The Elements of Plane and Solid GeometryLongmans, Green, and, Company, 1871 - 285 σελίδες |
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Αποτελέσματα 1 - 5 από τα 11.
Σελίδα 87
... touches the circle , and it passes through D by hypothesis . By similar reasoning another line DF may be drawn through D touching the circle in the point F on the other side of AD . Then in the two right - angled triangles DEA and DFA ...
... touches the circle , and it passes through D by hypothesis . By similar reasoning another line DF may be drawn through D touching the circle in the point F on the other side of AD . Then in the two right - angled triangles DEA and DFA ...
Σελίδα 88
... touching one circle , and termi- nated by the other circle in the points C and D. Prove that the triangles ABC and ABD are equi - angular to one an- other . 2. On the same base and on the same side of it there are two segments of ...
... touching one circle , and termi- nated by the other circle in the points C and D. Prove that the triangles ABC and ABD are equi - angular to one an- other . 2. On the same base and on the same side of it there are two segments of ...
Σελίδα 89
... touches a certain circle . 9. Two circles intersect in A and B , and CBD is drawn perpendicular to AB , to meet the circles in C and D. If EAF bisect the exterior angle between CA and DA prove that the tangents to the circles at E and F ...
... touches a certain circle . 9. Two circles intersect in A and B , and CBD is drawn perpendicular to AB , to meet the circles in C and D. If EAF bisect the exterior angle between CA and DA prove that the tangents to the circles at E and F ...
Σελίδα 110
... touching the circle CED . Because it is always possible to draw two tangents to the C Fig . 15 . I A B F circle CED from the point B ( Bk . II . Prop . 20 ) , let BC be one of these . Find the centre A of the circle CED and join AC ...
... touching the circle CED . Because it is always possible to draw two tangents to the C Fig . 15 . I A B F circle CED from the point B ( Bk . II . Prop . 20 ) , let BC be one of these . Find the centre A of the circle CED and join AC ...
Σελίδα 111
... touching the sides of the triangle ABC in the points D , E , and F. Find G the centre of this circle , and join GA , GB , and GC . Because AF and AE are tangents to the circle from the external point A , there- fore the angles GAE and ...
... touching the sides of the triangle ABC in the points D , E , and F. Find G the centre of this circle , and join GA , GB , and GC . Because AF and AE are tangents to the circle from the external point A , there- fore the angles GAE and ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC and DEF ABCD adjacent angles angle ABC angle ACB angle BAC BC is equal centre circumference coincide common measure construction Corollary diameter dicular dihedral angle distance divided equal angles equal to AC equidistant exterior angle figure four right angles given angle given circle given plane given point given ratio given straight line greater homologous inscribed intersecting straight lines length less Let ABC line of intersection locus magnitudes meet the circle middle point multiple number of sides opposite sides parallelogram pentagon perpen perpendicular plane AC point F produced Prop PROPOSITION PROPOSITION 13 Prove radii radius rectangle regular polygon respectively equal rhombus right angles segments side BC similar triangles Similarly situated square straight line AB straight line BC subtended tangent triangle ABC triangle DEF
Δημοφιλή αποσπάσματα
Σελίδα 15 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 101 - Through a given point to draw a straight line parallel to a given straight line. Let A be the given point, and BC the given straight line, it is required to draw a straight line through the point A, parallel to the line BC.
Σελίδα 126 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Σελίδα 222 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R
Σελίδα 188 - If the angle of a triangle be divided into two equal angles, by a straight line which also cuts the base ; the segments of the base shall have the same ratio which the other sides of the triangle have to one another...
Σελίδα 204 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Σελίδα 14 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Σελίδα 12 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.
Σελίδα 161 - Ir there be any number of magnitudes, and as many others, which, taken two and two in order, have the same ratio ; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to the last. NB This is usually cited by the words