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 14
... vertex . An angle -B is designated by naming its sides , or sometimes by simply naming its vertex ; thus , the above is called the angle BAC , or simply , the angle A. straight line meets 11. When one another , the two angles which they ...
... vertex . An angle -B is designated by naming its sides , or sometimes by simply naming its vertex ; thus , the above is called the angle BAC , or simply , the angle A. straight line meets 11. When one another , the two angles which they ...
Seite 16
... vertices of two angles , not consecutive . 24. A BASE of a polygon is any one of its sides on which the polygon is supposed to stand . 25. Triangles may be classified with reference to either their sides , or their angles . When ...
... vertices of two angles , not consecutive . 24. A BASE of a polygon is any one of its sides on which the polygon is supposed to stand . 25. Triangles may be classified with reference to either their sides , or their angles . When ...
Seite 25
... vertex E ; and because AC is equal to DF , the vertex C will coincide with the vertex F ; consequently , the side BC will coincide with the side EF ( A. 11 ) . The two triangles , therefore , coincide through- out , and are consequently ...
... vertex E ; and because AC is equal to DF , the vertex C will coincide with the vertex F ; consequently , the side BC will coincide with the side EF ( A. 11 ) . The two triangles , therefore , coincide through- out , and are consequently ...
Seite 26
... vertex C will coincide with the vertex F ; and because the angle C is equal to the angle F , the side CA will take the direction FD . Now , the vertex A being at the same time on the lines ED and FD , it must be at their intersection D ...
... vertex C will coincide with the vertex F ; and because the angle C is equal to the angle F , the side CA will take the direction FD . Now , the vertex A being at the same time on the lines ED and FD , it must be at their intersection D ...
Seite 30
... angles opposite the equal sides are equal . Let BAC be an isosceles triangle , having the side AB equal to the side AC : then the angle C is equal to the angle B. 31 Join the vertex A and the middle point D 30 GEOMETRY.
... angles opposite the equal sides are equal . Let BAC be an isosceles triangle , having the side AB equal to the side AC : then the angle C is equal to the angle B. 31 Join the vertex A and the middle point D 30 GEOMETRY.
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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
Beliebte Passagen
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.