Theoretical Geometry: Based on the Various Geometry Books by Godfrey and SiddonsThe University Press, 1926 - 173 σελίδες |
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Σελίδα xiii
... externally or internally , the distance between their centres is equal respectively to the sum or difference of their radii . CONSTRUCTIONS . Circumscribed and inscribed circles Circumscribed and inscribed polygons Escribed circle · 38 ...
... externally or internally , the distance between their centres is equal respectively to the sum or difference of their radii . CONSTRUCTIONS . Circumscribed and inscribed circles Circumscribed and inscribed polygons Escribed circle · 38 ...
Σελίδα xv
... externally in the ratio of the sides containing the angle THEOREM 59 ( i ) . If two chords of a circle intersect inside the circle , the rectangle contained by the segments of one is equal to the rectangle contained by the segments of ...
... externally in the ratio of the sides containing the angle THEOREM 59 ( i ) . If two chords of a circle intersect inside the circle , the rectangle contained by the segments of one is equal to the rectangle contained by the segments of ...
Σελίδα 83
... externally ( fig . 82 ) . Data The Os CMN , CPQ touch externally at C ; X and Y the centres . To prove XY passes through C. that Construction Draw ACB the common tangent at C. Join CX , CY . Proof [ CX , CY are not to be assumed to be ...
... externally ( fig . 82 ) . Data The Os CMN , CPQ touch externally at C ; X and Y the centres . To prove XY passes through C. that Construction Draw ACB the common tangent at C. Join CX , CY . Proof [ CX , CY are not to be assumed to be ...
Σελίδα 89
... externally at D , and touches AB , AC produced at F , E respectively ; O is the centre of the circle . 2 Prove that / BOC = 1⁄2 △ FOE = 90 ° · - Α 2 Ex . 46. The circle inscribed in a triangle ABC touches BC at X , CA at Y , AB at Z ...
... externally at D , and touches AB , AC produced at F , E respectively ; O is the centre of the circle . 2 Prove that / BOC = 1⁄2 △ FOE = 90 ° · - Α 2 Ex . 46. The circle inscribed in a triangle ABC touches BC at X , CA at Y , AB at Z ...
Σελίδα 90
... externally each of two fixed circles ( centres A , B ) . Prove that the difference of AO , BO remains constant . Ex ... externally at A and are touched at P , Q by a line PQ , then PQ subtends a right angle at A. Also PQ is bisected by ...
... externally each of two fixed circles ( centres A , B ) . Prove that the difference of AO , BO remains constant . Ex ... externally at A and are touched at P , Q by a line PQ , then PQ subtends a right angle at A. Also PQ is bisected by ...
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.