A Text-book of Geometry

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Ginn, 1888 - Geometry - 386 pages
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Page 42 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 142 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Page 128 - If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.
Page 126 - If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.
Page 209 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 155 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Page 150 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Page 185 - ... upon the sum of two straight lines is equivalent to the sum of the squares described on the two lines plus twice their rectangle. Note. By the "rectangle of two lines" is here meant the rectangle of which the two lines are the adjacent sides.
Page 134 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Page 13 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3.

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