Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United StatesA.S. Barnes, 1885 - 512 Seiten |
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Seite 97
... ALTITUDE OF A TRIANGLE is the perpendicular distance from the vertex of any angle to the opposite side , or the ... base of the triangle . PARALLELOGRAM is the perpen- 5. The ALTITUDE OF A dicular BOOK IV Proportions of Figures- Measurement ...
... ALTITUDE OF A TRIANGLE is the perpendicular distance from the vertex of any angle to the opposite side , or the ... base of the triangle . PARALLELOGRAM is the perpen- 5. The ALTITUDE OF A dicular BOOK IV Proportions of Figures- Measurement ...
Seite 98
... base . 6. The ALTITUDE OF A TRAPEZOID is the perpendicular distance between its parallel sides . These sides are called bases ; one the upper , and the other , the lower base . 7. The AREA OF A SURFACE is its numerical value expressed ...
... base . 6. The ALTITUDE OF A TRAPEZOID is the perpendicular distance between its parallel sides . These sides are called bases ; one the upper , and the other , the lower base . 7. The AREA OF A SURFACE is its numerical value expressed ...
Seite 99
... base and an equal altitude . Let the triangle ABC , and the parallelogram ABFD , have equal bases and equal altitudes : then the triangle is equal to one half of the parallelogram . For , let them be SO placed that the base of the ...
... base and an equal altitude . Let the triangle ABC , and the parallelogram ABFD , have equal bases and equal altitudes : then the triangle is equal to one half of the parallelogram . For , let them be SO placed that the base of the ...
Seite 103
... base and altitude ; that is , the number of superficial units in the rectangle , is equal to the product of the number of linear units in its base by the number of linear units in its altitude . The product of two lines is sometimes ...
... base and altitude ; that is , the number of superficial units in the rectangle , is equal to the product of the number of linear units in its base by the number of linear units in its altitude . The product of two lines is sometimes ...
Seite 104
... base and altitude . Let ABC be a triangle , BC its base , and AD its altitude : then its area is equal to BC AD . E For , from C , draw CE parallel to BA , and from A , draw AE parallel to BC . The area of the parallelogram BCEA is BC x ...
... base and altitude . Let ABC be a triangle , BC its base , and AD its altitude : then its area is equal to BC AD . E For , from C , draw CE parallel to BA , and from A , draw AE parallel to BC . The area of the parallelogram BCEA is BC x ...
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Häufige Begriffe und Wortgruppen
ABCD AC² adjacent angles altitude apothem Applying logarithms bisects centre chord circle circumference circumscribed cone consequently convex surface cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle inscribed intersection isosceles less Let ABC log sin lower base lune mantissa number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron principle demonstrated prism PROBLEM.-In PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment semi-circumference similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square straight line subtracting supplement Tang tangent THEOREM THEOREM.-Show tri-rectangular triangle ABC triangular prism triedral angle upper base vertex vertices volume whence
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Seite 28 - If two triangles have two sides of the one equal to two sides of the...
Seite 90 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Seite 18 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.
Seite 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Seite 253 - For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...
Seite 61 - 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.
Seite 94 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Seite 126 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Seite 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 125 - THEOREM. Similar triangles are to each other as the squares of their homologous sides.