The Essentials of GeometryD.C. Heath & Company, 1899 - 395 σελίδες |
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Σελίδα 165
... area of a rectangle is equal to the product of its base and altitude . Note . In all propositions relating to areas , the unit of surface ( § 302 ) is understood to be a square whose side is the linear unit . a M 1 N Given a and b , the ...
... area of a rectangle is equal to the product of its base and altitude . Note . In all propositions relating to areas , the unit of surface ( § 302 ) is understood to be a square whose side is the linear unit . a M 1 N Given a and b , the ...
Σελίδα 213
Webster Wells. 380. Cor . Of isoperimetric triangles , that which is equi lateral is the maximum . For if the maximum △ is not isosceles when any side is taken as the base , its area can be increased by making it isosceles . Then , the ...
Webster Wells. 380. Cor . Of isoperimetric triangles , that which is equi lateral is the maximum . For if the maximum △ is not isosceles when any side is taken as the base , its area can be increased by making it isosceles . Then , the ...
Σελίδα 216
... lateral . But this is impossible , since AF is > DG . Hence , ABC cannot be > BCD . In like manner , Z ABC cannot be ... area . A D B E A M Given ABC an equilateral A , and M an isoperimetric square . To Prove area Marea ABC . Proof ...
... lateral . But this is impossible , since AF is > DG . Hence , ABC cannot be > BCD . In like manner , Z ABC cannot be ... area . A D B E A M Given ABC an equilateral A , and M an isoperimetric square . To Prove area Marea ABC . Proof ...
Σελίδα 230
... lateral AEDF . ( area BCD : = area BCF- area BDF . ) E F D B C 86. If D is the middle point of side BC of triangle ABC , E the middle point of AD , F of BE , and G of CF , prove △ ABC equivalent to 8 A EFG . ( Draw CE ; then , area ABC = 2 ...
... lateral AEDF . ( area BCD : = area BCF- area BDF . ) E F D B C 86. If D is the middle point of side BC of triangle ABC , E the middle point of AD , F of BE , and G of CF , prove △ ABC equivalent to 8 A EFG . ( Draw CE ; then , area ABC = 2 ...
Σελίδα 274
... lateral faces ; the edges which are not sides of the bases are called the lateral edges , and the sum of the areas of the lateral faces the lateral area . The altitude is the perpendicular distance between the planes of the bases . 467 ...
... lateral faces ; the edges which are not sides of the bases are called the lateral edges , and the sum of the areas of the lateral faces the lateral area . The altitude is the perpendicular distance between the planes of the bases . 467 ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² adjacent angles altitude apothem approach the limit area ABC 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 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 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 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 261 - The projection of a point on a plane is the foot of the perpendicular drawn from the point to the plane.
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 73 - A chord is a straight line joining the extremities of an arc ; as AB.
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 170 - 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.
Σελίδα 224 - The perpendiculars from the vertices of a triangle to the opposite sides are the bisectors of the angles of the triangle formed by joining the feet of the perpendiculars.
Σελίδα 325 - A right circular cone may be generated by the revolution of a right triangle about one of its legs as an axis.