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ABCD acute Adding adjacent altitude base bisect BOOK called centre chord circle circumference circumscribed coincide common construct contained demonstration denote describe diagonals diameter difference distance divided draw drawn equal equilateral triangle equivalent expressed exterior angle extremities figure Find four geometry given given line given point Given.—Let greater half Hence hexagon hypotenuse inches included inscribed intersect isosceles triangle length less limit mean measure meet method middle points number of sides one-half parallel parallelogram pass perimeter perpendicular plane polygon problem proportional PROPOSITION prove Prove.—Then quadrilateral quantities radii radius ratio rectangle regular polygon respectively right angles right triangle segments sides similar square straight line suppose surface tangent theorem third triangle triangle ABC truth unit vertex vertices Whence
Side 112 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Side 60 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Side 57 - In an isosceles triangle the angles opposite the equal sides are equal.
Side 28 - AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.
Side 48 - If two parallel lines are cut by a transversal, the sum of the two interior angles on the same side of the transversal is two right angles.
Side 53 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Side 183 - If from a point without a circle a secant and a tangent are drawn, the tangent is the mean proportional between the whole secant and its external segment.
Side 156 - From this proposition it is evident, that the square described on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines.