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ABCD base bisected bisectors Book called centre chord circumference circumscribed common Constr Construction DEFINITION describe diagonal diameter difference divided draw drawn equal equilateral Euclid EXAMPLES EXERCISES external extremities figure fixed formed four given circle given point given straight line greater half Hence inches inscribed intersect Join length less Let ABC magnitudes meet middle point NOTE opposite sides parallel parallelogram pass perp perpendicular plane polygon PROBLEM produced Proof proportional PROPOSITION prove quadrilateral radius ratio rect rectangle contained regular remaining respectively right angles segment shew shewn sides similar Similarly square straight line drawn tangent THEOREM third touch triangle ABC twice vertex vertical angle whole
Seite 353 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Seite 65 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Seite 162 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Seite 326 - From this it is manifest that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the...
Seite 162 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square...
Seite 291 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Seite 79 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Seite 18 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Seite 242 - We may here notice that the perpendiculars from the vertices of a triangle to the opposite sides are concurrent ; their meet is called the orthocentre, and the triangle obtained by joining the feet of the perpendiculars is called the pedal triangle.