Final Report of the National Committee of Fifteen on Geometry Syllabus: July, 1912University of Chicago Press, 1912 - 54 pages |
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Common terms and phrases
algebraic statement altitude angles are equal applications axioms base bisect black-face type center of arc circumference circumscribed committee feels concrete setting congruent connection construction convex polygons Corollary course in geometry definition desirable discussion distance drawn elementary geometry emphasis exercises figures Find the locus FLORIAN CAJORI formal proof formula frustum geometric forms given line given line-segment given point High School hypotenuse importance informal proof inscribed interest intersection involved large number lateral area lines are parallel lists of theorems loci locus of points logical measured notation one-half the product parallel planes parallelogram parallelopiped perimeter perpendicular bisector plane geometry points equidistant postulate present principle prism proportional propositions radii radius regular polygon right angle right triangle roman type Section segments sides similar triangles slant height solid geometry sphere square straight angle straight line student suggested syllabus symbols tangent teacher teaching of geometry Thru a given thruout tions triangle ABC trigonometric ratios
Popular passages
Page 34 - Any side of a triangle is less than the sum of the other two and greater than their difference.
Page 38 - The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. 144. Theorem. The bisector of an exterior angle of a triangle divides the opposite side produced into segments proportional to the other two sides.
Page 36 - The perpendicular bisectors of the sides of a triangle meet in a point. 12. The bisectors of the angles of a triangle meet in a point. 13. The tangents to a circle from an external point are equal. 14...
Page 27 - Contrary to the usual conception, the locus idea is one that may very easily be made concrete and brought down to the comprehension of young pupils. For example, the opening of a book or of a door suggests a variety of loci. The same may be said of many concrete illustrations easily accessible to the pupil. In this way, loci problems may and should be introduced at certain stages of the subject. For example, in Book I : The locus of a point equidistant from two fixed points, equidistant from two...
Page 44 - An oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Hyp. OM is a right section of oblique prism AD', and OM ' a right prism whose altitude is equal to a lateral edge of AD'. To prove AD' =0= GM' . Proof. The lateral edges of GM
Page 4 - There is also the assumption that if unequals are added to unequals in the same order the sums are unequal in the same order, and that if unequals are subtracted from equals the remainders are unequal in the reverse order, these being the only ones relating to inequalities that are needed in elementary geometry. As to substitutions. In geometry it is continually necessary to make use of the assumption that a quantity may be substituted for its equal in an equation or in an inequality. Often this...
Page 41 - If a straight line is parallel to a plane, the intersection of the plane with any plane drawn through the line is parallel to the line.
Page 30 - In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector.
Page 39 - The sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse; a2 + b2 = c2.
Page 13 - Portraits of famous mathematicians may be recommended for the schoolroom. POINTS RELATING TO SOLID GEOMETRY. (a) Axioms and Postulates. The list of axioms already given need not be increased, but the following postulates may be added : (1) One plane and only one can be passed through two intersecting straight lines. Corollary. A plane is determined...