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. 1835 Excerpt: ...before another thing can be demonstrated. A proposition is that which proposes something to be done or demonstrated; it is a problem when it proposes any thing to be done, as to divide a given line into two equal parts, or to raise a perpendicular, &c.; and a theorem when it proposes something to be shown, as that ...
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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. 1835 Excerpt: ...before another thing can be demonstrated. A proposition is that which proposes something to be done or demonstrated; it is a problem when it proposes any thing to be done, as to divide a given line into two equal parts, or to raise a perpendicular, &c.; and a theorem when it proposes something to be shown, as that triangles of the same base and altitude are equal to each other, or that all the angles in the same segment of an arch are equal, &c. GEOMETRY, History of. The origin of geometry is ascribed by Herodotus to the Egyptians, who, in consequence of the inundations of the Nile, which carried away all their landmarks, were under the necessity of distinguishing and laying out their lands by the consideration of their figure and quantity, whence the word geometry in the Greek signifies literally landmeasuring. The Greeks, who cultivated this science more than any other people, doubtless learned the rudiments from the Egyptians; for Thales, who travelled into Egypt and acquired a sufficient knowledge of astronomy to calculate, must also have first become aixiuaintod with the principles of geometry to assist him in his asu-nomical inquiries. Pythagoras, the pupil and friend of Thales, distinguished himself by his discoveries in arithmetic, as well as geometry. He invented the multiplication table, called after him the Abacus Pythagoricus, and in geometry he discovered the thirty-second and forty-seventh propositions in the first book of Euclid's Elements. Soon after this flourished Anaximander, Anaximenes, Anaxagoras, Cleostratus, iEnopides, and Zenodorus, all celebrated geometricians, of whose works nothing remains except of the last. They were succeeded by Hipparchus, who rendered himself celebrated by the quadrature of the lines called after...
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