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一类比所谓类比,就是已知两个(类)事物具有某些共同的性质,从而推断它们在其它性质上也有可能相同的一种推理形式(我们称这两个事物互为“类比对象”),可见,类比推理实际上是一种猜测。自然,这种猜测有时是正确的,有时可能是错误的。要确认其正确,还必须经过严格的逻辑论证(事实上,数学中的某些定理、公式、法测往住运用类比推理提出问题,而后经过严密论证才被确立下来)。在论证时又往往借鉴在证明其类比对象的类似性质时所显示的方法。例1 平面几何中的射影定理表现为:“△ABC
One kind of analogy than the so-called analogy is the fact that two (class) things are known to have certain common properties, inferring that they are also likely to have the same reasoning form in other qualities (we call these two things “analogous objects” each other). As you can see, analogical reasoning is actually a kind of guess. Naturally, this kind of speculation is sometimes correct and sometimes it may be wrong. To confirm its correctness, we must go through rigorous logical arguments (in fact, some theorems, formulas, and methods in mathematics apply questions to analogical reasoning to ask questions, and then they are established after strict arguments). In the argumentation, it often borrows from the methods shown when proving the similar properties of its analogous objects. Example 1 The projective theorem in planar geometry reads: "△ABC