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 22
... angle ACE ( A. 3 ) , there remains , ACD ECB . In like manner , we find , A D B ACDACE ACD + DCB ; and , taking away the common angle ACD , we have , ACE = DCB . Hence , the proposition is proved . Cor . 1. If one of the angles ... ACB , BCD ...
... angle ACE ( A. 3 ) , there remains , ACD ECB . In like manner , we find , A D B ACDACE ACD + DCB ; and , taking away the common angle ACD , we have , ACE = DCB . Hence , the proposition is proved . Cor . 1. If one of the angles ... ACB , BCD ...
Seite 31
... angle B is equal to the angle C ; which was to be proved . B Cor . 1. An ... ACB : then is AC equal to AB , and consequently , the triangle is isosceles ... angle ACB equal to the included angle DBC , by hypothesis : hence , the two ...
... angle B is equal to the angle C ; which was to be proved . B Cor . 1. An ... ACB : then is AC equal to AB , and consequently , the triangle is isosceles ... angle ACB equal to the included angle DBC , by hypothesis : hence , the two ...
Seite 32
... angle is opposite the greater side . In the triangle ABC , let the angle ACB be greater than the angle ABC : then the side AB is greater than the side AC . For , draw CD , making the angle BCD equal to the angle B ( Post . 7 ) : then ...
... angle is opposite the greater side . In the triangle ABC , let the angle ACB be greater than the angle ABC : then the side AB is greater than the side AC . For , draw CD , making the angle BCD equal to the angle B ( Post . 7 ) : then ...
Seite 33
... angles ABC and FBC equal , because both are right angles : hence , the angles ACB and FCB are equal ( P. V. ) . But ACB is , by a hypothesis , a right angle : hence , FCB must also be a right angle , and consequently , the line ACF must ...
... angles ABC and FBC equal , because both are right angles : hence , the angles ACB and FCB are equal ( P. V. ) . But ACB is , by a hypothesis , a right angle : hence , FCB must also be a right angle , and consequently , the line ACF must ...
Seite 76
... angles ACB and DOE be commensurable ; that is , be exactly measured by a common unit : then are they pro- portional to the intercepted arcs AB and DE . m n B 8 M Let the angle M be a common unit ; and suppose , for example , that this ...
... angles ACB and DOE be commensurable ; that is , be exactly measured by a common unit : then are they pro- portional to the intercepted arcs AB and DE . m n B 8 M Let the angle M be a common unit ; and suppose , for example , that this ...
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Häufige Begriffe und Wortgruppen
AB² AC² altitude angle is equal apothem Applying logarithms axis base and altitude base multiplied bisects centre chord circumference cone consequently convex surface corresponding cosec cosine cotangent cylinder denote diagonals diameter distance divided draw drawn edges equal altitudes equal in volume equilateral feet find the area formula frustum given line given point greater hence homologous hypothenuse included angle inscribed circle inscribed polygon intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROBLEM.-To PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium segment similar sine slant height sphere spherical angle spherical polygon spherical triangle square straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices 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.