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Syllabus of Plane' Geometry: (corresponding to Euclid, Book I-VI) : Prepared ...
Cora Lenore Williams
Uten tilgangsbegrensning - 1905
according adjacent angles adjacent sides alternate angles angles are equal angles equal angles formed antecedent arcs assumption Book called chord circumfer circumference circumscribed common complete consequent determined diagonal diameter difference distance divides ence equal angles equal arcs equal bases equal circles equal respectively equal sides exterior external extremities ference figures follow four geometry given point given straight line greater angle half inter intercepts interior angles intersection kind less lies line joining magnitude meet middle point minor multiples negative opposite sides pair parallel parallelogram pass perpendicular plane polygon positive possible postulate produced Prop proportional quadrilateral radius ratio ratio are equal reciprocal rectangle relation right angle right-angled triangle sectors segment sense sides equal similar space squares stand straight angle straight line drawn subtended supplemental surface tangent Theor theorems third side tion touch transversal triangle is equal turning twice unequal vertex vertices
Side 26 - 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 27 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Hyp. In A ABC and A'B'C' AB = A'B'; AC = A'C'; ZA>ZA'.
Side 15 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Side 41 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Side 26 - ... less than the sum of the other two sides of the triangle.
Side 36 - Equal triangles, on equal bases, in the same straight line, and on the same side of it, are between the same parallels.
Side 23 - MAGNITUDES which have the same ratio to the same magnitude are equal to one another ; and those to which the same magnitude has the same ratio are equal to one another.
Side 35 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Side 33 - Any exterior angle of a triangle is equal to the sum of the two opposite interior angles.