The Essentials of GeometryD.C. Heath & Company, 1899 - 395 σελίδες |
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Σελίδα 105
... . EXERCISES . 70. Given the base and altitude of an isosceles triangle , to con- struct the triangle . 71. Given an acute angle , to construct its complement . PROP . XXVIII . PROBLEM . 204. From a given THE CIRCLE . 105.
... . EXERCISES . 70. Given the base and altitude of an isosceles triangle , to con- struct the triangle . 71. Given an acute angle , to construct its complement . PROP . XXVIII . PROBLEM . 204. From a given THE CIRCLE . 105.
Σελίδα 107
... construct its supplement . ( ? ) ( § 163 ) 73. Given a side of an equilateral triangle , to construct the tri- angle . 74. To construct an angle of 60 ° ( Ex . 73 ) ; of 30 ° ( Ex . 71 ) . 75. To construct an angle of 120 ° ( Ex . 72 ) ...
... construct its supplement . ( ? ) ( § 163 ) 73. Given a side of an equilateral triangle , to construct the tri- angle . 74. To construct an angle of 60 ° ( Ex . 73 ) ; of 30 ° ( Ex . 71 ) . 75. To construct an angle of 120 ° ( Ex . 72 ) ...
Σελίδα 108
... construct an angle equal to a given angle . D C E X Given the vertex , and OA a side , of an ≤ , and ≤ 0 ' . Required to construct , with O as the vertex and 108 PLANE GEOMETRY . - BOOK II .
... construct an angle equal to a given angle . D C E X Given the vertex , and OA a side , of an ≤ , and ≤ 0 ' . Required to construct , with O as the vertex and 108 PLANE GEOMETRY . - BOOK II .
Σελίδα 109
... construct Then , FCD = / CEB . CD || AB . ( § 208 ) ( ? ) EXERCISES . 76. To construct an angle of 45 ° ; of 135 ° ; of 2210 ; of 6710 . 77. Through a given point without a straight line to draw a line making a given angle with that ...
... construct Then , FCD = / CEB . CD || AB . ( § 208 ) ( ? ) EXERCISES . 76. To construct an angle of 45 ° ; of 135 ° ; of 2210 ; of 6710 . 77. Through a given point without a straight line to draw a line making a given angle with that ...
Σελίδα 110
... construct the third Z. --D E Construction . At any point E of the indefinite line CD , construct DEF = / A. ( § 208 ) Also , FEG adjacent to / DEF , and equal to B. Then , CEG is the required Z. ( The proof is left to the pupil . ) PROP ...
... construct the third Z. --D E Construction . At any point E of the indefinite line CD , construct DEF = / A. ( § 208 ) Also , FEG adjacent to / DEF , and equal to B. Then , CEG is the required Z. ( The proof is left to the pupil . ) PROP ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² adjacent angles altitude apothem approach the limit axis base and altitude BC² bisector bisects centre chord circle circumference circumscribed coincide cone of revolution Converse of Prop diagonals diameter diedral angle distance Draw line equal respectively equally distant equilateral equivalent exterior angle faces Find the area frustum Given line given point Hence homologous homologous sides hypotenuse intersecting isosceles triangle lateral area lateral edges line drawn line joining middle point number of sides parallel parallelogram parallelopiped perimeter perpendicular plane MN polyedral polyedron prism Prove pyramid quadrilateral radii radius rectangle regular inscribed regular polygon rhombus right angles right triangle segment side BC similar slant height spherical polygon spherical triangle square tangent tetraedron THEOREM trapezoid triangle ABC triangular prism triedral vertex vertices volume Whence
Δημοφιλή αποσπάσματα
Σελίδα 58 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Σελίδα 322 - A right circular cylinder may be generated by the revolution of a rectangle about one of its sides as an axis.
Σελίδα 371 - A zone is a portion of the surface of a sphere included between two parallel planes.
Σελίδα 49 - ... the three sides of one are equal, respectively, to the three sides of the other. 2. Two right triangles are congruent if...
Σελίδα 336 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The...
Σελίδα 151 - If one leg of a right triangle is double the other, the perpendicular from the vertex of the right angle to the hypotenuse divides it into segments which are to each other as 1 to 4.
Σελίδα 328 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 205 - S' denote the areas of two © whose radii are R and R', and diameters D and D', respectively. Then, | = "* § = ££ = £• <§337> That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters.
Σελίδα 73 - A chord is a straight line joining the extremities of an arc ; as AB.
Σελίδα 202 - The circumferences of two circles are to each other as their radii. Given C and C" the circumferences of two © whose radii are R and R', respectively.