Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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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 , ACD + ACE ACD + DCB ; E B and , taking away the common angle ACD , we have , ACE DCB . Hence , the proposition is proved . Cor . 1. If one of the angles about C all of the others will be right angles also . each of ...
... manner , we find , ACD + ACE ACD + DCB ; E B and , taking away the common angle ACD , we have , ACE DCB . Hence , the proposition is proved . Cor . 1. If one of the angles about C all of the others will be right angles also . each of ...
Page 25
... manner that the angle A shall coincide with the angle D , the side AB taking the direction DE , and A A B the side AC the direction DF . Then , because AB is equal to DE , the vertex 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 A A B the side AC the direction DF . Then , because AB is equal to DE , the vertex 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 will be a right angle also hence , if a line is perpendicular to one of two parallels , 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 will be a right angle also hence , if a line is perpendicular to one of two parallels , it is perpendicular to ...
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Common terms and phrases
ABē ABCD ACē adjacent angles altitude apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine slant height sphere spherical polygon spherical triangle square subtracted Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence
Popular passages
Page 126 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 59 - 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 18 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Page 104 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 6 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 28 - If two triangles have two sides of the one equal to two sides of the...
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 99 - The area of a parallelogram is equal to the product of its base and altitude.
Page 172 - If two planes are perpendicular to 'each other, a straight line drawn in one of them, perpendicular to their intersection, will be perpendicular to the other.
Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.