The Teaching of Geometry in Schools: A Report Prepared for the Mathematical AssociationG. Bell and sons, Limited, 1923 - 74 σελίδες |
Άλλες εκδόσεις - Προβολή όλων
The Teaching of Geometry in Schools: A Report Prepared for the Mathematical ... Mathematical Association Προβολή αποσπασμάτων - 1946 |
The Teaching of Geometry in Schools: A Report Prepared for the Mathematical ... Mathematical Association Προβολή αποσπασμάτων - 1946 |
Συχνά εμφανιζόμενοι όροι και φράσεις
algebra angle properties angles equal argument assume assumption beginner bisector bisects centre chords circle Committee conic conic sections construction corresponding course cross-ratio deductive definite difficulty direction discussion easy riders elementary geometry enunciation equal angles Euclid Euclidean Euclidean geometry examiner example exterior angle external angles fact fixed sequence follows formal formal geometry fundamental theorems group of theorems half-line idea incommensurables interest intersect length limits line-pair locus logical mathematics measurement method motion obvious organisation parallel lines parallel-postulate parallelogram perpendicular plane figures plane geometry Playfair's Axiom position possible postulate of similarity principle of congruence principle of similarity proof properties of parallels proved pupil Pythagoras question ratios recognised rectangle reductio ad absurdum reference relation Report riders right angles rotation Section similar figures similar triangles solid geometry Stage straight lines superposition symmetry tangent teacher text-book theory of parallels tion transversal treatment trigonometrical
Δημοφιλή αποσπάσματα
Σελίδα 74 - If there be two straight lines, one of which is divided into any number of parts; the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Σελίδα 50 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Σελίδα 73 - That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles...
Σελίδα 74 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Σελίδα 74 - In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle.
Σελίδα 73 - PROPOSITION 4 // two triangles have the two sides equal to two sides respectively, and have the angles contained by the equal straight lines equal, they will also have the base equal to the base, the triangle will be equal to the triangle, and the remaining angles will be equal to the remaining angles respectively, namely those which the equal sides subtend.
Σελίδα 73 - In isosceles triangles, the angles at the base are equal to one another, and, if the equal straight lines be produced further, the angles under the base will be equal to one another.
Σελίδα 70 - From henceforth space in itself and time in itself sink to mere shadows, and only a kind of union of the two preserves an independent existence.
Σελίδα 74 - If an angle of a triangle be bisected and the straight line cutting the angle cut the base also, the segments of the base will have the same ratio as the remaining sides of the triangle ; and, if the segments of the base have the same ratio as the remaining sides of the triangle, the straight line joined from the vertex to the point of section will bisect the angle of the triangle.
Σελίδα 74 - A straight line falling on parallel straight lines makes the alternate angles equal to one another...