印度古因明到新因明实现了类比推理向演绎推理的飞跃；

The coming of new Indian Hetuvidya realized its logical leap from inductive reasoning to deductive reasoning.

严粲还善于运用归纳总结、类比推理和联系上下文的方法来解释词语。

Yan Can was also good at using the summarized, analogical reasoning and communication methods to explain the context of words.

论述了合情推理的两种常用方法：归纳推理和类比推理在大学数学中的应用。

The main research of this text matches two in common use methods that plausibie reasonings:apply generalize reasonings and analogy reasoning to the college mathematics.