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adjacent angles adjoining sides angles are equal angles equal angles opposite bisects Book called centre chord circle a regular circumference circumscribe conjugate angles construct a triangle contrapositive denoted diagonal distance divided internally equal altitude equal angles equal circles equimultiples given angle given point given ratio given rectilineal figure given straight line greater angle hypotenuse identically equal inscribe interior angles intersect less lines are proportional locus middle point minor arcs multiple obtuse angle opposite angles pair parallel straight lines parallelogram perpendicular PLANE GEOMETRY point of contact point of division polygon Prob quadrilateral radii radius ratio compounded ratios are equal rectangle contained right angles right-angled triangle Rule of Conversion SECTION sectors segments side opposite sides equal Similar rectilineal figures square straight angle straight line drawn straight line joining subtended Superposition SYLLABUS OF PLANE tangent Theor Theorem triangles are identically unequal vertex whence whole numbers
Page 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.
Page 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.
Page 13 - Any two sides of a triangle are together greater than the third side.
Page 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.
Page 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.
Page 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.
Page 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.
Page 28 - In the same circle, or in equal circles, equal arcs are subtended by equal chords : and conversely, equal chords subtend equal arcs.
Page 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.