A Text-book of Geometry |
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ABCD AC² acute angle adjacent angles altitude angles are equal base bisector bisects called centre chord circumference circumscribed coincide decagon diagonals diameter divide draw equal respectively equiangular equiangular polygon equidistant equilateral triangle exterior angle feet figure Find the area given circle given line given point given straight line given triangle greater Hence homologous sides hypotenuse inches intersecting isosceles trapezoid isosceles triangle legs length line drawn line joining middle points number of sides obtuse opposite sides parallel parallelogram perimeter perpendicular PROBLEM prove Proof Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radii ratio rectangle regular inscribed regular polygon rhombus right angle right triangle SCHOLIUM secant segments similar polygons square equivalent straight angle subtended tangent THEOREM third side trapezoid triangle ABC triangle is equal vertex vertices
Popular passages
Page 64 - 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 187 - 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 148 - 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 134 - 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 132 - 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 161 - 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 156 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Page 213 - 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 46 - 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 191 - ... 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.