The Geometrical Companion: In which the Elements of Abstract Geometry are Familiarised, Illustrated, and Rendered Practically Useful

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John Taylor, 1828 - Geometry - 169 pages
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Page 13 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Page 106 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Page 67 - In any right-angled triangle, the square which is described on the side subtending the right angle is equal to the squares described on the sides which contain the right angle.
Page 66 - If two triangles have two angles of the one equal respectively to two angles of the other, the third angles are equal.
Page 160 - If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle.
Page 87 - A rectilineal figure is said to be described about a circle, when each side of the circumscribed figure touches the circumference of the circle. 5. In like manner, a circle is said to be inscribed...
Page 23 - When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of these angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Page 129 - FGL have an angle in one equal to an angle in the other, and their...
Page 120 - There are two Causes of Beauty, natural and customary. Natural is from Geometry, consisting in Uniformity (that is Equality) and Proportion. Customary Beauty is begotten by the Use of our Senses to those Objects which are usually pleasing to us for other Causes, as Familiarity or particular Inclination breeds a Love to Things not in themselves lovely. Here lies the great Occasion of Errors; here is tried the Architect's Judgment: but always the true Test is natural or geometrical Beauty.
Page 120 - Beauty is a harmony of objects, begetting pleasure by the eye. There are two causes of beauty, natural and customary. Natural is from GEOMETRY, consisting in uniformity (that is, equality) and proportion. Customary beauty is begotten by the use of our senses...

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