研究了代数量的取值可正可负的原因，在此基础上把代数量分成了与矢量数乘有关的代数量、几何光学中的代数量以及表示状态的代数量三类，并用实例进行了说明；而把代数量等式分成了由同一类物理量的代数量关系式、由矢量式转化而来的代数量关系式以及由不同标量构成的代数量关系式三类，其中对由矢量式转化而来的代数量关系式，以牛顿定律的应用实例，通过多种不同解题过程进行了深入分析；对由不同标量构成的代数量关系式中各代数量正负号的约定方法进行了详细说明。%The algebraic quantities are divided into three types according to the reasons why they can be taken positive or negative values, namely algebraic quantities related to scalar products, algebraic quantities in geometrical optics and algebraic quantities expressing states. Moreover they are explained by actual examples. Then the algebraic expressions are also discussed from three aspects, i. e. algebraic expressions composed of a sort of physical quantities, algebraic expressions translated from vector expressions and algebraic expressions consisted of different scalar products. The second one is analyzed in depth by applying Newton’ s law in different processes. In the third one, the promissory method for various algebraic quantities is interpreted in detail.
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