A Text-book of Geometry
Ginn, 1889 - Geometry, Analytic - 242 pages
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ABCD acute altitude Apply base bisector bisects called centre chord circle circumference circumscribed coincide common construct contained describe diagonal diameter difference distance divide draw drawn equal equidistant equivalent extremities fall feet figure Find formed four given circle given line given point given straight line greater Hence homologous sides hypotenuse inches included increased indefinitely inscribed intercept intersecting isosceles joining legs length less limit mean measured meet middle point parallel parallelogram passes perimeter perpendicular polygon PROBLEM Proof proportional PROPOSITION prove prove Proof quantities radii radius ratio rectangle regular polygon respectively right angle right triangle secant segments shortest sides similar similar polygons square straight line Suppose tangent THEOREM touch triangle triangle ABC unit vertex vertices
Page 62 - The line which joins the middle points of two sides of a triangle is parallel to the third side, and is equal to half the third side.
Page 185 - Two triangles having 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.
Page 146 - If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar. In the triangles ABC and A'B'C', let ZA = Z A', and let AB : A'B' = AC : A'C'. To prove that the A ABC and A'B'C' are similar. In this case we prove the A similar by proving them mutually equiangular. Proof. Place the A A'B'C...
Page 132 - 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 130 - 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 159 - 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 154 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Page 211 - 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 44 - If two triangles have two sides of one equal, respectively, to two sides of the other, but the included angle of the first greater than the included angle of the second, the third side of the first is greater than the third side of the second...
Page 189 - ... 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.