## An Elementary Geometry |

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Page 66

William Frothingham Bradbury. THEOREM III . 9. The intersections of two

William Frothingham Bradbury. THEOREM III . 9. The intersections of two

**parallel planes**with a third plane are parallel . Let A B and CD be the intersec- M tions of the plane A D with the paral- lel planes MN and PQ ; then A B and CD ... Page 67

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**planes**of these angles are**parallel**. For , since two**intersecting**lines determine a**plane**, the**plane**of P B A C N E D the lines A B and BC must be**parallel**to the**plane**of the lines DE and EF , as A B and B C are respectively**parallel**... Page 71

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**parallel planes**are equal polygons . Let the prism A H be intersected by the par- allel planes LN and QS ; then LN and QS are equal polygons . For LM , MN , NO , & c . are respectively parallel to QR , RS , ST , & c . L ( IV . 9 ) , and ... Page 72

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**plane parallel**to the base is equal to the base . 18. Cor . 2. A section of a cylinder made by a**plane**paral- lel to the base is a circle equal to the base . THEOREM III . 19. Prisms having equivalent bases and equal altitudes are ... Page 73

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**planes**through the several points of division**parallel**to the sides of the par- allelopiped , there will be formed a number of cubes equal to each other ( 19 ) , and each equal to the cube whose edge is the linear unit . It is evi- dent ...### Other editions - View all

### 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.