The Essentials of GeometryD.C. Heath & Company, 1899 - 395 σελίδες |
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Σελίδα 273
... volume of a solid is its ratio to another solid , called the unit of volume , adopted arbitrarily as the unit of measure ( § 180 ) . The usual unit of volume is a cube ( § 474 ) whose edge is some linear unit ; for example , a cubic ...
... volume of a solid is its ratio to another solid , called the unit of volume , adopted arbitrarily as the unit of measure ( § 180 ) . The usual unit of volume is a cube ( § 474 ) whose edge is some linear unit ; for example , a cubic ...
Σελίδα 280
... volume of the rectangular parallelopiped . CASE I. When the altitudes are commensurable . P B Given P and Q rect . parallelopipeds , with equal bases , and commensurable altitudes , AA ' and BB ' . To Prove P Q = AA ' BB ' Proof . Let ...
... volume of the rectangular parallelopiped . CASE I. When the altitudes are commensurable . P B Given P and Q rect . parallelopipeds , with equal bases , and commensurable altitudes , AA ' and BB ' . To Prove P Q = AA ' BB ' Proof . Let ...
Σελίδα 283
... volumes . 2. Find the ratio of the volumes of two rectangular parallelopipeds , whose dimensions are 8 , 12 , and 21 , and 14 , 15 , and 24 , respectively . 3. The diagonals of a parallelopiped bisect each other . ( To prove that AC and ...
... volumes . 2. Find the ratio of the volumes of two rectangular parallelopipeds , whose dimensions are 8 , 12 , and 21 , and 14 , 15 , and 24 , respectively . 3. The diagonals of a parallelopiped bisect each other . ( To prove that AC and ...
Σελίδα 284
... volume of a rectangular parallelopiped is equal to the product of its three dimensions . P с a 1 Given a , b , and c the dimensions of rect . parallelopiped P , and the unit of volume ; that is , a cube whose edge is the linear unit ...
... volume of a rectangular parallelopiped is equal to the product of its three dimensions . P с a 1 Given a , b , and c the dimensions of rect . parallelopiped P , and the unit of volume ; that is , a cube whose edge is the linear unit ...
Σελίδα 285
... volume , and the area of the entire surface of a cube whose edge is 3 in . 7. Find the area of the entire surface of a rectangular parallelo- piped , the dimensions of whose base are 11 and 13 , and volume 858 . 8. Find the volume of a ...
... volume , and the area of the entire surface of a cube whose edge is 3 in . 7. Find the area of the entire surface of a rectangular parallelo- piped , the dimensions of whose base are 11 and 13 , and volume 858 . 8. Find the volume of a ...
Άλλες εκδόσεις - Προβολή όλων
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.