First Lessons in Geometry: Upon the Model of Colburn's First Lessons in Arithmetic

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J. Munroe & Company, 1847 - Geometry - 164 pages
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Page 16 - He had demonstrated, unaided by any book or teacher, the proposition, that the sum of the angles of a plane triangle is equal to two right angles.
Page 125 - Most good practical workmen have several means for getting the cut of the mitre, and to them this demonstration will appear unnecessary, but I have seen many men make sad blunders, for want of knowing this simple rule. PROBLEM 12.
Page 22 - A CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 21 - ... that the angle inscribed in a semicircle is a right angle, and to have testified his joy by a sacrifice to the Muses!
Page 156 - Side subtending the Obtuse Angle, is Greater than the Sum of the Squares of the other two Sides, by Twice the Rectangle of the Base and the Distance of the Perpendicular from the Obtuse Angle.
Page 77 - A polygon of three sides is a triangle ; of four, a quadrilateral; of five, a pentagon ; of six, a hexagon ; of seven, a heptagon; of eight, an octagon; of nine, a nonagon; of ten, a decagon; of twelve, a dodecagon.
Page 4 - Theory soon descends to guide and assist the operations of practice. To the geometrical speculations of the Greeks, we may distinctly trace whatever progress the moderns have been enabled to achieve in mechanics, navigation, and the various complicated arts of life. A refined analysis has unfolded the harmony of the celestial motions, and conducted the philosopher, through a maze of intricate phenomena, to the great laws appointed for the government of the Universe.
Page 23 - Of four-sided figures, a square is that which has all its sides equal, and all its angles right angles.
Page 24 - If the product of two quantities be equal to the product of two others, two of them may be made the extremes and the other two the means of a proportion.
Page 99 - Lines drawn from a point within a triangle to the extremities of the base include an angle greater than the vertical angle of the triangle, (v.

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