xml:space="preserve">Zů einem exempel. </s>
            <s xml:space="preserve">Ich nimb den triangel G F B/ von welchem (als ich ge
              <lb/>
            ſagt hab) ich nit beſchleüß daß er ein Orthogonus oder gleiche eck habe/ ſon
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            der er ſeye wie er wölle/ ſo verr er auß der größeren circkel theil ſeye/ ſo ſag
              <lb/>
            ich daß die proportz der gantzen geraden viereckechten ſchooß/ gegenn dem
              <lb/>
            das auß der geraden ſchooß (damit ich ein exempel gebe) kommen B G in
              <lb/>
            die geſtrackte ſchooß G F/ iſt der ſchooß geleich des vmbkertẽ eck G/ ſo von
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            dem B G vnd G F begriffen/ gegen der vmbkerten ſchooßen vnderſcheid/
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            vnder wölchen vmbkerten ſchößen/ die ein des bogen F B ſchooß iſt der drit
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            ten ſeiten/ der ander aber ein bogen des vnderſcheid G B vnd G F der vor-
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            genden bogen.</s>
            <s xml:space="preserve"/>
          </p>
          <figure>
            <variables xml:space="preserve">c a b e f d</variables>
          </figure>
          <p>
            <s xml:space="preserve">Damit du aber verſtãdeſt was ein rechter vnd
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            vmbkerter Sinus oder ſchooß ſeye/ ſolt du wüſ-
              <lb/>
            ſen daß die geſtrackte linien ſo vnder dem bogenn
              <lb/>
            gezogen/ ein chorda oder ſeytten genennet wirt.
              <lb/>
            </s>
            <s xml:space="preserve">Dieweil aber diſe zůgleich von des circkels diame
              <lb/>
            ter abgetheylet wirt/ neñet man den halbẽ theil/
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            die geſtrackte ſchooß an dem ſelbigen halbenn bo-
              <lb/>
            gen. </s>
            <s xml:space="preserve">Geſtrackt aber/ welches ein theil des Diame
              <lb/>
            ter iſt/ ſo ſich von der rechtẽ ſchooß gegen dem bo-
              <lb/>
            gen ſtrecket/ vnd wirt ein ſchooß genẽnet/ gegen
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            des ſelbigen bogen halben theil. </s>
            <s xml:space="preserve">Nimb ein exem-
              <lb/>
            pel. </s>
            <s xml:space="preserve">in dem circkel A B C D/ heißet A E B ein ſeytten oder ſchnůr an dem
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            bogen A C B. </s>
            <s xml:space="preserve">deßhalben theile ſie D E C durch das kommend Centrum A
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            B durch geleiche theil in E/ welche auch in geleiche geſtrackte theil zerſchnei
              <lb/>
            den/ als Euclides anzeigt/ vnnd den bogen A B gleicher geſtalt durch ge-
              <lb/>
            leiche theil inn C. </s>
            <s xml:space="preserve">deßhalben wirt E B ein rechte ſchooß ſein B C/ vnnd E
              <lb/>
            C ein vmbkerte ſchooß des A C. </s>
            <s xml:space="preserve">Wann man nun den bogen A C B erken-
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            net/ haben wir auß dem Ptolemeo die ſchnůr A B. </s>
            <s xml:space="preserve">deßhalben auch E B/
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            dann es iſt das halb an A B.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">Alſo wann man einen bogenn für ſtellet/ ſo iſt die rechte ſchooß der halb
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            theil an der ſchnůr oder ſeytten des zwifachen bogen. </s>
            <s xml:space="preserve">wann wir den ſelbigẽ
              <lb/>
            hand/ haben wir auch den vmbkerten bogen/ auß des Euclidis demonſtra
              <lb/>
            tionen vnd beweiſungen/ wañ man E B in ſich ſelbs zeücht/ vñ diſen qua-
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            draten vnd viereckechten theil auß dem quadraten F C zeücht/ vnnd des ü-
              <lb/>
            berblibenen/ wann man die ſeyten oder wurtzel nimmet/ welches die größe
              <lb/>
            F E iſt. </s>
            <s xml:space="preserve">wann man die ſelbigen abzeücht vonn F C/ ſo bleibt E C die vmb-
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            kerte ſchooß. </s>
            <s xml:space="preserve">wir haben auch von deßwegen/ vnnd weil es treffenlich nutz-
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            lich/ die tafel verordnet. </s>
            <s xml:space="preserve">Ich hab aber auß Ptolemei taflen die gerechten
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            ſchooß außgezogen/ vnnd die vmbkerten auß der gerechten oder geſtrack-
              <lb/>
            ten gemachet. </s>
            <s xml:space="preserve">Wann aber auch etliche minutien vnnd brüchzaal im bogen
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            an den tbeilen hangend/ ſo zeüch ihr zaal in der brüchzaal vnderſcheid/ ſo
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            wirt daß außgebracht der ſecunden zaal ſein/ welche man zů den ſchoßen
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            thůn ſoll.</s>
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          </p>
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