Theoretical Geometry: Based on the Various Geometry Books by Godfrey and SiddonsThe University Press, 1926 - 173 σελίδες |
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Σελίδα x
... 54 • COR . 3. The locus of the vertices of equivalent triangles on the same base and on the same side of it is an unlimited straight line parallel to the base 54 THEOREM 28. If a triangle and a parallelogram stand on X CONTENTS.
... 54 • COR . 3. The locus of the vertices of equivalent triangles on the same base and on the same side of it is an unlimited straight line parallel to the base 54 THEOREM 28. If a triangle and a parallelogram stand on X CONTENTS.
Σελίδα xiii
... vertices of triangles with equal vertical angles standing on the same side of a common base is an arc of a circle • THEOREM 47. The opposite angles of any ... vertex 95 96 96 PAGE THEOREM 51. If a straight line touch a circle CONTENTS xiii.
... vertices of triangles with equal vertical angles standing on the same side of a common base is an arc of a circle • THEOREM 47. The opposite angles of any ... vertex 95 96 96 PAGE THEOREM 51. If a straight line touch a circle CONTENTS xiii.
Σελίδα 14
... vertices = n × 2 rt . ≤ s , .. the interior angles ( 2n - 4 ) rt . s . ] = 4 Some writers and schedules give the corollary the greater promi- nence ; but for actual use the theorem is much the more useful . The corollary may be proved ...
... vertices = n × 2 rt . ≤ s , .. the interior angles ( 2n - 4 ) rt . s . ] = 4 Some writers and schedules give the corollary the greater promi- nence ; but for actual use the theorem is much the more useful . The corollary may be proved ...
Σελίδα 15
... vertices A , B , C .... Proof There are n triangles AOB , BOC , COD .... Fig . 11 . The sum of the angles of each triangle is 2 rt . △ s . B .. The sum of all the angles in the n triangles is 2n rt . △ s . But all the angles of the ...
... vertices A , B , C .... Proof There are n triangles AOB , BOC , COD .... Fig . 11 . The sum of the angles of each triangle is 2 rt . △ s . B .. The sum of all the angles in the n triangles is 2n rt . △ s . But all the angles of the ...
Σελίδα 16
... vertex to the two opposite vertices . - Ex . 20. Prove that the sum of the angles of a polygon of n sides is ( 2n − 4 ) right angles by joining one vertex to each of the other vertices . Ex . 21. BE and CF are the perpendiculars from B ...
... vertex to the two opposite vertices . - Ex . 20. Prove that the sum of the angles of a polygon of n sides is ( 2n − 4 ) right angles by joining one vertex to each of the other vertices . Ex . 21. BE and CF are the perpendiculars from B ...
Συχνά εμφανιζόμενοι όροι και φράσεις
AABC altitude base BC chord circle centre circle whose centre circles intersect circles touch circumcircle circumference common tangent concyclic concyclic points congruent Constr cut BC cyclic quadrilateral Data ABC diameter divided drawn parallel equal circles equiangular equidistant equilateral triangle equivalent triangles Euclid figure fixed point given circle given point given straight line given triangle hypotenuse internal bisector isosceles trapezium isosceles triangle LAOB LAPB length line drawn opposite sides parallel to BC parallelogram parallelogram ABCD perpendicular bisector Playfair's Axiom polygon produced to meet prove that Construction Pythagoras Q. E. D. COR quadrilateral ABCD radii of equal radius ratio rectangle contained rhombus right angles right-angled triangle segment Show side BC square subtends tangent tetrahedron THEOREM touch externally trapezium triangle ABC vertex
Δημοφιλή αποσπάσματα
Σελίδα 20 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Σελίδα 46 - 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.
Σελίδα 29 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα vii - When a straight line cuts two other straight lines, if (i) a pair of alternate angles are equal, or (ii) a pair of corresponding angles are equal, or (iii) a pair of interior angles on the same side of the cutting line are together equal to two right angles, then the two straight lines are parallel ; and the converse.
Σελίδα 62 - If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the two parts.
Σελίδα 76 - A straight line, drawn from the centre of a circle to bisect a chord which is not a diameter, is at right angles to the chord ; conversely, the perpendicular to a chord from the centre bisects the chord. There is one circle, and one only, which passes through three given points not in a straight line. In equal circles (or, in the same circle) (i) if two...
Σελίδα xiv - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Σελίδα 70 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Σελίδα 59 - In a right-angled triangle the square on the side subtending the right angle is equal to the sum of the squares on the sides containing the right angle.
Σελίδα 92 - Angles in the same segment of a circle are equal; and. if the line joining two points subtends equal angles at two other points on the same side of it, the four points lie on a circle.