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Elements of Euclid [Selections from Book 1-6] Adapted to Modern Methods in ...
No preview available - 2015
ABCD AC and CB AC is equal altitude angle AOB BA and AC bisecting the angle centre chord circles touch circumference coincide Const conv decagon diagonal diameter divided draw equal angles equal to BC equal to twice equiangular equilateral triangle Euclid exterior angle geometrical given angle given circle given line given point given straight line greater half the perimeter hence hypotenuse inscribed isosceles triangle less Let ABC line drawn meet middle point multiple opposite sides parallel to BC parallelogram perpendicular polygon produced Proposition Q. E. D. Prop radius ratio rectangle contained rectilineal figure reflex angle regular polygon remaining angles required to prove right angles right-angled triangle schol segments shew shewn side BC square on AC tangent triangle ABC twice the rectangle twice the square World—shewing
Page 68 - 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.
Page 50 - If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram is double of the triangle.
Page 89 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section.
Page 30 - Any two sides of a triangle are together greater than the third side.
Page 208 - Tin; rectangle, contained by the diagonals of a quadrilateral inscribed in a circle, is equal to the sum of the rectangles contained by its opposite sides. Let ABCD be any quadrilateral inscribed in a circle...
Page 91 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.