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according analogy analysis appear applied argument Aristotle Aristotle's attempt attention axioms body called causes circumstances common compared concerning conclusions consequence consideration considered contains definitions demonstration discovery distinction doctrine doubt effect employed equal essential evidence examination example existence experience expressed fact faculties figure former geometry given human idea illustration important individual induction inference instance judgment knowledge language laws lead learned less light logic manner mathematical means method mind moral nature necessary Note notions object observation occasion opinion original particular passage phenomena philosophical physical possible precision present principles probable proof proposition question readers reasoning refer Reid relation remark respect rest result rules says seems sense speculations step sufficient supposed syllogism theory thing thought tion true truth understanding universe various whole writers
Seite 132 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Seite 61 - For if we will reflect on our own ways of thinking, we shall find, that sometimes the mind perceives the agreement or disagreement of two ideas immediately by themselves, without the intervention of any other : and this I think we may call intuitive knowledge.
Seite 113 - I shall only appeal to the thirty- seventh proposition of the first book, in which it is proved that triangles on the same base, and between the same parallels, are equal...
Seite 70 - I demonstrated the proposition of the abstract idea of a triangle. [And here it must be acknowledged that a man may consider a figure merely as triangular, without attending to the particular qualities of the angles, or relations of the sides. So far he may abstract; but this will never prove that he can frame an abstract, general, inconsistent idea of a triangle.
Seite 156 - He had another particularity, of which none of his friends ever ventured to ask an explanation. It appeared to me some superstitious habit which he had contracted early, and from which he had never called upon his reason to disentangle him. This was his anxious care to go out or in at a door or passage, by a certain number of steps from a certain point, or at least so...
Seite 331 - You would perceive, by trie sample I have given you, that I make Cleanthes the hero of the dialogue. Whatever you can think of to strengthen that side of the argument, will be most acceptable to me.
Seite 5 - Tis with our judgments as our watches, none Go just alike, yet each believes his own.
Seite 237 - As in mathematics, so in natural philosophy, the investigation of difficult things by the method of analysis, ought ever to precede the method of composition. This analysis consists in making experiments and observations, and in drawing general conclusions from them by induction, and admitting of no objections against the conclusions, but such as are taken from experiments, or other certain truths.