The Elements of Plane and Solid GeometryLongmans, Green, and, Company, 1871 - 285 páginas |
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Página 25
... half their sum . 2. If a straight line be drawn from the vertex of a triangle to the middle point of the opposite side , prove that this line will be less than half the sum of the sides which meet in the vertex , and greater than half ...
... half their sum . 2. If a straight line be drawn from the vertex of a triangle to the middle point of the opposite side , prove that this line will be less than half the sum of the sides which meet in the vertex , and greater than half ...
Página 26
... half the sum of DA and DB . If CB cuts AD in E , prove that EA is greater than EB , and EC greater than ED . SECTION II . - ON ANGLES . PROPOSITION II . From a given point in a given straight line , it is always possible to draw a ...
... half the sum of DA and DB . If CB cuts AD in E , prove that EA is greater than EB , and EC greater than ED . SECTION II . - ON ANGLES . PROPOSITION II . From a given point in a given straight line , it is always possible to draw a ...
Página 33
... half the sum or half the difference of the angles DCA and DCB , according as CD is without or within the angle ACB . 3. Prove that the perpendiculars drawn from the ex- tremities of the base of an isosceles triangle upon the opposite ...
... half the sum or half the difference of the angles DCA and DCB , according as CD is without or within the angle ACB . 3. Prove that the perpendiculars drawn from the ex- tremities of the base of an isosceles triangle upon the opposite ...
Página 44
... half of BC . 2. If AC and BD be two parallel straight lines , and ABO CDO two lines meeting in O , such that the intercepts AB and CD are equal , prove that AO will be equal to CO , and BO to DO . 3. If the lines containing one of two ...
... half of BC . 2. If AC and BD be two parallel straight lines , and ABO CDO two lines meeting in O , such that the intercepts AB and CD are equal , prove that AO will be equal to CO , and BO to DO . 3. If the lines containing one of two ...
Página 50
... half the vertical angle . 2. Prove that a convex polygon cannot have more than three acute interior angles . 3. Prove that an angle of a triangle is equal to , less , or greater than a right angle according as the line drawn from it to ...
... half the vertical angle . 2. Prove that a convex polygon cannot have more than three acute interior angles . 3. Prove that an angle of a triangle is equal to , less , or greater than a right angle according as the line drawn from it to ...
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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