The Elements of Plane and Solid Geometry |
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Page 58
... radius of the circle is situated within the circle ; and every point in the plane of the circle whose distance from the centre is greater than the radius of the circle is situated without the circle . Let A be the centre of any given ...
... radius of the circle is situated within the circle ; and every point in the plane of the circle whose distance from the centre is greater than the radius of the circle is situated without the circle . Let A be the centre of any given ...
Page 59
... radius of the circle ; and every point on AB be- tween A and P is at a distance from A less than the radius of the circle . Therefore every in- definite straight line Fig . 1 . A B P drawn from A meets the circle in one point , and one ...
... radius of the circle ; and every point on AB be- tween A and P is at a distance from A less than the radius of the circle . Therefore every in- definite straight line Fig . 1 . A B P drawn from A meets the circle in one point , and one ...
Page 60
... radius of GEF , then AB shall meet GEF in two points , and two points only , equidistant from D. Because DB is an indefinite straight line , therefore it is always possible to find a point H in DB such that DH is equal to the radius of ...
... radius of GEF , then AB shall meet GEF in two points , and two points only , equidistant from D. Because DB is an indefinite straight line , therefore it is always possible to find a point H in DB such that DH is equal to the radius of ...
Page 61
... radius of the circle , the straight line will meet the circle in the foot of the perpendicular so drawn , and in no other point ; and also that if the length of this perpen- dicular be greater than the radius of the circle , the ...
... radius of the circle , the straight line will meet the circle in the foot of the perpendicular so drawn , and in no other point ; and also that if the length of this perpen- dicular be greater than the radius of the circle , the ...
Page 68
... radius of the circle . If the diameter AEB be drawn , prove that the angle DEB is three times the angle DAB , E being the centre . SECTION II . - ON ANGLES IN CIRCLES . PROPOSITION 9 . In equal circles equal angles at the centres are ...
... radius of the circle . If the diameter AEB be drawn , prove that the angle DEB is three times the angle DAB , E being the centre . SECTION II . - ON ANGLES IN CIRCLES . PROPOSITION 9 . In equal circles equal angles at the centres are ...
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Common terms and phrases
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
Popular passages
Page 15 - If two triangles have two sides of the one equal to two sides of the...
Page 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.
Page 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.
Page 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
Page 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...
Page 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'.
Page 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.
Page 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.
Page 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