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 78
... similar manner , it may be shown that the fourth term can not be less than AD : hence , it must be equal to AD ; therefore , we have , angle ACB angle ACD :: arc AB : arc AD ; which was to be proved . Cor . 1. The intercepted arcs are ...
... similar manner , it may be shown that the fourth term can not be less than AD : hence , it must be equal to AD ; therefore , we have , angle ACB angle ACD :: arc AB : arc AD ; which was to be proved . Cor . 1. The intercepted arcs are ...
Seite 97
... SIMILAR POLYGONS are polygons which are mutually equiangular , and which have the sides about the equal angles , taken in the same order , proportional . 2. In similar polygons , the parts which are similarly placed in each , are called ...
... SIMILAR POLYGONS are polygons which are mutually equiangular , and which have the sides about the equal angles , taken in the same order , proportional . 2. In similar polygons , the parts which are similarly placed in each , are called ...
Seite 117
... similar . Let the triangles ABC and DEF have the angle A equal to the angle D , the angle B to the angle E , and the angle C to the angle F : then they are similar . For , place the triangle DEF upon the triangle ABC , so that the angle ...
... similar . Let the triangles ABC and DEF have the angle A equal to the angle D , the angle B to the angle E , and the angle C to the angle F : then they are similar . For , place the triangle DEF upon the triangle ABC , so that the angle ...
Seite 118
... similar ( D. 1 ) ; which was to be proved . Cor . If two triangles have two angles in one , equal to two angles in the other , each to each , they are similar ( B. I. , P. XXV . , C. 2 ) . PROPOSITION XIX . THEOREM . Triangles which ...
... similar ( D. 1 ) ; which was to be proved . Cor . If two triangles have two angles in one , equal to two angles in the other , each to each , they are similar ( B. I. , P. XXV . , C. 2 ) . PROPOSITION XIX . THEOREM . Triangles which ...
Seite 119
... similar . For , on BA lay off BG equal to ED ; on BC on BC lay off EF , and draw BH equal to GH . Then , because BG is equal to ED , and BH to EF , A A F we have , BA : BG :: BC : BH ; hence , GH is parallel to AC ( P. XVI . ) ; and ...
... similar . For , on BA lay off BG equal to ED ; on BC on BC lay off EF , and draw BH equal to GH . Then , because BG is equal to ED , and BH to EF , A A F we have , BA : BG :: BC : BH ; hence , GH is parallel to AC ( P. XVI . ) ; and ...
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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.