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ABCD AC is equal ADDITIONAL PROPOSITION angle ABC angle ACB angle BAC anharmonic arc ABC bisected centre of similitude chord circle ABC coincide Constr Construction Coroll cut the circle describe a circle diagonal diameter draw equal angles equal circles equiangular equimultiples Euclid EXERCISES exterior angle figure given circle given point given straight line given triangle greater harmonic range hypotenuse inscribed intersect isosceles triangle Let ABC meet middle points opposite sides pair parallel parallelogram pencil pentagon perpendicular polygon Proof Prop PROPOSITION 13 Ptolemy's Theorem quadrilateral radical axis radius ratio compounded rectangle contained required to prove respectively rhombus right angles shew sides BC Similarly square on AC straight line drawn straight line joining subtend tangent theorem triangle ABC triangle DEF triangles are equal twice the rectangle vertices Wherefore
Página 61 - Any two sides of a triangle are together greater than the third side.
Página 70 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Página 146 - 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...
Página 378 - To find a mean proportional between two given straight lines. Let AB, BC be the two given straight lines ; it is required to find a mean proportional between them. Place AB, BC in a straight line, and upon AC describe the semicircle ADC, and from the point B draw (9.
Página 137 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Página 78 - ... the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Página 307 - To inscribe, an equilateral and equiangular pentagon in a given circle. Let ABCDE be the given circle. It is required to inscribe an equilateral...
Página 426 - PROPOSITION 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle*.
Página 250 - If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other. Let the two straight lines AC, BD, within the circle ABCD, cut one another in the point E : the rectangle contained by AE, EC is equal to the rectangle contained by BE, ED.