Elementary Plane Geometry: Inductive and Deductive

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Ginn, 1903 - Geometry - 144 pages

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Page 68 - In any right-angled triangle, the square which is described on the side subtending the right angle is equal to the sum of the squares described on the sides which contain the right angle.
Page 95 - When it is affirmed (for instance) that " if two straight lines in a circle intersect each other, the rectangle contained by the segments of the one is equal to the rectangle contained by the segments of the other...
Page 42 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 40 - Thus when it is said that the sum of the three angles of any triangle is equal to two right angles, this is a theorem, the truth of which is demonstrated by Geometry.
Page 91 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Page 17 - Euclid's, and show by construction that its truth was known to us ; to demonstrate, for example, that the angles at the base of an isosceles triangle are equal...
Page 18 - If two angles of a triangle are equal, the sides opposite to these angles are equal 21 ^THEOREM 14.
Page 86 - The angle at the centre of a circle is double the angle at the circumference on the same arc.
Page 88 - The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles, with converse.
Page 96 - BC, contained by the whole of the cutting line, and the part of it without the circle, is equal to the square of BD which meets it ; therefore the straight line BD touches the circle ACD : (in.

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