Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
From inside the book
Results 1-5 of 58
Page 6
... 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 ; and , taking away the common angle ACD ,. we have , ACE DCB . Hence , the proposition is proved . Cor . 1. If one of the angles about all of the others will be right angles also . each of its ...
... manner , we find , ACD + ACE = 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 about all of the others will be right angles also . each of its ...
Page 25
... manner that the angle A shall coincide with the angle D , the side AB taking the direction DE , and AA B E Then , because AB is . the side AC the direction DF . equal to DE , the vertex B will coincide with the vertex E ; and because AC ...
... manner that the angle A shall coincide with the angle D , the side AB taking the direction DE , and AA B E Then , because AB is . the side AC the direction DF . equal to DE , the vertex B will coincide with the vertex E ; and because AC ...
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 ...
Page 41
... manner , it may be shown that BGH and GHC are equal . Cor . 3. If a straight line meet two parallels , the opposite exterior and interior angles will be equal . The angles DHG and HGA are equal , from what has just been shown . The ...
... manner , it may be shown that BGH and GHC are equal . Cor . 3. If a straight line meet two parallels , the opposite exterior and interior angles will be equal . The angles DHG and HGA are equal , from what has just been shown . The ...
Other editions - View all
Common terms and phrases
ABē ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following