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...Chapter euclid s elements book i constructions theuseofrulerandcompass can be read as a on how to construct certain geometric gures efciently and accurately using ruler compass ascertaining the validity rst three postulates before are basic use of postulate draw straight line from any point with straightedge one connects two given points b form segment ab there is only such this uniqueness assumed for example in proof produce nite continuously c so that ac contains thersttwopostulatescanbecombinedintoasingleone throughtwodistinct unique describe circle center distance by another collapsible constructs pass through we denote shows radius equal seg ment denition trilateral an equilateral triangle which has its sides isosceles alone scalene unequal remark seems take exclusive sense but it more convenient these inclusive also...