Mathematics: Course of Study for Senior and Junior High Schools

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Department of Education, 1924 - Mathematics - 169 pages
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Page 109 - If from a point without a circle, a tangent and a secant are drawn, the tangent is the mean proportional between the whole secant and its external segment.
Page 104 - Plane demonstrative geometry. The principal purposes of the instruction in this subject are: To exercise further the spatial imagination of the student, to make him familiar with the great basal propositions and their applications, to develop understanding and appreciation of a deductive proof and the ability to use this method of reasoning where it is applicable, and to form habits of precise and succinct statement, of the logical organization of ideas, and of logical memory.
Page 110 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 109 - 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'.
Page 117 - The angle of two arcs of great circles is equal to the angle of their planes, and is measured by the arc of a great circle described from its vertex as a pole and included between its sides (produced if necessary). Let AB and AB...
Page 106 - Two triangles are equal if two sides and the included angle of the one are equal respectively to two sides and the included angle of the other (sas = sas). Hyp. In A ABC and A'B'C', AB = A'B', BC = B'C', and Z B = Z B'.
Page 117 - The area of a zone is equal to the product of its altitude by the circumference of a great circle.
Page 117 - The shortest line that can be drawn on the surface of a sphere between two points is the arc of a great circle, not greater than a semicircumference, joining the two points.
Page 109 - If a straight line is drawn through two sides of a triangle parallel to the third side, it divides these sides proportionally.
Page 116 - A point on the surface of a sphere, which is at the distance of a quadrant from each of two other points, not the extremities of. a diameter, is the pole of the great circle passing through these points.

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