An Elementary Geometry |
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Page 26
... means . 6. When three quantities are in proportion , e . g . a : b = b : c , the second is called a mean proportional between the other two ; and the third , a third proportional to the first and second . 7. A proportion is transformed ...
... means . 6. When three quantities are in proportion , e . g . a : b = b : c , the second is called a mean proportional between the other two ; and the third , a third proportional to the first and second . 7. A proportion is transformed ...
Page 38
... mean proportional between the whole hypothenuse and the segment adjacent to that side cut off by the perpendicular drawn from the vertex of the right angle to the hypothenuse . 26. Cor . 2. As ABD and BCD are similar triangles AD : DB ...
... mean proportional between the whole hypothenuse and the segment adjacent to that side cut off by the perpendicular drawn from the vertex of the right angle to the hypothenuse . 26. Cor . 2. As ABD and BCD are similar triangles AD : DB ...
Page 39
... mean proportional between the segments of the base . THEOREM XII . 27. The square described on the hypothenuse of a right angle is equivalent to the sum of the squares described upon the other two sides . Let ABC be a triangle right ...
... mean proportional between the segments of the base . THEOREM XII . 27. The square described on the hypothenuse of a right angle is equivalent to the sum of the squares described upon the other two sides . Let ABC be a triangle right ...
Page 63
... mean proportional be- tween the segments of the diameter . Join AB , BC . ( 23. ) ( II . 26. ) 70. If from one end of a chord a diame- ter is drawn , and from the other end a per- B A C D pendicular to this diameter , the chord is a mean ...
... mean proportional be- tween the segments of the diameter . Join AB , BC . ( 23. ) ( II . 26. ) 70. If from one end of a chord a diame- ter is drawn , and from the other end a per- B A C D pendicular to this diameter , the chord is a mean ...
Page 100
... mean proportional between the altitude and base of the given parallelogram ( 26 ) , and it will be a side of the re- quired square . PROBLEM XXV . 35. To construct a square equivalent to 100 PLANE GEOMETRY .
... mean proportional between the altitude and base of the given parallelogram ( 26 ) , and it will be a side of the re- quired square . PROBLEM XXV . 35. To construct a square equivalent to 100 PLANE GEOMETRY .
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Common terms and phrases
ABC and DEF ABCD adjacent altitude angle ABC apothem base and altitude bisect centre chord circ circumference coincide cone construct the triangle convex surface Corollary cube cylinder 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 given triangle half the arc hexagon homologous sides hypothenuse included angle infinite number inscribed internal angles intersection isosceles triangle Let ABCDEF line joining mean proportional measured by half number of sides opposite sides parallel planes parallelogram parallelopiped perimeter perpendicular plane parallel propositions 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 VIII 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.