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according angles are equal angles equal antecedent arcs Axioms base Book called centre chord circumference circumscribe common conjugate consequent construct corresponding Definitions denoted described diagonal difference distance divided equal altitude equal angles equal bases equal circles externally extremes follows formed former four GEOMETRY given angle given circle given point given ratio given straight line greater greater angle half Hence identically equal inscribe intercepts interior angles intersect kind less line joining locus magnitudes major mean meet middle point minor arcs multiple opposite pair parallel parallelogram passes perpendicular plane polygon position PROB produced proportional radii radius ratio ratio compounded ratios are equal rectangle contained regular respectively right angles Rule of Conversion sectors segments side opposite sides similar square stand straight line drawn subtended Superposition SYLLABUS taken tangent THEOR Theorem third touch triangle true unequal vertex whence whole
Side 14 - 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.
Side 14 - Of all the straight lines that can be drawn to a given straight line from a given point outside it, the perpendicular is the shortest.
Side 13 - Any two sides of a triangle are together greater than the third side.
Side 23 - Iff 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.
Side 13 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Side 34 - If the distance between the centres of two circles is equal to the difference of their radii, the two circles will touch each other internally.
Side 56 - If three straight lines be proportionals, the rectangle contained by the extremes is equal to the square on the mean ; and conversely, if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines are proportionals.
Side 28 - In the same circle, or in equal circles, equal arcs are subtended by equal chords : and conversely, equal chords subtend equal arcs.
Side 4 - The enunciation of a Theorem consists of two parts, — the hypothesis, or that which is assumed, and the conclusion, or that which is asserted to follow therefrom. Thus in the typical Theorem, If A is B, then C is D, (i), the hypothesis is that A is B, and the conclusion, that C is D.