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

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page |< < (dxiiij) of 997 > >|
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            <s xml:id="echoid-s16439" xml:space="preserve">
              <pb o="dxiiij" file="0570" n="570" rhead="Von mancherlei wunderbaren"/>
            iſt auch diſes ſo darauß kommen bekannt/ wann diſes auch durch die dritt
              <lb/>
            bekannte größe abgetheylet/ wirt er die vnbekannte größe eroffnen. </s>
            <s xml:id="echoid-s16440" xml:space="preserve">Die-
              <lb/>
            weil aber in den dreyen erſtẽ proportzen allwegen die erſte größe/ für ein gan
              <lb/>
            tze ſchoß geſtellet wirt/ namlich für lx grad/ wirt ſie auch bekant ſein. </s>
            <s xml:id="echoid-s16441" xml:space="preserve">wann
              <lb/>
            nun vnder den anderẽ dreyẽ quantitetẽ oder größenen die ein bekant/ wirt
              <lb/>
            auch die dritt bekant ſein. </s>
            <s xml:id="echoid-s16442" xml:space="preserve">Darũb iſt gnůg wañ man in den dreyẽ taflen zwo
              <lb/>
            bekañte ſetzet/ ſie ſeyẽ beid beſeytz/ oder die eine an der ſeyttẽ/ vnd die ander
              <lb/>
            in der mitte/ damit die dritt dargegen über bekañt ſeye. </s>
            <s xml:id="echoid-s16443" xml:space="preserve">Deßhalbẽ ſeind die
              <lb/>
            dritt vñ ander größe allwegen beſeitz/ vnd die vierdt in dem bodẽ oder mit-
              <lb/>
            te/ dañ wañ man diſe durch lx zeücht oder multipliciert/ bringt ſie eben als
              <lb/>
            vyl wie die anderen zwo. </s>
            <s xml:id="echoid-s16444" xml:space="preserve">Dieweil aber die ander vnd drit quantitet kleiner
              <lb/>
            dañ die gantz ſchooß/ wirt auch des Euclidis beweyſung inn dem fünfften
              <lb/>
            bůch der elementẽ vñ gründẽ/ die vierdte am kleinſten ſein. </s>
            <s xml:id="echoid-s16445" xml:space="preserve">darumb iſt der
              <lb/>
            mittelſt bogen allwegen kleiner dañ die beid/ ſo beſeitz ſthond. </s>
            <s xml:id="echoid-s16446" xml:space="preserve">er ſetzet aber
              <lb/>
            der gemeldten ſchoßen bogen/ damit die arbeit gemindert/ vnd die zeit ge-
              <lb/>
            ſparet werde. </s>
            <s xml:id="echoid-s16447" xml:space="preserve">Vnd diſes gantz ſicher/ dieweil ein jede ſchoß jren bogen in al-
              <lb/>
            len circklen hatt ſo gegen jr ſtim̃et # Weil nun diſes bekannt/ damit er die
              <lb/>
            vnbekañten bogen/ durch die bekante auß den taflen ſůche/ ſo zeücht er die
              <lb/>
            zů der einen propoſition/ auß den dreien/ welche zůerſt beſchriben. </s>
            <s xml:id="echoid-s16448" xml:space="preserve">Alſo ſey-
              <lb/>
            en inn vier orthen A D E F/ welche vnder zwen Trigonen oder triangel ge
              <lb/>
            ſtellet/ B E F/ vnd C D F/ vnd ſeyend zwen geſtrackte eck E vnd D/ als in
              <lb/>
            der erſten ordnũg zwo ſeiten/ welche nit ſeyend A D vnd A C. </s>
            <s xml:id="echoid-s16449" xml:space="preserve">ſag ich die an
              <lb/>
            deren zwo ſeyend bekañt. </s>
            <s xml:id="echoid-s16450" xml:space="preserve">Deßhalben ſeyen zů erſt D A vnd D F/ ich ver
              <lb/>
            ſthon den triangel C D F/ ſo wirt die proportz der gantzenn ſchoß gegen der
              <lb/>
            ſchoß F B/ dz überbliben D F ſein/ wie die ſchoß A D des überblibenẽ D C/
              <lb/>
            gegen der ſchoß F E des überblibnẽ F C. </s>
            <s xml:id="echoid-s16451" xml:space="preserve">Wañ man nun A D vñ D F für die
              <lb/>
            ſeytten hatt/ wirt in der mitte der bogen F E ſein. </s>
            <s xml:id="echoid-s16452" xml:space="preserve">Wir wöllen aber F E in
              <lb/>
            der mitle nem̃en (wie ich geſagt hab) dañ in der anderẽ angezognen propoſi
              <lb/>
            tion F E/ deren wir vns hie gebrauchen/ iſt die vierdte größe. </s>
            <s xml:id="echoid-s16453" xml:space="preserve">Wañ nun A
              <lb/>
            D vnd F E bekañt weren/ oder F E vnnd F D/ ſo ſůcheſt du F E in dem bo
              <lb/>
            den oder mitle/ vñ A D o{der} F B/ das übrig F D in der ſeytten/ vñ wz in der
              <lb/>
            ſeitten iſt/ das iſt darbey oder ob der taflen (dañ es ſeind beide der bogẽ/ ſo
              <lb/>
            beſeytz ſthond/ zaalẽ) wurde auch durch die ſelbigen des dritten bogen zaal
              <lb/>
            ſein. </s>
            <s xml:id="echoid-s16454" xml:space="preserve">Wañ man aber C F vnd F B hette/ vnd begerteſt D A. </s>
            <s xml:id="echoid-s16455" xml:space="preserve">ſo weiſt du wol
              <lb/>
            daß E F bekañt ſeye/ dañ dz überig iſt F C/ alſo wirſt du D A haben. </s>
            <s xml:id="echoid-s16456" xml:space="preserve">der ge-
              <lb/>
            ſtalt möchteſt du auch D C haben/ dañ es iſt dz überbliben D A. </s>
            <s xml:id="echoid-s16457" xml:space="preserve">Alſo wann
              <lb/>
            du F D vnd D A hetteſt/ vnd begerteſt A E/ wirſt du F E habẽ (als gemel-
              <lb/>
            det worden) durch die ſelb ander propoſitiõ/ vnd wz noch überblibẽ nam̃lich
              <lb/>
            F C. </s>
            <s xml:id="echoid-s16458" xml:space="preserve">Deßhalben haſt du am triangel B E F auch am recht angel/ dz die pro
              <lb/>
            portz der gantzen ſchoß gegen der ſchoß F C/ vnd dz überig der ſeytẽ F E iſt/
              <lb/>
            als die ſchoß von dem überigẽ B C/ gegen der ſchoß F D/ der überigẽ ſeittẽ/
              <lb/>
            ſo vnder der außgeſtrecktẽ ſthet. </s>
            <s xml:id="echoid-s16459" xml:space="preserve">Darũb gang mit dem D F in die mitte/ vñ
              <lb/>
            mit F C beſeytz/ ſo wirt der bogen an der ſeitten erfunden ſein.</s>
            <s xml:id="echoid-s16460" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16461" xml:space="preserve">Wann aber zwen bogen A D vnnd A E bekannt/ wellend wir durch die
              <lb/>
            ſelb erſt inn die tafel faren mit den bogen ſo beſeytz ſthond A E vnd A D/
              <lb/>
            ſo wirſt du den bogen des übrigen eck F haben. </s>
            <s xml:id="echoid-s16462" xml:space="preserve">Weil auch durch die dritt pro
              <lb/>
            poſition des eck D proportz gegen dem eck F wie die ſchooß C F iſt/ gegen
              <lb/>
            der ſchoß C D/ vñ die ſchooß D iſt die gantze ſchooß/ dañ das D iſt gerad/
              <lb/>
            </s>
          </p>
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