Essentials of Solid GeometryGinn & Company, 1924 - 238 σελίδες |
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Σελίδα
... exercises . The lists of propositions prepared under the authority of the National Committee on Mathematical Requirements and of the College Entrance Examination Board have been followed as closely as the best principles of sequence and ...
... exercises . The lists of propositions prepared under the authority of the National Committee on Mathematical Requirements and of the College Entrance Examination Board have been followed as closely as the best principles of sequence and ...
Σελίδα 1
... exercises of solid geometry , we shall often need to refer to the definitions , assumptions , and propositions of plane geometry as authorities for the statements which form the various steps in the proofs . Pages 2-18 contain such ...
... exercises of solid geometry , we shall often need to refer to the definitions , assumptions , and propositions of plane geometry as authorities for the statements which form the various steps in the proofs . Pages 2-18 contain such ...
Σελίδα 20
... they have at least one other point in common . It is evident that they must then coincide or else that they must intersect in a straight line , Exercises . Planes 1. We commonly say that we live 20 BOOK VI LINES AND PLANES.
... they have at least one other point in common . It is evident that they must then coincide or else that they must intersect in a straight line , Exercises . Planes 1. We commonly say that we live 20 BOOK VI LINES AND PLANES.
Σελίδα 21
David Eugene Smith. Exercises . Planes 1. We commonly say that we live in a space of three dimensions , these dimensions being length , width , and thickness . We may , then , consider a plane as a space of how many and what dimensions ...
David Eugene Smith. Exercises . Planes 1. We commonly say that we live in a space of three dimensions , these dimensions being length , width , and thickness . We may , then , consider a plane as a space of how many and what dimensions ...
Σελίδα 29
... the student has already found , a locus is usually a line ; in solid geometry a locus may be a line or it may be a surface . Exercises . Lines and Planes 1. Equal oblique lines drawn §§ 43-46 29 PERPENDICULARS AND OBLIQUES.
... the student has already found , a locus is usually a line ; in solid geometry a locus may be a line or it may be a surface . Exercises . Lines and Planes 1. Equal oblique lines drawn §§ 43-46 29 PERPENDICULARS AND OBLIQUES.
Συχνά εμφανιζόμενοι όροι και φράσεις
AABC ABC and A'B'C altitude altitude h angles are equal axis bisects called chord circle circumscribed cone of revolution congruent conic surface Consider Ex Corollary corresponding cube cubic diagonal diameter dihedral angles distance Draw equivalent Exercises face angles Find the area Find the volume formed formula frustum given line given point Hence inches inscribed intersection isosceles lateral area lateral edges lateral faces line segment locus of points lower base measuring number of degrees oblique opposite parallel planes parallelogram perimeter perpendicular plane geometry plane passing pole polyhedral angles Proof Proposition Prove radii rectangular parallelepiped regular polygon regular polyhedrons regular pyramid right angles right circular cylinder Similarly slant height sphere of radius spherical degrees spherical excess spherical polygon spherical triangle straight line tangent tetrahedron Theorem third side total surface triangular prism trihedral upper base vertex vertices zone
Δημοφιλή αποσπάσματα
Σελίδα 7 - The line joining the midpoints of two sides of a triangle is parallel to the third side and equal to one-half of it.
Σελίδα 40 - A line which joins the midpoints of two sides of a triangle is parallel to the third side and equal to half of it.
Σελίδα 176 - 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 10 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Σελίδα 15 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 77 - The height of a cone is the perpendicular distance from the vertex to the plane of the base.
Σελίδα 3 - If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third.
Σελίδα 24 - If a straight line is perpendicular to each of two other straight lines at their point of intersection, it is perpendicular to the plane of the two lines.
Σελίδα 16 - If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other.
Σελίδα 15 - The sum of the squares of two sides of a triangle is equal to twice the square of half the third side increased by twice the square of the median upon that side.