An Elementary Geometry |
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Page 70
... describes the convex surface , and the other two sides the two circular bases . Thus the rectangle ABCD revolving about BC would describe the cylinder , the side A D the convex surface , and A B , DC the circular bases . H D B 13. The ...
... describes the convex surface , and the other two sides the two circular bases . Thus the rectangle ABCD revolving about BC would describe the cylinder , the side A D the convex surface , and A B , DC the circular bases . H D B 13. The ...
Page 89
... describe arcs cutting one another at C and D ; join C and D cutting AB at E , and the line AB is bisected at E. For C and D being each equally distant from A and B , the line CD must be perpendicu- lar to AB at its middle point ...
... describe arcs cutting one another at C and D ; join C and D cutting AB at E , and the line AB is bisected at E. For C and D being each equally distant from A and B , the line CD must be perpendicu- lar to AB at its middle point ...
Page 90
... describe an arc cutting A B in D and E ; with D and E F EX B C D E as centres , with a radius greater than 4- DC , describe arcs intersecting at F. Draw CF , and it is the perpendicular required ( converse of I. 53 ) . Second Method ...
... describe an arc cutting A B in D and E ; with D and E F EX B C D E as centres , with a radius greater than 4- DC , describe arcs intersecting at F. Draw CF , and it is the perpendicular required ( converse of I. 53 ) . Second Method ...
Page 96
... describe a cir- cle cutting the given circle in B and E D A D. Draw A B and A D , and each will be tangent to the given circle through the given point . For drawing the radii C'B , CD , the angles B , D are each right angles ( III . 23 ) ...
... describe a cir- cle cutting the given circle in B and E D A D. Draw A B and A D , and each will be tangent to the given circle through the given point . For drawing the radii C'B , CD , the angles B , D are each right angles ( III . 23 ) ...
Page 100
... describe a semicircumference . any point , as B , in A B draw the perpen- dicular B C equal to a side of the given square ; through C draw CD parallel to A C B E A B , cutting the circumference in D ; draw DE perpendicular to AB . AE ...
... describe a semicircumference . any point , as B , in A B draw the perpen- dicular B C equal to a side of the given square ; through C draw CD parallel to A C B E A B , cutting the circumference in D ; draw DE perpendicular to AB . AE ...
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Common terms and phrases
A B C ABCD adjacent altitude angle ABC apothem arcs A B base and altitude bisect centre chord circ circumference cone construct the triangle convex surface Corollary cube cylinder diagonals diameter distance divided dodecagon EATON'S equal altitudes equally distant equiangular equilateral feet frustum given angle given circle given line given point given side given square half the arc hexagon homologous sides hypothenuse included angle infinite number inscribed internal angles intersection isosceles triangle Let ABCDEF line joining lines A B measured by half number of sides opposite sides parallel planes parallelogram parallelopiped perimeter perpendicular plane parallel quadrilateral radii radius ratio rectangle regular polygon respectively equal rhombus right angles right prism right pyramid right triangle Scholium secant segment similar triangles slant height sphere tangent THEOREM VII trapezoid triangle ABC vertex
Popular passages
Page 25 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Page 30 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 27 - If the product of two quantities is equal to the product of two others, the...
Page 43 - The area of a regular polygon is equal to half the product of its perimeter and apothem.
Page 11 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Page 23 - If two triangles have two sides of one respectively equal to two sides of the other, but the third sides unequal...
Page 20 - ... polygon, is equal to twice as many right angles as the polygon has sides minus two.
Page 49 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 70 - A right cylinder is a solid described by the revolution of a rectangle about one of its sides.
Page 64 - DEFINITIONS. 1 . A straight line is perpendicular to a plane, when it is perpendicular to every straight line of the plane which it meets.