Rider Papers on Euclid: Books i and Ii, Graduated and Arranged in Order of Difficulty; with an Introduction on Teaching Euclid

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Macmillan and Company, 1891 - 79 pagina's
 

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Pagina 63 - PROP. VIII. THEOR. If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Pagina 23 - 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.
Pagina 59 - Any two sides of a triangle are together greater than the third side.
Pagina 60 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Pagina 63 - 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 on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Pagina 58 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Pagina 62 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Pagina 62 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.

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