Schröder, Ernst: Vorlesungen über die Algebra der Logik. Bd. 2, Abt. 1. Leipzig, 1891.§ 39. Die denkbaren Umfangsbeziehungen überhaupt. XXII0. Tafel der 128 Unterfälle von a.
§ 39. Die denkbaren Umfangsbeziehungen überhaupt. XXII0. Tafel der 128 Unterfälle von a.
<TEI> <text> <body> <div n="1"> <div n="2"> <div n="3"> <pb facs="#f0175" n="151"/> <fw place="top" type="header">§ 39. Die denkbaren Umfangsbeziehungen überhaupt.</fw><lb/> <p> <hi rendition="#c">XXII<hi rendition="#sup">0</hi>. <hi rendition="#g">Tafel der</hi> 128 <hi rendition="#g">Unterfälle</hi> von <hi rendition="#i">a</hi>.</hi> </p><lb/> <table> <row> <cell>1) 0 · <hi rendition="#i">a</hi></cell> <cell>128 = 2 + 3 + 4 + 5 + 6 + 7 + 8 = <hi rendition="#i">a</hi></cell> </row><lb/> <row> <cell>2 = <hi rendition="#i">h k l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h k</hi></cell> <cell>127 = 3 + 4 + 5 + 6 + 7 + 8 = (<hi rendition="#i">h</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi>) <hi rendition="#i">a</hi> = <hi rendition="#i">h k</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell> </row><lb/> <row> <cell>3 = <hi rendition="#i">h k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi> = <hi rendition="#i">h l</hi> = <hi rendition="#i">h n</hi></cell> <cell>126 = 2 + 4 + 5 + 6 + 7 + 8 = (<hi rendition="#i">h</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">l</hi><hi rendition="#sub">1</hi>) <hi rendition="#i">a</hi> = <hi rendition="#i">h n</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi> = <hi rendition="#i">n</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell> </row><lb/> <row> <cell>4 = <hi rendition="#i">h k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">n</hi><hi rendition="#sub">1</hi></cell> <cell>125 = 2 + 3 + 5 + 6 + 7 + 8 = <hi rendition="#i">k</hi> + (<hi rendition="#i">h</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">l</hi>) <hi rendition="#i">a</hi> = <hi rendition="#i">k</hi> + <hi rendition="#i">h n</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell> </row><lb/> <row> <cell>5 = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k l</hi> = <hi rendition="#i">k l</hi> = <hi rendition="#i">k m</hi></cell> <cell>124 = 2 + 3 + 4 + 6 + 7 + 8 = (<hi rendition="#i">k</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">l</hi><hi rendition="#sub">1</hi>) <hi rendition="#i">a</hi> = <hi rendition="#i">k m</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi> = <hi rendition="#i">m</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell> </row><lb/> <row> <cell>6 = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k m</hi><hi rendition="#sub">1</hi></cell> <cell>123 = 2 + 3 + 4 + 5 + 7 + 8 = <hi rendition="#i">h</hi> + (<hi rendition="#i">k</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">l</hi>) <hi rendition="#i">a</hi> = <hi rendition="#i">h</hi> + <hi rendition="#i">k m</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell> </row><lb/> <row> <cell>7 = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l a</hi></cell> <cell>122 = 2 + 3 + 4 + 5 + 6 + 8 = <hi rendition="#i">h</hi> + <hi rendition="#i">k</hi> + <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell> </row><lb/> <row> <cell>8 = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell> <cell>121 = 2 + 3 + 4 + 5 + 6 + 7 = <hi rendition="#i">h</hi> + <hi rendition="#i">k</hi> + <hi rendition="#i">l a</hi></cell> </row><lb/> <row> <cell>9 = 2 + 3 = <hi rendition="#i">h</hi> (<hi rendition="#i">k</hi> + <hi rendition="#i">l</hi>) = <hi rendition="#i">h</hi> (<hi rendition="#i">k</hi> + <hi rendition="#i">n</hi>)</cell> <cell>120 = 4 + 5 + 6 + 7 + 8 = (<hi rendition="#i">h</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi><hi rendition="#sub">1</hi>) <hi rendition="#i">a</hi> = <hi rendition="#i">h k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">n</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell> </row><lb/> <row> <cell>10 = 2 + 4 = <hi rendition="#i">h l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h n</hi><hi rendition="#sub">1</hi></cell> <cell>119 = 3 + 5 + 6 + 7 + 8 = (<hi rendition="#i">h</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">l</hi>) <hi rendition="#i">a</hi> = <hi rendition="#i">h n</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell> </row><lb/> <row> <cell>11 = 2 + 5 = <hi rendition="#i">k</hi> (<hi rendition="#i">h</hi> + <hi rendition="#i">l</hi> = <hi rendition="#i">k</hi> (<hi rendition="#i">h</hi> + <hi rendition="#i">m</hi>)</cell> <cell>118 = 3 + 4 + 6 + 7 + 8 = (<hi rendition="#i">k</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi><hi rendition="#sub">1</hi>) <hi rendition="#i">a</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k m</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell> </row><lb/> <row> <cell>12 = 2 + 6 = <hi rendition="#i">k l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">k m</hi><hi rendition="#sub">1</hi></cell> <cell>117 = 3 + 4 + 5 + 7 + 8 = (<hi rendition="#i">k</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">l</hi>) <hi rendition="#i">a</hi> = <hi rendition="#i">k m</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell> </row><lb/> <row> <cell>13 = 2 + 7 = <hi rendition="#i">h k</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l a</hi></cell> <cell>116 = 3 + 4 + 5 + 6 + 8 = <hi rendition="#i">h k</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell> </row><lb/> <row> <cell>14 = 2 + 8 = <hi rendition="#i">h k</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell> <cell>115 = 3 + 4 + 5 + 6 + 7 = <hi rendition="#i">h k</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l a</hi></cell> </row><lb/> <row> <cell>15 = 3 + 4 = <hi rendition="#i">h k</hi><hi rendition="#sub">1</hi></cell> <cell>114 = 2 + 5 + 6 + 7 + 8 = <hi rendition="#i">k</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell> </row><lb/> <row> <cell>16 = 3 + 5 = (<hi rendition="#i">h</hi> + <hi rendition="#i">k</hi>) <hi rendition="#i">l</hi> = <hi rendition="#i">h n</hi> + <hi rendition="#i">k m</hi></cell> <cell>113 = 2 + 4 + 6 + 7 + 8 = (<hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">l</hi><hi rendition="#sub">1</hi>) <hi rendition="#i">a</hi> = <hi rendition="#i">m</hi><hi rendition="#sub">1</hi> <hi rendition="#i">n</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell> </row><lb/> <row> <cell>17 = 3 + 6 = <hi rendition="#i">h l</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h n</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k m</hi><hi rendition="#sub">1</hi></cell> <cell>112 = 2 + 4 + 5 + 7 + 8 = <hi rendition="#i">h l</hi><hi rendition="#sub">1</hi> + (<hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi><hi rendition="#sub">1</hi>) <hi rendition="#i">a</hi> = <hi rendition="#i">k m</hi> + <hi rendition="#i">h n</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell> </row><lb/> <row> <cell>18 = 3 + 7 = <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l a</hi></cell> <cell>111 = 2 + 4 + 5 + 6 + 8 = <hi rendition="#i">k</hi> + <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell> </row><lb/> <row> <cell>19 = 3 + 8 = <hi rendition="#i">h l</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi> = <hi rendition="#i">h n</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell> <cell>110 = 2 + 4 + 5 + 6 + 7 = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l a</hi> + (<hi rendition="#i">h</hi> + <hi rendition="#i">k</hi>) <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">k</hi> + <hi rendition="#i">h n</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l a</hi></cell> </row><lb/> <row> <cell>20 = 4 + 5 = <hi rendition="#i">k l</hi> + <hi rendition="#i">h k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">k m</hi> + <hi rendition="#i">h k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">n</hi><hi rendition="#sub">1</hi></cell> <cell>109 = 2 + 3 + 6 + 7 + 8 = <hi rendition="#i">k l</hi><hi rendition="#sub">1</hi> + (<hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi><hi rendition="#sub">1</hi>) <hi rendition="#i">a</hi> = <hi rendition="#i">h n</hi> + <hi rendition="#i">k m</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell> </row><lb/> </table> </div> </div> </div> </body> </text> </TEI> [151/0175]
§ 39. Die denkbaren Umfangsbeziehungen überhaupt.
XXII0. Tafel der 128 Unterfälle von a.
1) 0 · a 128 = 2 + 3 + 4 + 5 + 6 + 7 + 8 = a
2 = h k l1 = h k 127 = 3 + 4 + 5 + 6 + 7 + 8 = (h1 + k1) a = h k1 + h1 a = h1 k + k1 a
3 = h k1 l = h l = h n 126 = 2 + 4 + 5 + 6 + 7 + 8 = (h1 + l1) a = h n1 + h1 a = n1 a
4 = h k1 l1 = h k1 n1 125 = 2 + 3 + 5 + 6 + 7 + 8 = k + (h1 + l) a = k + h n + h1 a
5 = h1 k l = k l = k m 124 = 2 + 3 + 4 + 6 + 7 + 8 = (k1 + l1) a = k m1 + k1 a = m1 a
6 = h1 k l1 = h1 k m1 123 = 2 + 3 + 4 + 5 + 7 + 8 = h + (k1 + l) a = h + k m + k1 a
7 = h1 k1 l a 122 = 2 + 3 + 4 + 5 + 6 + 8 = h + k + l1 a
8 = h1 k1 l1 a 121 = 2 + 3 + 4 + 5 + 6 + 7 = h + k + l a
9 = 2 + 3 = h (k + l) = h (k + n) 120 = 4 + 5 + 6 + 7 + 8 = (h1 + k1 l1) a = h k1 n1 + h1 a
10 = 2 + 4 = h l1 = h n1 119 = 3 + 5 + 6 + 7 + 8 = (h1 + l) a = h n + h1 a
11 = 2 + 5 = k (h + l = k (h + m) 118 = 3 + 4 + 6 + 7 + 8 = (k1 + h1 l1) a = h1 k m1 + k1 a
12 = 2 + 6 = k l1 = k m1 117 = 3 + 4 + 5 + 7 + 8 = (k1 + l) a = k m + k1 a
13 = 2 + 7 = h k + h1 k1 l a 116 = 3 + 4 + 5 + 6 + 8 = h k1 + h1 k + h1 k1 l1 a
14 = 2 + 8 = h k + h1 k1 l1 a 115 = 3 + 4 + 5 + 6 + 7 = h k1 + h1 k + h1 k1 l a
15 = 3 + 4 = h k1 114 = 2 + 5 + 6 + 7 + 8 = k + h1 a
16 = 3 + 5 = (h + k) l = h n + k m 113 = 2 + 4 + 6 + 7 + 8 = (h1 k1 + l1) a = m1 n1 a
17 = 3 + 6 = h l + h1 k l1 = h n + h1 k m1 112 = 2 + 4 + 5 + 7 + 8 = h l1 + (h1 l + k1 l1) a = k m + h n1 + h1 k1 a
18 = 3 + 7 = k1 l a 111 = 2 + 4 + 5 + 6 + 8 = k + l1 a
19 = 3 + 8 = h l + h1 k1 l1 a = h n + h1 k1 l1 a 110 = 2 + 4 + 5 + 6 + 7 = h1 l a + (h + k) l1 = k + h n1 + h1 l a
20 = 4 + 5 = k l + h k1 l1 = k m + h k1 n1 109 = 2 + 3 + 6 + 7 + 8 = k l1 + (k1 l + h1 l1) a = h n + k m1 + h1 k1 a
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Zitationshilfe: | Schröder, Ernst: Vorlesungen über die Algebra der Logik. Bd. 2, Abt. 1. Leipzig, 1891, S. 151. In: Deutsches Textarchiv <https://www.deutschestextarchiv.de/schroeder_logik0201_1891/175>, abgerufen am 18.02.2025. |