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absurd AC and CB AC by Prop AC is equal angle ABC angle ACD angle BAC angle equal angles by Prop arch bisected centre circumference co-efficient common Const construct contained oftener divided divisor double equal angles equal by Ax equal by Constr equal by Hypoth equal by Prop equal to AC equal to twice equation equi-multiples equi-submultiples equiangular equilateral external angle fore fraction given angle given circle given line given right line greater half a right less multiplying opposite parallel parallelogram perpendicular produced PROPOSITION quotient ratio rectangle under AC remaining angles remaining side right angles right line AB right line AC Schol segment side AC similar similarly demonstrated squares of AC submultiple subtract term THEOREM tiple touches the circle triangle BAC twice the rectangle twice the square
Side 20 - If two triangles have two sides of the one equal to two sides of the...
Side 209 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Side 218 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 114 - To reduce fractions of different denominators to equivalent fractions having a common denominator. RULE.! Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Side 90 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Side 129 - In any proportion, the product of the means is equal to the product of the extremes.
Side 163 - Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order.
Side 215 - ... are to one another in the duplicate ratio of their homologous sides.