Schröder, Ernst: Vorlesungen über die Algebra der Logik. Bd. 2, Abt. 1. Leipzig, 1891.§ 37. Produkte und Summen der Grundbeziehungen. VI0. Produkte der Grundbeziehungen mit den Hülfs-beziehungen h, h1, k, k1.
§ 37. Produkte und Summen der Grundbeziehungen. VI0. Produkte der Grundbeziehungen mit den Hülfs-beziehungen h, h1, k, k1.
<TEI> <text> <body> <div n="1"> <div n="2"> <div n="3"> <p> <pb facs="#f0149" n="125"/> <fw place="top" type="header">§ 37. Produkte und Summen der Grundbeziehungen.</fw><lb/> <hi rendition="#c">VI<hi rendition="#sup">0</hi>. <hi rendition="#g">Produkte der Grundbeziehungen mit den Hülfs-<lb/> beziehungen</hi> <hi rendition="#i">h</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><lb/> <table> <row> <cell><hi rendition="#i">h k</hi> = <hi rendition="#i">h k a</hi>,</cell> <cell><hi rendition="#i">h k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi>,</cell> <cell><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 a</hi>,</cell> <cell><hi rendition="#i">h</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</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> + <hi rendition="#i">a</hi><hi rendition="#sub">1</hi>.</cell> </row><lb/> <row> <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi> = 0,</cell> <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi>,</cell> <cell><hi rendition="#i">a h</hi> = <hi rendition="#i">h</hi>,</cell> <cell><hi rendition="#i">a h</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><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi> = 0,</cell> <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi>,</cell> <cell><hi rendition="#i">a k</hi> = <hi rendition="#i">k</hi>,</cell> <cell><hi rendition="#i">a k</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><hi rendition="#i">b h</hi> = <hi rendition="#i">h k</hi>,</cell> <cell><hi rendition="#i">b h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">e</hi> + <hi rendition="#i">δ</hi>,</cell> <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi> = <hi rendition="#i">h k</hi><hi rendition="#sub">1</hi>,</cell> <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</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> + <hi rendition="#i">α</hi> + <hi rendition="#i">γ</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">b k</hi> = <hi rendition="#i">k</hi>,</cell> <cell><hi rendition="#i">b k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">β</hi> + <hi rendition="#i">δ</hi>,</cell> <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi> = 0,</cell> <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi></cell> </row><lb/> <row> <cell><hi rendition="#i">c h</hi> = <hi rendition="#i">h</hi>,</cell> <cell><hi rendition="#i">c h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">γ</hi> + <hi rendition="#i">δ</hi>,</cell> <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi> = 0,</cell> <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">c</hi><hi rendition="#sub">1</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">c k</hi> = <hi rendition="#i">h k</hi>,</cell> <cell><hi rendition="#i">c k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">f</hi> + <hi rendition="#i">δ</hi>,</cell> <cell><hi rendition="#i">c</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>,</cell> <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</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> + <hi rendition="#i">α</hi> + <hi rendition="#i">β</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">d h</hi> = <hi rendition="#i">h k</hi>,</cell> <cell><hi rendition="#i">d h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">δ</hi>,</cell> <cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi> = <hi rendition="#i">h k</hi><hi rendition="#sub">1</hi>,</cell> <cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">c</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">γ</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">d k</hi> = <hi rendition="#i">h k</hi>,</cell> <cell><hi rendition="#i">d k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">δ</hi>,</cell> <cell><hi rendition="#i">d</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>,</cell> <cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">β</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">e h</hi> = 0,</cell> <cell><hi rendition="#i">e h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">e</hi>,</cell> <cell><hi rendition="#i">e</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi> = <hi rendition="#i">h</hi>,</cell> <cell><hi rendition="#i">e</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</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> + <hi rendition="#i">α</hi> + <hi rendition="#i">γ</hi> + <hi rendition="#i">δ</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">e k</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi>,</cell> <cell><hi rendition="#i">e k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">β</hi>,</cell> <cell><hi rendition="#i">e</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi> = <hi rendition="#i">h k</hi>,</cell> <cell><hi rendition="#i">e</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">δ</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">f h</hi> = <hi rendition="#i">h k</hi><hi rendition="#sub">1</hi>,</cell> <cell><hi rendition="#i">f h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">γ</hi>,</cell> <cell><hi rendition="#i">f</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi> = <hi rendition="#i">h k</hi>,</cell> <cell><hi rendition="#i">f</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">c</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">δ</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">f k</hi> = 0,</cell> <cell><hi rendition="#i">f k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">f</hi>,</cell> <cell><hi rendition="#i">f</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi> = <hi rendition="#i">k</hi>,</cell> <cell><hi rendition="#i">f</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</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> + <hi rendition="#i">α</hi> + <hi rendition="#i">β</hi> + <hi rendition="#i">δ</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">g h</hi> = 0,</cell> <cell><hi rendition="#i">g h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">g</hi>,</cell> <cell><hi rendition="#i">g</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi> = <hi rendition="#i">h</hi>,</cell> <cell><hi rendition="#i">g</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi> + <hi rendition="#i">β</hi> + <hi rendition="#i">γ</hi> + <hi rendition="#i">δ</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">g k</hi> = 0,</cell> <cell><hi rendition="#i">g k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">g</hi>,</cell> <cell><hi rendition="#i">g</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi> = <hi rendition="#i">k</hi>,</cell> <cell><hi rendition="#i">g</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi> + <hi rendition="#i">β</hi> + <hi rendition="#i">γ</hi> + <hi rendition="#i">δ</hi>.</cell> </row><lb/> </table> <hi rendition="#c">VII<hi rendition="#sup">0</hi>. <hi rendition="#g">Summen der Grundbeziehungen mit den</hi> <hi rendition="#i">h</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><lb/> <table> <row> <cell><hi rendition="#i">h</hi> + <hi rendition="#i">k</hi> = (<hi rendition="#i">h</hi> + <hi rendition="#i">k</hi>) <hi rendition="#i">a</hi>,</cell> <cell><hi rendition="#i">h</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">e</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">β</hi>,</cell> <cell><hi rendition="#i">h</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">f</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">γ</hi>,</cell> <cell><hi rendition="#i">h</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">δ</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">h</hi> + <hi rendition="#i">a</hi><hi rendition="#sub">1</hi>,</cell> <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi>,</cell> <cell><hi rendition="#i">a</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">a</hi>,</cell> <cell><hi rendition="#i">a</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = i,</cell> </row><lb/> <row> <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">k</hi> + <hi rendition="#i">a</hi><hi rendition="#sub">1</hi>,</cell> <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">k</hi><hi rendition="#sub">1</hi>,</cell> <cell><hi rendition="#i">a</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">a</hi>,</cell> <cell><hi rendition="#i">a</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = i,</cell> </row><lb/> <row> <cell><hi rendition="#i">b</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">h</hi> + <hi rendition="#i">b</hi>,</cell> <cell><hi rendition="#i">b</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">f</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">γ</hi>,</cell> <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">h</hi> + <hi rendition="#i">b</hi><hi rendition="#sub">1</hi>,</cell> <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">δ</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">b</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">b</hi>,</cell> <cell><hi rendition="#i">b</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = i,</cell> <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">α</hi> + <hi rendition="#i">γ</hi>,</cell> <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">k</hi><hi rendition="#sub">1</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">c</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">c</hi>,</cell> <cell><hi rendition="#i">c</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = i,</cell> <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">α</hi> + <hi rendition="#i">β</hi>,</cell> <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">c</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">k</hi> + <hi rendition="#i">c</hi>,</cell> <cell><hi rendition="#i">c</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">c</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">β</hi>,</cell> <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">k</hi> + <hi rendition="#i">c</hi><hi rendition="#sub">1</hi>,</cell> <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">δ</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">d</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">h</hi> + <hi rendition="#i">δ</hi>,</cell> <cell><hi rendition="#i">d</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">f</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">γ</hi>,</cell> <cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">α</hi> + <hi rendition="#i">β</hi> + <hi rendition="#i">γ</hi>,</cell> <cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">δ</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">d</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">k</hi> + <hi rendition="#i">δ</hi>,</cell> <cell><hi rendition="#i">d</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">e</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">β</hi>,</cell> <cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">α</hi> + <hi rendition="#i">β</hi> + <hi rendition="#i">γ</hi>,</cell> <cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">δ</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">e</hi> + <hi rendition="#i">h</hi> = (<hi rendition="#i">h</hi> + <hi rendition="#i">k</hi>) + <hi rendition="#i">β</hi>,</cell> <cell><hi rendition="#i">e</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi>,</cell> <cell><hi rendition="#i">e</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">e</hi><hi rendition="#sub">1</hi>,</cell> <cell><hi rendition="#i">e</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = i,</cell> </row><lb/> <row> <cell><hi rendition="#i">e</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">k</hi> + <hi rendition="#i">β</hi>,</cell> <cell><hi rendition="#i">e</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">δ</hi>,</cell> <cell><hi rendition="#i">e</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">α</hi> + <hi rendition="#i">γ</hi> + <hi rendition="#i">δ</hi>,</cell> <cell><hi rendition="#i">e</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">e</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">β</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">f</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">h</hi> + <hi rendition="#i">γ</hi>,</cell> <cell><hi rendition="#i">f</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">δ</hi>,</cell> <cell><hi rendition="#i">f</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">α</hi> + <hi rendition="#i">β</hi> + <hi rendition="#i">δ</hi>,</cell> <cell><hi rendition="#i">f</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">f</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">γ</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">f</hi> + <hi rendition="#i">k</hi> = (<hi rendition="#i">h</hi> + <hi rendition="#i">k</hi>) + <hi rendition="#i">γ</hi>,</cell> <cell><hi rendition="#i">f</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">k</hi><hi rendition="#sub">1</hi>,</cell> <cell><hi rendition="#i">f</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">f</hi><hi rendition="#sub">1</hi>,</cell> <cell><hi rendition="#i">f</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = i,</cell> </row><lb/> <row> <cell><hi rendition="#i">g</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">h</hi> + <hi rendition="#i">α</hi>,</cell> <cell><hi rendition="#i">g</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi>,</cell> <cell><hi rendition="#i">g</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">g</hi><hi rendition="#sub">1</hi>,</cell> <cell><hi rendition="#i">g</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = i,</cell> </row><lb/> <row> <cell><hi rendition="#i">g</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">k</hi> + <hi rendition="#i">α</hi>,</cell> <cell><hi rendition="#i">g</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">k</hi><hi rendition="#sub">1</hi>,</cell> <cell><hi rendition="#i">g</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">g</hi><hi rendition="#sub">1</hi>,</cell> <cell><hi rendition="#i">g</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = i.</cell> </row><lb/> </table> </p> </div> </div> </div> </body> </text> </TEI> [125/0149]
§ 37. Produkte und Summen der Grundbeziehungen.
VI0. Produkte der Grundbeziehungen mit den Hülfs-
beziehungen h, h1, k, k1.
h k = h k a, h k1 = h k1 a, h1 k = h1 k a, h1 k1 = h1 k1 a + a1.
a1 h = 0, a1 h1 = a1, a h = h, a h1 = h1 a,
a1 k = 0, a1 k1 = a1, a k = k, a k1 = k1 a,
b h = h k, b h1 = e + δ, b1 h = h k1, b1 h1 = h1 k1 a + α + γ,
b k = k, b k1 = β + δ, b1 k = 0, b1 k1 = b1
c h = h, c h1 = γ + δ, c1 h = 0, c1 h1 = c1,
c k = h k, c k1 = f + δ, c1 k = h1 k, c1 k1 = h1 k1 a + α + β,
d h = h k, d h1 = δ, d1 h = h k1, d1 h1 = c1 + γ,
d k = h k, d k1 = δ, d1 k = h1 k, d1 k1 = b1 + β,
e h = 0, e h1 = e, e1 h = h, e1 h1 = h1 k1 a + α + γ + δ,
e k = h1 k, e k1 = β, e1 k = h k, e1 k1 = b1 + δ,
f h = h k1, f h1 = γ, f1 h = h k, f1 h1 = c1 + δ,
f k = 0, f k1 = f, f1 k = k, f1 k1 = h1 k1 a + α + β + δ,
g h = 0, g h1 = g, g1 h = h, g1 h1 = h1 a + β + γ + δ,
g k = 0, g k1 = g, g1 k = k, g1 k1 = k1 a + β + γ + δ.
VII0. Summen der Grundbeziehungen mit den h, h1, k, k1.
h + k = (h + k) a, h + k1 = e1 + β, h1 + k = f1 + γ, h1 + k1 = d1 + δ,
a1 + h = h + a1, a1 + h1 = h1, a + h = a, a + h1 = i,
a1 + k = k + a1, a1 + k1 = k1, a + k = a, a + k1 = i,
b + h = h + b, b + h1 = f1 + γ, b1 + h = h + b1, b1 + h1 = d1 + δ,
b + k = b, b + k1 = i, b1 + k = a + α + γ, b1 + k1 = k1,
c + h = c, c + h1 = i, c1 + h = a + α + β, c1 + h1 = h1,
c + k = k + c, c + k1 = c1 + β, c1 + k = k + c1, c1 + k1 = d1 + δ,
d + h = h + δ, d + h1 = f1 + γ, d1 + h = a + α + β + γ, d1 + h1 = d1 + δ,
d + k = k + δ, d + k1 = e1 + β, d1 + k = a + α + β + γ, d1 + k1 = d1 + δ,
e + h = (h + k) + β, e + h1 = h1, e1 + h = e1, e1 + h1 = i,
e + k = k + β, e + k1 = d1 + δ, e1 + k = a + α + γ + δ, e1 + k1 = e1 + β,
f + h = h + γ, f + h1 = d1 + δ, f1 + h = a + α + β + δ, f1 + h1 = f1 + γ,
f + k = (h + k) + γ, f + k1 = k1, f1 + k = f1, f1 + k1 = i,
g + h = h + α, g + h1 = h1, g1 + h = g1, g1 + h1 = i,
g + k = k + α, g + k1 = k1, g1 + k = g1, g1 + k1 = i.
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