Euclid's Elements of Geometry

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Bell and Daldy, 1872 - 261 pagina's
 

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Pagina 18 - If two triangles have two sides of the one equal to two sides of the...
Pagina 28 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Pagina 207 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Pagina 216 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Pagina 127 - In any proportion, the product of the means is equal to the product of the extremes.
Pagina 161 - Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order.
Pagina 112 - To reduce fractions of different denominators to equivalent fractions having a common denominator. RULE.! Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Pagina 213 - ... are to one another in the duplicate ratio of their homologous sides.
Pagina 163 - Convertendo ; when it is .concluded, that if there be four magnitudes proportional, the first is to the sum or difference of the first and second, as the third is to the sum or difference of the third and fourth.
Pagina 88 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.

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