An Elementary Geometry |
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Page 2
... Scholium . The boundaries of solids are surfaces ; of surfaces , lines ; the ends of lines are points . 14. A Theorem is something to be proved . 15. A Problem is something to be done . 16. A Proposition is either a theorem or a problem ...
... Scholium . The boundaries of solids are surfaces ; of surfaces , lines ; the ends of lines are points . 14. A Theorem is something to be proved . 15. A Problem is something to be done . 16. A Proposition is either a theorem or a problem ...
Page 14
... triangles ABC and AD C , having two sides and the included angle of the one equal to two sides and the included angle of the other , are equal ( 40 ) . 49. Scholium . In equal triangles the equal angles are 14 PLANE GEOMETRY .
... triangles ABC and AD C , having two sides and the included angle of the one equal to two sides and the included angle of the other , are equal ( 40 ) . 49. Scholium . In equal triangles the equal angles are 14 PLANE GEOMETRY .
Page 15
William Frothingham Bradbury. 49. Scholium . In equal triangles the equal angles are oppo- site the equal sides . THEOREM XIV .. 50. Two right triangles having the hypothenuse and a side of the one respectively equal to the hypothenuse ...
William Frothingham Bradbury. 49. Scholium . In equal triangles the equal angles are oppo- site the equal sides . THEOREM XIV .. 50. Two right triangles having the hypothenuse and a side of the one respectively equal to the hypothenuse ...
Page 27
... Scholium . A proportion is an equation ; and making the product of the extremes equal to the product of the means is merely clearing the equation of fractions . THEOREM II . 14. If the product of two quantities is equal to the product ...
... Scholium . A proportion is an equation ; and making the product of the extremes equal to the product of the means is merely clearing the equation of fractions . THEOREM II . 14. If the product of two quantities is equal to the product ...
Page 33
... Scholium . If AD and AB have no common measure , the linear unit may be taken as small as we please , that is , so small that the remainders will be infinitesimal , and can be ncg- lected . 9. Corollary . The area of a square is the its ...
... Scholium . If AD and AB have no common measure , the linear unit may be taken as small as we please , that is , so small that the remainders will be infinitesimal , and can be ncg- lected . 9. Corollary . The area of a square is the its ...
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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.