An Elementary Geometry |
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Page 31
... base ; as B D. B 4. The Altitude of a parallelogram is the perpendicular distance from the opposite side to the base ; as IK . 5. The Altitude of a trapezoid is the perpendicular distance between its paral- lel sides ; as PR ...
... base ; as B D. B 4. The Altitude of a parallelogram is the perpendicular distance from the opposite side to the base ; as IK . 5. The Altitude of a trapezoid is the perpendicular distance between its paral- lel sides ; as PR ...
Page 32
... base and altitude . Let ABCD be a rectangle ; its area = AD × AB . BOPQRC G V F M S L AHIJK D Suppose AB and AD to be divided into any number of equal parts , A E , EF , AH , HI , & c . , and through the E points of division , lines EL ...
... base and altitude . Let ABCD be a rectangle ; its area = AD × AB . BOPQRC G V F M S L AHIJK D Suppose AB and AD to be divided into any number of equal parts , A E , EF , AH , HI , & c . , and through the E points of division , lines EL ...
Page 33
... base and altitude . Let DF be the altitude of the paral- lelogram ABCD ; then the area of ABCD = A D X D F. EB A 1 FC D At A draw the perpendicular A E meet- ing CB produced in E ; AEFD is a rectangle equivalent to the parallelogram ...
... base and altitude . Let DF be the altitude of the paral- lelogram ABCD ; then the area of ABCD = A D X D F. EB A 1 FC D At A draw the perpendicular A E meet- ing CB produced in E ; AEFD is a rectangle equivalent to the parallelogram ...
Page 35
... altitude and the line joining the middle points of the sides which are not parallel . THEOREM VI . 16. A line drawn ... base DE and the same altitude , viz . , the perpendicular distance between the two parallels DE and BC ...
... altitude and the line joining the middle points of the sides which are not parallel . THEOREM VI . 16. A line drawn ... base DE and the same altitude , viz . , the perpendicular distance between the two parallels DE and BC ...
Page 44
... base is 20 feet and altitude 12 feet ? 3. What is the area of a triangle whose base is 14 feet and altitude 8 feet ? 4. What is the square surface of a board 15 feet long , and 16 inches wide at one end and 9 inches at the other ? What ...
... base is 20 feet and altitude 12 feet ? 3. What is the area of a triangle whose base is 14 feet and altitude 8 feet ? 4. What is the square surface of a board 15 feet long , and 16 inches wide at one end and 9 inches at the other ? What ...
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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.