Essentials of Solid GeometryGinn & Company, 1924 - 238 σελίδες |
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Σελίδα 21
... n lines , no two of which are parallel , meet a given line l , how many planes are determined , and upon what postulate does your answer depend ? Proposition 1. Intersection of Planes 32. Theorem . If two § 31 21 PLANE DETERMINED.
... n lines , no two of which are parallel , meet a given line l , how many planes are determined , and upon what postulate does your answer depend ? Proposition 1. Intersection of Planes 32. Theorem . If two § 31 21 PLANE DETERMINED.
Σελίδα 22
David Eugene Smith. Proposition 1. Intersection of Planes 32. Theorem . If two planes meet , they intersect in a straight line . զ A p B Given two planes p and q which meet . Prove that p and q intersect in a st . line . Proof . Since p ...
David Eugene Smith. Proposition 1. Intersection of Planes 32. Theorem . If two planes meet , they intersect in a straight line . զ A p B Given two planes p and q which meet . Prove that p and q intersect in a st . line . Proof . Since p ...
Σελίδα 24
... ,3 Then , since AQ = A'Q ( § 7 , 2 ) , OQ is to AA ' at O. § 19 , 4 Hence AO is to any line in the plane m through O , and thus is to m . § 33 Proposition 3. Perpendiculars to a Line 38. Theorem . Every 24 BOOK VI LINES AND PLANES.
... ,3 Then , since AQ = A'Q ( § 7 , 2 ) , OQ is to AA ' at O. § 19 , 4 Hence AO is to any line in the plane m through O , and thus is to m . § 33 Proposition 3. Perpendiculars to a Line 38. Theorem . Every 24 BOOK VI LINES AND PLANES.
Σελίδα 25
... YY ' . Then m , the plane of OP and OQ , is to YY ' at O ( §38 ) . Now prove that m is the only plane by using Post . 7 . IP m Proposition 4. Perpendicular through Internal Point 41. Theorem . Through §§ 37-40 25 PERPENDICULARS TO A LINE.
... YY ' . Then m , the plane of OP and OQ , is to YY ' at O ( §38 ) . Now prove that m is the only plane by using Post . 7 . IP m Proposition 4. Perpendicular through Internal Point 41. Theorem . Through §§ 37-40 25 PERPENDICULARS TO A LINE.
Σελίδα 26
... to b . $ 33 Hence and PQ ' would lie in both x and y , $ 38 PQ ' would coincide with PQ . .. PQ is the one and only 1 to m through P. Proposition 5. Perpendicular through External Point 42. Theorem . Through 26 BOOK VI LINES AND PLANES.
... to b . $ 33 Hence and PQ ' would lie in both x and y , $ 38 PQ ' would coincide with PQ . .. PQ is the one and only 1 to m through P. Proposition 5. Perpendicular through External Point 42. Theorem . Through 26 BOOK VI LINES AND PLANES.
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.