← elements / Elements 2.0 (G Index) G.569 XI.def.24 ← Prev Pseudocode · Heath Next → G.569 similar cones and cylinders¶ XI.def.24 Similar cones and cylinders are those in which the:term:axes <G.564> and the:term:diameters of the bases <G.566> are:term:proportional <G.180>. similar_cones_cylinders_def 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.12" [label="G.12", tooltip="G.12 (I.def.19): Rectilineal figures are contained by segments: trilateral by three, quadrilateral by four, and multilateral by more than four.", fillcolor="#224422", URL="../G.12/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.170" [label="G.170", tooltip="G.170 (V.def.2): The greater is amultiple of the less when it ismeasured by the less.", fillcolor="#224422", URL="../G.170/index.html", target="_top"]; "G.176" [label="G.176", tooltip="G.176 (V.def.5): Magnitudes are said tobe in the same ratio, the first to the second and the third to the fourth, when, if anyequimultiples whatever be taken of the first and third, and any equimul...", fillcolor="#224422", URL="../G.176/index.html", target="_top"]; "G.180" [label="G.180", tooltip="G.180 (V.def.6): Let magnitudes which have thesame ratio be calledproportional.", fillcolor="#224422", URL="../G.180/index.html", target="_top"]; "G.564" [label="G.564", tooltip="G.564 (XI.def.19): Theaxis of the cone is thesegment which remains fixed and about which thetriangle is turned.", fillcolor="#224422", URL="../G.564/index.html", target="_top"]; "G.566" [label="G.566", tooltip="G.566 (XI.def.20): And thebase is thecircle described by thesegment which is carried round.", fillcolor="#224422", URL="../G.566/index.html", target="_top"]; "G.567" [label="G.567", tooltip="G.567 (XI.def.22): Theaxis of the cylinder is thesegment which remains fixed and about which the parallelogram is turned.", fillcolor="#224422", URL="../G.567/index.html", target="_top"]; "G.568" [label="G.568", tooltip="G.568 (XI.def.23): And thebases are thecircles described by the two sides opposite to one another which are carried round.", fillcolor="#224422", URL="../G.568/index.html", target="_top"]; "G.569" [label="G.569", tooltip="G.569 (XI.def.24): Similar cones and cylinders are those in which theaxes and thediameters of the bases areproportional.", 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.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.12" -> "G.4"; "G.564" -> "G.4"; "G.566" -> "G.4"; "G.567" -> "G.4"; "G.6" -> "G.5"; "G.7" -> "G.5"; "G.10" -> "G.6"; "G.10" -> "G.7"; "G.9" -> "G.8"; "G.10" -> "G.9"; "G.12" -> "G.9"; "G.566" -> "G.10"; "G.568" -> "G.10"; "G.564" -> "G.12"; "G.170" -> "G.169"; "G.176" -> "G.170"; "G.180" -> "G.176"; "G.569" -> "G.180"; "G.569" -> "G.564"; "G.569" -> "G.566"; "G.569" -> "G.567"; "G.569" -> "G.568"; } Required for¶ G.570