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 36
... hypothenuse and a side of the one equal to the hypothenuse and a side of the other , each to each , the triangles are equal in all respects . Let the right - angled triangles ABC and DEF have the hypothenuse AC equal to DF , and the ...
... hypothenuse and a side of the one equal to the hypothenuse and a side of the other , each to each , the triangles are equal in all respects . Let the right - angled triangles ABC and DEF have the hypothenuse AC equal to DF , and the ...
Seite 66
... hypothenuse CA equal to CB , and the side CD com- C B mon ; the triangles are , therefore , equal in all respects : hence , AD is equal to DB . Again , because CG is perpen- 67 dicular to AB , at its middle point , 66 GEOMETRY .
... hypothenuse CA equal to CB , and the side CD com- C B mon ; the triangles are , therefore , equal in all respects : hence , AD is equal to DB . Again , because CG is perpen- 67 dicular to AB , at its middle point , 66 GEOMETRY .
Seite 92
... hypothenuse AC , and the side BC equal to DC ; and consequently , they are equal in all respects ( B. I. , P. XVII . ) : hence , AB is equal to AD , and angle CAB is equal to the angle CAD . The tangents are therefore equal , and the ...
... hypothenuse AC , and the side BC equal to DC ; and consequently , they are equal in all respects ( B. I. , P. XVII . ) : hence , AB is equal to AD , and angle CAB is equal to the angle CAD . The tangents are therefore equal , and the ...
Seite 108
... hypothenuse of a right - angled triangle , is equal to the sum of the squares described on the two other sides . Let ABC be a triangle , right- angled at A : then BC AB + AC2 . = Construct the square BG on the side BC , the square AH ...
... hypothenuse of a right - angled triangle , is equal to the sum of the squares described on the two other sides . Let ABC be a triangle , right- angled at A : then BC AB + AC2 . = Construct the square BG on the side BC , the square AH ...
Seite 109
... hypothenuse dimin- ished by the square of the other side : thus , AB = 2 BC2 - AC2 ; or , AC2 BC AB . = - Cor . 2. If from the vertex of the right angle , a per- pendicular be drawn to the hypothenuse , dividing it into two segments ...
... hypothenuse dimin- ished by the square of the other side : thus , AB = 2 BC2 - AC2 ; or , AC2 BC AB . = - Cor . 2. If from the vertex of the right angle , a per- pendicular be drawn to the hypothenuse , dividing it into two segments ...
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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.