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according adjacent alternate altitude angles are equal angles equal angles opposite antecedent application arcs Areas Axioms base Book called centre chord circle circumference common conjugate consequent construct contrapositive Crown 8vo Definitions demonstrated described difference distance divided drawing Edition equal angles externally extremes formed former four fourth GEOMETRY given angle given point given ratio given straight line greater greater angle Hence hypothesis identically equal inscribe intercepts interior angles kind less line joining locus logical magnitudes major mean meet multiple opposite opposite angles pair parallel parallelogram passing perpendicular PLANE GEOMETRY polygon position PROB PROBLEMS produced projection proportional Propositions quadrilateral radius ratio ratio compounded rectangle contained rectilineal figure regular right angles satisfying Schools Section segments side opposite sides similar square straight line drawn Superposition surface taken tangent THEOR Theorem third triangle true unequal vertex vertices whence whole
Page 6 - 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 48 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 11 - Assuming that the areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles...
Page 52 - JACKSON — GEOMETRICAL CONIC SECTIONS. An Elementary Treatise in which the Conic Sections are defined as the Plane Sections of a Cone, and treated by the Method of Projection. By J. STUART JACKSON, MA, late Fellow of Gonville and Caius College, Cambridge.
Page 18 - In a right.angled triangle, the square on the hypotenuse is equal to the sum of the squares on the sides containing the right angle . . . . 130 Applications of Pythagoras' theorem . . . . 132 THEOREM 6.
Page 7 - 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 52 - PUCKLE— AN ELEMENTARY TREATISE ON CONIC SECTIONS AND ALGEBRAIC GEOMETRY. With Numerous Examples and Hints for their Solution ; especially designed for the Use of Beginners. By GH PUCKLE, MA New Edition, revised and enlarged.
Page 8 - 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 17 - 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.