G.504 planes cut common

XI.3

If two planes cut one another, their common section is a segment.
planes_cut_common()
prove the line / D B / is a segment
B F E D A C
assert Let the two planes < A B >, < B C > cut one another, and let the line / D B / be their common section
construct If not, from D to B let / D E B / be joined in the plane < A B >, and in the plane < B C > / D F B /.
assert Then / D E B /, / D F B / will have the same extremities, and will clearly enclose an area:
assert ⇒⇐
assert / D E B /, / D F B / are not segments
∴ Similarly we can prove that neither will there be any other segment joined from D to B except / D B / the common section of the planes < A B >, < B C >

Dependency Graph

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Required for

G.507, G.508, G.509, G.510, G.511, G.512, G.513, G.514, G.515, G.517, G.518, G.522, G.523, G.528, G.530, G.531, G.532, G.541, G.542, G.543, G.544, G.545, G.546, G.547, G.549, G.550, G.554, G.555, G.556, G.557, G.558, G.559, G.560, G.563, G.565, G.570, G.571, G.572, G.573, G.577, G.578, G.592, G.594, G.597, G.600, G.601