Plane and Solid GeometryMacmillan, 1902 - 370 σελίδες |
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Σελίδα xii
... hence . perpendicular , or is per- pendicular to . parallel , or is parallel to . parallels . axiom . circumference . complement . construction . corollary . corresponding . definition . exercise . exterior . homologous . is similar to ...
... hence . perpendicular , or is per- pendicular to . parallel , or is parallel to . parallels . axiom . circumference . complement . construction . corollary . corresponding . definition . exercise . exterior . homologous . is similar to ...
Σελίδα 9
... Hence DEFL ABC . 53. All right angles are equal . Q.E.D. ( Ax . 7. ) 54. At a given point in a given line there can be but one perpendicular to the line . ( 53 ) 55. The complements of the same or of equal angles are equal . ( Ax . 3 ...
... Hence DEFL ABC . 53. All right angles are equal . Q.E.D. ( Ax . 7. ) 54. At a given point in a given line there can be but one perpendicular to the line . ( 53 ) 55. The complements of the same or of equal angles are equal . ( Ax . 3 ...
Σελίδα 16
... Hence BCD > < B . By joining the midpoint of AC to B , it follows in t anner that But ZACGL A. ZACGBCD , ( vertical 4 ) . Hence < BCD > A. Ex . 43. If four points , A , B , C , and D , in a straight line be a point , E , without , then ...
... Hence BCD > < B . By joining the midpoint of AC to B , it follows in t anner that But ZACGL A. ZACGBCD , ( vertical 4 ) . Hence < BCD > A. Ex . 43. If four points , A , B , C , and D , in a straight line be a point , E , without , then ...
Σελίδα 18
... Hence AC and DF are parallel . 81. SCHOLIUM . That the lines AC and DF cannot the side of A and D can be proved by the same method - 82. REMARK . - In order to demonstrate that two 1 parallel , prove the equality of a pair of alternate ...
... Hence AC and DF are parallel . 81. SCHOLIUM . That the lines AC and DF cannot the side of A and D can be proved by the same method - 82. REMARK . - In order to demonstrate that two 1 parallel , prove the equality of a pair of alternate ...
Σελίδα 20
... Hence CDEF , ( alt . int . being equal ) . Q.E.D. 86. REMARK . Lines are demonstrated to be parallel by proving that ( a ) Two alternate interior angles are equal , ( b ) Two corresponding angles are equal , or ( c ) Two interior angles ...
... Hence CDEF , ( alt . int . being equal ) . Q.E.D. 86. REMARK . Lines are demonstrated to be parallel by proving that ( a ) Two alternate interior angles are equal , ( b ) Two corresponding angles are equal , or ( c ) Two interior angles ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angles are equal bisect bisector chord circumference circumscribed cone construct a triangle cylinder diagonals diagram for Prop diameter diedral angles divide draw drawn equiangular equiangular polygon equilateral triangle equivalent exterior angle face angles Find the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous homologous sides hypotenuse inches inscribed intersecting isosceles triangle joining the midpoints lateral area lateral edges line joining mean proportional median opposite sides parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION prove Proof quadrilateral radii ratio rectangle regular polygon respectively equal rhombus right angles right triangle SCHOLIUM segment similar triangles sphere spherical polygon spherical triangle square straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal triedral vertex
Δημοφιλή αποσπάσματα
Σελίδα 45 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Σελίδα 119 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 180 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Σελίδα 31 - The median to the base of an isosceles triangle is perpendicular to the base.
Σελίδα 305 - A cylinder is a solid bounded by a cylindrical surface and two parallel planes; the bases of a cylinder are the parallel planes; and the lateral surface is the cylindrical surface.
Σελίδα 337 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...
Σελίδα 250 - A straight line perpendicular to one of two parallel planes is perpendicular to the other also.
Σελίδα 297 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Σελίδα 105 - I. When the given point, A, is in the circumference. HINT. — What is the angle formed by a radius and a tangent at its extremity ? II. When the given point, A, is without the circle. \ Construction. Join A, and 0 the center of the given circle. On OA as a diameter, construct a circumference, intersecting the given circumference in B and C.
Σελίδα 276 - An oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Hyp. GM is a right section of oblique prism AD', and OM ' a right prism whose altitude is equal to a lateral edge of AD'. To prove AD' =s= GM'. Proof. The lateral edges of GM