G.502 part segment plane

XI.1

A part of a segment cannot be in the plane of reference and a part in a plane more elevated.
part_segment_plane()
prove a part of a segment cannot be in the plane of reference, and a part in a plane more elevated
C D B A
assert If possible, let a part / A B / of / A B C / be in the plane of reference, and a part / B C / in a plane more elevated
assert There will then be in the plane of reference some segment continuous with / A B / in a segment
assert Let it be / B D /
assert / A B / is a common segment of / A B C /, / A B D /:
assert ⇒⇐, inasmuch as, if we describe a circle with center B and distance / A B /, the diameters will cut off unequal arcs of the circle
∴ a part of a segment cannot be in the plane of reference, and a part in a plane more elevated

Dependency Graph

digraph { bgcolor="transparent"; node [shape=box, style="rounded,filled", fontname="Helvetica", fontsize=11, color="#d6d3cd", fontcolor="#ffffff"]; edge [color="#8c857b", fontcolor="#8c857b", arrowsize=0.75]; rankdir="TB"; "G.1" [label="G.1", tooltip="G.1 (I.def.1): A point A is that which has no part.", fillcolor="#224422", URL="../G.1/index.html", target="_top"]; "G.2" [label="G.2", tooltip="G.2 (I.def.2): A line [ A B ] is a projection of a relationship of two points A, B.", fillcolor="#224422", URL="../G.2/index.html", target="_top"]; "G.3" [label="G.3", tooltip="G.3 (I.def.3): The extremities of a segment / A B / are points A, B.", fillcolor="#224422", URL="../G.3/index.html", target="_top"]; "G.4" [label="G.4", tooltip="G.4 (I.def.4): A segment / A B / is a portion of a line [ A B ] between two points A, B on the line.", fillcolor="#224422", URL="../G.4/index.html", target="_top"]; "G.5" [label="G.5", tooltip="G.5 (I.def.5): A surface is that which has length and breadth only.", fillcolor="#224422", URL="../G.5/index.html", target="_top"]; "G.6" [label="G.6", tooltip="G.6 (I.def.6): The extremities of a surface are lines or arcs.", fillcolor="#224422", URL="../G.6/index.html", target="_top"]; "G.7" [label="G.7", tooltip="G.7 (I.def.7): A plane surface lies evenly with the lines on itself.", fillcolor="#224422", URL="../G.7/index.html", target="_top"]; "G.8" [label="G.8", tooltip="G.8 (I.def.13): A boundary is the extremity of anything.", fillcolor="#224422", URL="../G.8/index.html", target="_top"]; "G.9" [label="G.9", tooltip="G.9 (I.def.14): A figure is that which is contained by any boundary or boundaries.", fillcolor="#224422", URL="../G.9/index.html", target="_top"]; "G.10" [label="G.10", tooltip="G.10 (I.def.15): A circle ( A B ) is a plane figure contained by one arc defined by a center A and a point B establishing its defining radius / A B /, such that all segments / A B /, / A C /, / A D...", fillcolor="#224422", URL="../G.10/index.html", target="_top"]; "G.11" [label="G.11", tooltip="G.11 (I.def.16): The point A within the circle ( A B ) from which all segments / A B /, / A C / to the arc are equal is called the center of the circle.", fillcolor="#224422", URL="../G.11/index.html", target="_top"]; "G.61" [label="G.61", tooltip="G.61 (I.def.17): A diameter of a circle is any segment drawn through the center and terminated in both directions by the arc of the circle; it bisects the circle.", fillcolor="#224422", URL="../G.61/index.html", target="_top"]; "G.169" [label="G.169", tooltip="G.169 (V.def.1): A magnitude is apart of a magnitude, the less of the greater, when it measures the greater.", fillcolor="#224422", URL="../G.169/index.html", target="_top"]; "G.247" [label="G.247", tooltip="G.247 (VII.def.1): Anunit is that by virtue of which each of the things that exist is called one.", fillcolor="#224422", URL="../G.247/index.html", target="_top"]; "G.248" [label="G.248", tooltip="G.248 (VII.def.2): Anumber is a multitude composed ofunits.", fillcolor="#224422", URL="../G.248/index.html", target="_top"]; "G.253" [label="G.253", tooltip="G.253 (VII.def.3): Anumber is apart of a number, the less of the greater, when itmeasures the greater;", fillcolor="#224422", URL="../G.253/index.html", target="_top"]; "G.502" [label="G.502", tooltip="G.502 (XI.1): A part of a segment cannot be in the plane of reference and a part in a plane more elevated.", penwidth=2.5, color="#e8b85a", fillcolor="#4a453b", URL="index.html", target="_top"]; "G.2" -> "G.1"; "G.3" -> "G.1"; "G.4" -> "G.1"; "G.10" -> "G.1"; "G.11" -> "G.1"; "G.3" -> "G.2"; "G.4" -> "G.2"; "G.6" -> "G.2"; "G.7" -> "G.2"; "G.4" -> "G.3"; "G.6" -> "G.3"; "G.8" -> "G.3"; "G.7" -> "G.4"; "G.10" -> "G.4"; "G.11" -> "G.4"; "G.61" -> "G.4"; "G.502" -> "G.4"; "G.6" -> "G.5"; "G.7" -> "G.5"; "G.10" -> "G.6"; "G.10" -> "G.7"; "G.502" -> "G.7"; "G.9" -> "G.8"; "G.10" -> "G.9"; "G.11" -> "G.10"; "G.61" -> "G.10"; "G.502" -> "G.10"; "G.61" -> "G.11"; "G.502" -> "G.11"; "G.502" -> "G.61"; "G.253" -> "G.169"; "G.248" -> "G.247"; "G.253" -> "G.248"; "G.502" -> "G.253"; }

Required for

G.503, G.508, G.510, G.511, G.512, G.513, G.514, G.518, G.519, G.520, G.522, 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