Verwandte Artikel zu Lessons in logic
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Inhaltsangabe
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1870 Excerpt: ...of mineral for examination, may be able to separate completely the several chemical elements of which it is composed and ascertain their nature and comparative quantities; this is chemical analysis. In other cases the chemist mixes together carefully weighed quantities of certain simple substances and combines them into a new compound substance; this is chemical synthesis. Logical analysis and synthesis must not be confused with the physical actions, but they are nevertheless actions of mind of an analogous character. In logical synthesis we begin with the simplest possible notions or ideas, and combine them together. We have the best possible example in the elements of Geometry. In Euclid we begin with certain simple notions of points, straight lines, angles, right angles, circles, &c. Putting together three straight lines we make a triangle; joining to this the notion of a right-angle, we form the notion of a right-angled triangle. Joining four other equal lines at right angles to each other we gain the idea of a square, and if we then conceive such a square to be formed upon each of the sides of a right-angled triangle, and reason from the necessary qualities of these figures, we discover that the two squares upon the sides containing the right angle must together be exactly equal to the square upon the third side, as shewn in the 47th Proposition of Euclid's first book. This is a perfect instance of combining simple ideas into more complex ones. We have often, however, in Geometry to pursue the opposite course of Analysis. A complicated geometrical figure may be given to us, and we may have, in order to prove the properties which it possesses, to resolve it into its separate parts, and to consider the properties of those parts each distinct from the...
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Reseña del editor
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1870 Excerpt: ...of mineral for examination, may be able to separate completely the several chemical elements of which it is composed and ascertain their nature and comparative quantities; this is chemical analysis. In other cases the chemist mixes together carefully weighed quantities of certain simple substances and combines them into a new compound substance; this is chemical synthesis. Logical analysis and synthesis must not be confused with the physical actions, but they are nevertheless actions of mind of an analogous character. In logical synthesis we begin with the simplest possible notions or ideas, and combine them together. We have the best possible example in the elements of Geometry. In Euclid we begin with certain simple notions of points, straight lines, angles, right angles, circles, &c. Putting together three straight lines we make a triangle; joining to this the notion of a right-angle, we form the notion of a right-angled triangle. Joining four other equal lines at right angles to each other we gain the idea of a square, and if we then conceive such a square to be formed upon each of the sides of a right-angled triangle, and reason from the necessary qualities of these figures, we discover that the two squares upon the sides containing the right angle must together be exactly equal to the square upon the third side, as shewn in the 47th Proposition of Euclid's first book. This is a perfect instance of combining simple ideas into more complex ones. We have often, however, in Geometry to pursue the opposite course of Analysis. A complicated geometrical figure may be given to us, and we may have, in order to prove the properties which it possesses, to resolve it into its separate parts, and to consider the properties of those parts each distinct from the...
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