Final Report of the National Committee of Fifteen on Geometry Syllabus1912 - Geometry - 88 pages |
Other editions - View all
Common terms and phrases
algebra altitude angles are equal applications arithmetic axioms base bisect circle committee feels congruent construction Corollary course in geometry D'Alembert definition DeMorgan distances drawn edition of Euclid Education elementary geometry elementary mathematics emphasis England etry Euclid exercises fifth book figures Find the locus Florian Cajori formal proof frustum geom Geometrical Teaching given line given line-segment given point grades half the product high school incommensurables informal proof inscribed intersection introduced Klein Legendre lists of theorems loci locus of points logical measured method method of exhaustion National Education Association parallel lines parallelepiped perimeter plane geometry points equidistant postulate practical prism problems propositions pupil radius recommended reductio ad absurdum regular polygon right angle right triangle Schotten segments sides similar solid geometry sphere spherical square statements straight line student study of geometry syllabus tangent teacher teaching of geometry text-book tions triangle ABC trigonometry volume
Popular passages
Page 71 - Any side of a triangle is less than the sum of the other two sides...
Page 76 - 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 29 - Any proof of a Proposition will be accepted which appears to the Examiners to form part of a systematic treatment of the subject...
Page 72 - C' [A2.] (3) a = a' b = bc = c' [A3.] (4) a = a' c = c' C = C'=90° [A4.] (State these in detail and in English. See preface, article 7.) 2. A triangle is determined when the following are given: (1) a, b, C; (2) a, B, C; (3) a, b, c; (4) a, c, C = 90°.
Page 74 - 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 84 - 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 24 - To the credit of teachers be it said, that the fifth book was quite generally omitted. But DeMorgan's activity, in this line did not end here. In 1836 he published The Connexion of Number and Magnitude, An attempt to explain the fifth book of Euclid. For fifty years this tract was not duly appreciated ; later it began to wield a wide influence ; it is on this tract that the substitute for the fifth book given in the Syllabus of the Association for the Improvement of Geometrical Teaching is modeled...
Page 33 - If unequals are added to unequals in the same order, the sums are unequal in the same order; if unequals are subtracted from equals the remainders are unequal in the reverse order.
Page 66 - 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 78 - Pythagorean theorem states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.