Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page iii
... manner impairing the gener- ality of the truths evolved . The term solid , used not only by Legendre , but by many other authors , to denote a limited portion of space , seems calculated to introduce the foreign idea of matter into a ...
... manner impairing the gener- ality of the truths evolved . The term solid , used not only by Legendre , but by many other authors , to denote a limited portion of space , seems calculated to introduce the foreign idea of matter into a ...
Page vi
... Manner of Using the Table ,. Multiplication by Logarithms , Division by Logarithms , ... Arithmetical Complement ,. Raising to Powers by Logarithms , Extraction of Roots by Logarithms , PLANE TRIGONOMETRY . Plane Trigonometry Defined ...
... Manner of Using the Table ,. Multiplication by Logarithms , Division by Logarithms , ... Arithmetical Complement ,. Raising to Powers by Logarithms , Extraction of Roots by Logarithms , PLANE TRIGONOMETRY . Plane Trigonometry Defined ...
Page 22
... manner , we find , ACDACE ACD + DCB ; = and , taking away the common angle ACD , we have , ACE = DCB . Hence , the proposition is proved . B Cor . 1. If one of the angles about C is a right angle , all of the others are right angles ...
... manner , we find , ACDACE ACD + DCB ; = and , taking away the common angle ACD , we have , ACE = DCB . Hence , the proposition is proved . B Cor . 1. If one of the angles about C is a right angle , all of the others are right angles ...
Page 25
... manner that the angle A shall coincide with the angle D , the side AB taking the direction DE , and the side AC the B direction DF . Then , because AB is equal to DE , the ver- tex B will coincide with the vertex E ; and because AC is ...
... manner that the angle A shall coincide with the angle D , the side AB taking the direction DE , and the side AC the B direction DF . Then , because AB is equal to DE , the ver- tex B will coincide with the vertex E ; and because AC is ...
Page 40
... manner , it may be proved that the sum of HGA and GHC is equal to two right angles . Cor . 1. If HGB is a right angle , GHD is a right angle also : hence , if a line is perpendicular to one of two par- allels , it is perpendicular to ...
... manner , it may be proved that the sum of HGA and GHC is equal to two right angles . Cor . 1. If HGB is a right angle , GHD is a right angle also : hence , if a line is perpendicular to one of two par- allels , it is perpendicular to ...
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Common terms and phrases
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
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 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...
Page 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.
Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 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...
Page 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.
Page 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.
Page 126 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 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.
Page 125 - THEOREM. Similar triangles are to each other as the squares of their homologous sides.