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according altitude angles are equal angles equal antecedent arcs base bisects Book called centre chord circumference circumscribe common conjugate consequent construct corresponding Definitions denoted describe diameter difference distance divided draw equal angles equal circles externally extremes formed former four GEOMETRY given angle given circle given point given ratio given straight line greater angle Hence identically equal inscribed intercepts interior angles internally intersection kind less Limits Loci locus magnitudes major mean meet minor arcs multiple opposite opposite angles pair parallel parallelogram passes perpendicular point of contact polygon position PROB produced proof proportional proposition quadrilateral radii radius ratio compounded ratios are equal rectangle contained rectilineal figure regular respectively right angles Rule of Conversion sectors segment sides similar square stand straight line drawn subtended Superposition SYLLABUS taken tangent THEOR Theorem third touch triangle true unequal vertex whence whole wholly
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.