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这本球面三角学有它一定的优点:例如,介紹了球面三角学与平面三角学之間的联系,使讀者能体会球面三角公式与平面三角公式的內在关系;但也有它一定的缺点,这可能是翻譯上的毛病,也可能有些地方是排版上的錯誤。我僅就1953年10月初版、1955年1月3版的譯本提出以下几点意見。如有不当之处,請讀者多加批評与指導! (一) 兩球面三角形的圣等(或相等)与对称是有区別的(前者可以疊合,后者不能疊合),不应該混为一談。固然有些書上把兩三角形的对称叫做对称相等,而把全等叫做絕对相等,但在提法上也应該区分开。譯本在給对称三角形下定义的时候,也很明确地把对称三角形与全等三角形划清了界限;但在定理証明的过程中便忽視了这一点。例如23頁有这样
This spherical trigonometry has its advantages: for example, it describes the connection between spherical trigonometry and plane trigonometry, enabling readers to understand the inner relationship between spherical trigonometric formulas and planar trigonometric formulas; but it also has its own disadvantages. It may be a translation error, or it may be a typographical error in some places. I only made the following points on the translation of the first edition in October 1953 and the third edition in January 1955. If there are any mistakes, please ask the readers to provide more criticism and guidance! (A) There are differences between the holy (or equal) and the symmetry of the two spherical triangles (the former can be superimposed, the latter cannot be superimposed), and should not be mixed Talk about it. Although some books call the symmetry of the two triangles equal to equal symmetry, and equal equivalences are absolutely equal, they should also be distinguished in reference. When a translation is defined under a symmetric triangle, it is also clear that the symmetric triangle and the congruent triangle are delimited; however, this is ignored in the proof of the theorem. For example, there is such a 23 page