As for projections of a1 and a3, and they are connected by direct a1ay and a3ay, perpendicular OY axes. But as this axis on an epyura holds two positions, a1ay cannot be continuation of a piece of a3ay.
Fairly and the return i.e. if on the planes of projections the points of a1 and a2 located on the straight lines crossing OX axis in this point at right angle are given, they are projections of some point And. This point is defined perpendiculars, vosstavlenny of points of a1 and a2 to the planes H and
The projective drawing on which of projections with all that on them is represented, are combined defined one with another, is called (from fr. epure – the drawing). In drawing it is shown points And.
The planes of projections in this case are defined with an accuracy only to transfer (drawing). They are usually parallel to themselves so that all points of a subject over the plane H and before As the provision of an axis X12 uncertain, formation of an epyur in this case does not need to be connected with rotation of the planes round a coordinate axis. Upon transition to an epyur of the H and V plane combine so that heteronymic projections of points were on vertical straight lines.
Further epyura and without coordinate axes will meet. So arrive in practice at the image of subjects when it is essential only itself a subject, but not its provision of the planes of projections.
However in practice of the image of designs, cars and various engineering constructions there is a in creation of additional projections. Arrive so for the only purpose — to make the projective drawing clearer, legible.
It is possible to prove that projections of a point are always located on straight lines, axes OH and crossing this axis in the same point. Really, the projecting beams of Aa1 and Aa2 the plane, perpendicular projections and the line of their crossing — an axis OH. This plane crosses H and V on straight lines a1 ax and a1 ax, which form with an axis of OX and with each other right angles with top in a point ax.
Let's notice that the provision of the planes of projections in space can appear other. For example, both planes, being mutually perpendicular, can be vertical But also in this case the assumption of orientation of heteronymic projections of points is higher than an axis remains fair.
The final type of all combined planes of projections is given in drawing. On this drawing of an axis of OX and OZ, lying in not the mobile plane V, are represented only once, and the axis of OY is shown. It is explained by that, rotating with the plane H, OY axis on an epyura with OZ axis, and rotating together with the plane W, the same axis is combined with OX axis.