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according analogy analysis appear applied argument Aristotle attempt attention axioms bodies called causes chap circumstances common concerning conclusions consequence consideration considered definition demonstration discovery distinction doctrine effect Elements employed equal essential evidence examination example existence experience expressed fact faculties former geometry give given human idea illustration important individual induction inference inquiries instance intellectual judgment knowledge known language latter laws learned less light logical 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 reference Reid relation remark respect rest result rules says seems sense speculations step sufficient supposed theorem theory things thought tion true truth understanding universe various whole writers
Página 73 - 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.
Página 125 - In like manner, when it is said, that " triangles on the same base, and between the same parallels, are equal...
Página 82 - 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.
Página 8 - One in their nature, which are two in ours ! And Reason raise o'er Instinct as you can, In this 'tis God directs, in that 'tis man.
Página 146 - 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...
Página 132 - In sum, in what matter soever there is place for addition and subtraction, there also is place for reason; and where these have no place, there reason has nothing at all to do.
Página 15 - Tis with our judgments as our watches, none Go just alike, yet each believes his own.
Página 273 - 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.
Página 67 - The same degree of understanding (he afterwards observes) which makes a man capable of acting with common prudence in life, makes him capable of discerning what is true and what is false, in matters that are selfevident, and which he distinctly apprehends.