对相交二直线夹角投影的研究

Research on Projection of Angle Formed by Two Intersecting Lines in Space

在空间相交二直线成锐角或钝角,且均不平行于某一投影面的条件下,本文找到一种作图方法,确定该二直线对投影面的倾角,使得该二直线的夹角在该投影面上的投影仍能反映实形,而且解答是无限多的.用同样的作图方法可以找到空间一个>0°、<180°的指定的任意角的两个边对投影面的合适倾角,使得其投影成为一个包括0°和180°在内的被指定的任意角,解答也是无限多的.本文讨论了空间相交二直线的夹角及该二直线各自对投影面的倾角和该夹角的投影之间的数量关系,推出了几个计算公式.

If the angle between two intersecting lines in space is an acute angle or an obtuse angle, and the two lines are both oblique to the projection plane, a method of draughting has been found to determine the angles between the projection plane and the two lines so that the projection of the angle on that projection plane is equal to the angle itself. The results are limitless. By the same method, we can determine the angles with projection plane of the two sides of a given arbitrary angle in space, which is 〉0°and 〈180°, so that its projection can be a designated arbitrary angle, including 0° and 180°. And the results are also limitless. The third part of the article deals with calculations. Several formulas are established.