The Elements of Plane and Solid GeometryLongmans, Green, and, Company, 1871 - 285 sider |
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Resultat 1-5 av 17
Side 25
... double that sum . 4. ABC is a triangle ; on AB , produced if necessary , take AD equal to AC , and on AC take AE equal to AB and draw DE meeting BC in F. Prove that AF bisects the angle BAC . 5. ABC is an isosceles triangle , of which ...
... double that sum . 4. ABC is a triangle ; on AB , produced if necessary , take AD equal to AC , and on AC take AE equal to AB and draw DE meeting BC in F. Prove that AF bisects the angle BAC . 5. ABC is an isosceles triangle , of which ...
Side 33
... double of the less ; find what fraction the less is of two right angles . 7. From a given point in a given straight line , two straight lines , and only two , can be drawn , so that each may make a given angle with the given line . Note ...
... double of the less ; find what fraction the less is of two right angles . 7. From a given point in a given straight line , two straight lines , and only two , can be drawn , so that each may make a given angle with the given line . Note ...
Side 50
... double of the other , the hypothenuse will be double the smaller side . 8. Every parallelogram whose diagonals are equal is a rectangle , every parallelogram whose diagonals are perpen- dicular to each other is a rhombus , and one whose ...
... double of the other , the hypothenuse will be double the smaller side . 8. Every parallelogram whose diagonals are equal is a rectangle , every parallelogram whose diagonals are perpen- dicular to each other is a rhombus , and one whose ...
Side 70
... double of that at the circumference . Let ABC be a circle and O its centre , and let BOC be an angle at the centre O , and BAC an angle at the point A of Fig . 10 . A Fig . 11 . B E B D E D the circumference , subtended by the same arc ...
... double of that at the circumference . Let ABC be a circle and O its centre , and let BOC be an angle at the centre O , and BAC an angle at the point A of Fig . 10 . A Fig . 11 . B E B D E D the circumference , subtended by the same arc ...
Side 71
... double of OAB . Similarly , EOC is double of OAC , therefore EOB + EOC is double of OAB + OAC , that is , BOC is double of BAC . Next , let B and C lie on the same side of AE , as in Fig . I I. It may be proved as before that EOB is ...
... double of OAB . Similarly , EOC is double of OAC , therefore EOB + EOC is double of OAB + OAC , that is , BOC is double of BAC . Next , let B and C lie on the same side of AE , as in Fig . I I. It may be proved as before that EOB is ...
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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
Populære avsnitt
Side 15 - If two triangles have two sides of the one equal to two sides of the...
Side 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.
Side 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.
Side 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
Side 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...
Side 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'.
Side 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.
Side 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.
Side 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