An Elementary Geometry |
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Page 4
... four right angles . Let the angles ABD , DBE , EBF , FBG , GBA , be formed in the same plane about the point B. Produce AB ; then the sum of the angles above the line AC is equal to two right angles ; and also , the sum of the angles ...
... four right angles . Let the angles ABD , DBE , EBF , FBG , GBA , be formed in the same plane about the point B. Produce AB ; then the sum of the angles above the line AC is equal to two right angles ; and also , the sum of the angles ...
Page 5
... four right angles . THEOREM II . 10. If at a point in a straight line two other straight lines upon opposite sides of it make the sum of the adjacent angles equal to two right angles , these two lines form a straight line . Let the ...
... four right angles . THEOREM II . 10. If at a point in a straight line two other straight lines upon opposite sides of it make the sum of the adjacent angles equal to two right angles , these two lines form a straight line . Let the ...
Page 9
... four sides is called a quadrilateral ; one of five , a pentagon ; one of six , a hexagon ; one of eight , an octagon ; one of ten , a decagon . TRIANGLES . 26. A Scalene Triangle is one which has B no two of its sides equal ; as A B C ...
... four sides is called a quadrilateral ; one of five , a pentagon ; one of six , a hexagon ; one of eight , an octagon ; one of ten , a decagon . TRIANGLES . 26. A Scalene Triangle is one which has B no two of its sides equal ; as A B C ...
Page 20
... four angles formed at a point on the same side of a straight line , in the same plane , contain respectively 15 ° , 27 ° , and 99 ° , how many degrees does the fourth angle contain ? 5. If five of six angles formed in a plane about a ...
... four angles formed at a point on the same side of a straight line , in the same plane , contain respectively 15 ° , 27 ° , and 99 ° , how many degrees does the fourth angle contain ? 5. If five of six angles formed in a plane about a ...
Page 24
... four right angles . A a B F E 95. If a pavement is to be laid with blocks of the same regular form , prove that their upper faces must be equilateral triangles , squares , or hexagons . ( 67. ) ( 9. ) · 96. If two kinds of regular ...
... four right angles . A a B F E 95. If a pavement is to be laid with blocks of the same regular form , prove that their upper faces must be equilateral triangles , squares , or hexagons . ( 67. ) ( 9. ) · 96. If two kinds of regular ...
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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.