Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 27
... extremities of any side , their sum will be . less than that of the two remaining sides of the triangle . A Let be any point within the triangle BAC , and let the lines OB , OC , be drawn to the extremities of any side , as BC : then ...
... extremities of any side , their sum will be . less than that of the two remaining sides of the triangle . A Let be any point within the triangle BAC , and let the lines OB , OC , be drawn to the extremities of any side , as BC : then ...
Page 35
... extremities of the line : 2o . Any point , without the perpendicular , will be unequally distant from the extremities . Let АВ be a given straight line , C its middle point , and EF the perpendicular . Then will any point of EF be ...
... extremities of the line : 2o . Any point , without the perpendicular , will be unequally distant from the extremities . Let АВ be a given straight line , C its middle point , and EF the perpendicular . Then will any point of EF be ...
Page 59
... extremities of arc . Any chord belongs to two arcs : the smaller one is meant , unless the contrary is expressed . 6. A SEGMENT is a part of a circle included between an arc and its chord . 7. A SECTOR is a part of a circle included ...
... extremities of arc . Any chord belongs to two arcs : the smaller one is meant , unless the contrary is expressed . 6. A SEGMENT is a part of a circle included between an arc and its chord . 7. A SECTOR is a part of a circle included ...
Page 61
... extremity , as A : then will AB be greater than AD . Draw the radius CD . In the tri- angle ACD , we have AD less than ( B. I. , P. equal to A the sum of AC and CD VII . ) . But this sum is AB ( D. 3 ) : hence , AB is greater than AD ...
... extremity , as A : then will AB be greater than AD . Draw the radius CD . In the tri- angle ACD , we have AD less than ( B. I. , P. equal to A the sum of AC and CD VII . ) . But this sum is AB ( D. 3 ) : hence , AB is greater than AD ...
Page 90
... extremity ; and consequently , they are tangent to the given circle ( P. IX . ) . Corollary . The right - angled triangles ABC and ADC , have a common hypothenuse AC , and the side BC equal to DC ; and consequently , they are equal in ...
... extremity ; and consequently , they are tangent to the given circle ( P. IX . ) . Corollary . The right - angled triangles ABC and ADC , have a common hypothenuse AC , and the side BC equal to DC ; and consequently , they are equal in ...
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Common terms and phrases
AB² 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