Plane and Solid GeometryMacmillan, 1902 - 370 σελίδες |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 10
... Proof . 21 = 22 . 21 is a supplement of 3 , 2 is a supplement of 3 , ( two adjacent angles whose exterior sides are in a straight line are supplementary ) . .. 21 = 22 , ( supplements of equal & are equal ) . Q.E.D. Ex . 26. If , in the ...
... Proof . 21 = 22 . 21 is a supplement of 3 , 2 is a supplement of 3 , ( two adjacent angles whose exterior sides are in a straight line are supplementary ) . .. 21 = 22 , ( supplements of equal & are equal ) . Q.E.D. Ex . 26. If , in the ...
Σελίδα 12
... In triangles ABC and A'B'C ' , AB A'B ' , ZA ZA ' , and BB ' . To prove = = △ ABC = △ A'B'C ' . Proof . Apply AABC to AA'B'C ' so that AB shall coin- cide with A'B ' . BC will take the direction of B'C ' , ( 12 PLANE GEOMETRY.
... In triangles ABC and A'B'C ' , AB A'B ' , ZA ZA ' , and BB ' . To prove = = △ ABC = △ A'B'C ' . Proof . Apply AABC to AA'B'C ' so that AB shall coin- cide with A'B ' . BC will take the direction of B'C ' , ( 12 PLANE GEOMETRY.
Σελίδα 14
... Proof . Apply △ ABC to △ A'B'C ' so that BC shall coincide with B'C ' . BA will take the direction of B'A ' , ( LB = LB ' by hyp . ) . The point A will fall upon the point A ' , ( AB = A'B ' by hyp . ) . .. AC will coincide with A'C ...
... Proof . Apply △ ABC to △ A'B'C ' so that BC shall coincide with B'C ' . BA will take the direction of B'A ' , ( LB = LB ' by hyp . ) . The point A will fall upon the point A ' , ( AB = A'B ' by hyp . ) . .. AC will coincide with A'C ...
Σελίδα 16
Arthur Schultze, Frank Louis Sevenoak. Proof . Let E be the midpoint of BC . Draw AE and pro- duce it its own length to F. Draw FC . B In But AABE and FCE , AE - EF and BE = EC . △ BEA = / FEC , ( vertical 4 ) . . : . Δ ΑΒΕ = Δ FCE ...
Arthur Schultze, Frank Louis Sevenoak. Proof . Let E be the midpoint of BC . Draw AE and pro- duce it its own length to F. Draw FC . B In But AABE and FCE , AE - EF and BE = EC . △ BEA = / FEC , ( vertical 4 ) . . : . Δ ΑΒΕ = Δ FCE ...
Σελίδα 18
... Proof . AC and DF either meet or are parallel . Suppose they meet in G. Then BEG is a triangle whose exterior ABE is equal to a remote interior △ BEG , which is impossible . Hence AC and DF are parallel . Q.E.D. 81. SCHOLIUM . That the ...
... Proof . AC and DF either meet or are parallel . Suppose they meet in G. Then BEG is a triangle whose exterior ABE is equal to a remote interior △ BEG , which is impossible . Hence AC and DF are parallel . Q.E.D. 81. SCHOLIUM . That the ...
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 a point Find the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous 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 PROPOSITION prove Proof quadrilateral radii ratio rectangle regular polygon respectively equal rhombus right angles right triangle SCHOLIUM segments 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