The Elements of Plane and Solid GeometryLongmans, Green, and, Company, 1871 - 285 páginas |
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Página 77
... inscribed in a circle , and O is the point of intersection of its diagonals ; through O a chord EOF is drawn , such that O is its middle point . Prove that O is also the middle point of the part of this chord intercepted between any two ...
... inscribed in a circle , and O is the point of intersection of its diagonals ; through O a chord EOF is drawn , such that O is its middle point . Prove that O is also the middle point of the part of this chord intercepted between any two ...
Página 89
... inscribed in a circle O whose centre is joined to the middle point D of the arc BC , and AD is drawn . Prove that the angle ADO is half the difference of the angles B and C. 7. Two circles intersect in A , and through A the secants ABC ...
... inscribed in a circle O whose centre is joined to the middle point D of the arc BC , and AD is drawn . Prove that the angle ADO is half the difference of the angles B and C. 7. Two circles intersect in A , and through A the secants ABC ...
Página 110
... B. If the given point is on the circle it is only necessary to draw the diameter through this point and at the point to draw a straight line perpendicular to this diameter . PROBLEM 13 . To inscribe a circle in a given IIO Geometry .
... B. If the given point is on the circle it is only necessary to draw the diameter through this point and at the point to draw a straight line perpendicular to this diameter . PROBLEM 13 . To inscribe a circle in a given IIO Geometry .
Página 111
Henry William Watson. PROBLEM 13 . To inscribe a circle in a given triangle . Let ABC be the given triangle . It is required to inscribe a circle in ABC . If possible , let there be a circle touching the sides of the triangle ABC in the ...
Henry William Watson. PROBLEM 13 . To inscribe a circle in a given triangle . Let ABC be the given triangle . It is required to inscribe a circle in ABC . If possible , let there be a circle touching the sides of the triangle ABC in the ...
Página 219
... inscribed in a polygon when each side of the polygon is a tangent to the circle , and in this case the polygon is said to be described about the circle . PROPOSITION 27 . It is always possible to describe a circle about and to inscribe ...
... inscribed in a polygon when each side of the polygon is a tangent to the circle , and in this case the polygon is said to be described about the circle . PROPOSITION 27 . It is always possible to describe a circle about and to inscribe ...
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Términos y frases comunes
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
Pasajes populares
Página 15 - If two triangles have two sides of the one equal to two sides of the...
Página 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.
Página 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.
Página 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
Página 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...
Página 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'.
Página 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.
Página 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.
Página 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