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
... homologous . The corresponding angles are homologous angles , the corresponding sides are homologous sides , the corresponding diagonals are homologous diagonals , and so on . 3. SIMILAR ARCS , SECTORS , or SEGMENTS , in different cir ...
... homologous . The corresponding angles are homologous angles , the corresponding sides are homologous sides , the corresponding diagonals are homologous diagonals , and so on . 3. SIMILAR ARCS , SECTORS , or SEGMENTS , in different cir ...
Seite 122
... homologous . Cor . 2. The homologous angles are those included by sides respectively parallel or perpendicular to each other . Scholium . When two triangles have their sides perpen- dicular , each to each , they may have a different ...
... homologous . Cor . 2. The homologous angles are those included by sides respectively parallel or perpendicular to each other . Scholium . When two triangles have their sides perpen- dicular , each to each , they may have a different ...
Seite 124
... homologous sides are proportional : hence , BC : AB :: AB : BD . In like manner , BC : AC :: AC : DC ; which was to be proved . 3 ° . AD is a mean proportional between BD and DC . For , the triangles ADB and ADC being similar , their ...
... homologous sides are proportional : hence , BC : AB :: AB : BD . In like manner , BC : AC :: AC : DC ; which was to be proved . 3 ° . AD is a mean proportional between BD and DC . For , the triangles ADB and ADC being similar , their ...
Seite 126
... homologous , DE is parallel to BC , and we have , AD : AB :: AE : AC ; hence ( B. II . , P. IV . ) , we have , ADE : ABE :: ABE ABC ; : that is , ABE is a mean proportional between ADE and ABC . B E BOOK IV . PROPOSITION XXV . THEOREM ...
... homologous , DE is parallel to BC , and we have , AD : AB :: AE : AC ; hence ( B. II . , P. IV . ) , we have , ADE : ABE :: ABE ABC ; : that is , ABE is a mean proportional between ADE and ABC . B E BOOK IV . PROPOSITION XXV . THEOREM ...
Seite 127
... homologous sides . Let the triangles ABC and DEF be similar , the angle A being equal to the angle D , B to E , and C to F : then the triangles are to each other as the squares of any two homologous sides . Because the angles A and D ...
... homologous sides . Let the triangles ABC and DEF be similar , the angle A being equal to the angle D , B to E , and C to F : then the triangles are to each other as the squares of any two homologous sides . Because the angles A and D ...
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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.