Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 18
... drawn between two points . 12. The shortest distance between any two points is mea- sured on the straight line which joins them . 13. Through the same point , only one line can be drawn parallel to a given line .. POSTULATES . 1. A ...
... drawn between two points . 12. The shortest distance between any two points is mea- sured on the straight line which joins them . 13. Through the same point , only one line can be drawn parallel to a given line .. POSTULATES . 1. A ...
Page 19
... drawn to a given line , either from a point without , or from a point on the line . 7. A line may be drawn , making with a given line an angle equal to a given angle . 8. A line may be drawn through a given point , parallel to a given ...
... drawn to a given line , either from a point without , or from a point on the line . 7. A line may be drawn , making with a given line an angle equal to a given angle . 8. A line may be drawn through a given point , parallel to a given ...
Page 28
... drawn , making the angle CAG equal to the angle D ( Post . 7 ) ; make AG equal to -DE , and draw GC . Then will the triangles AGC and DEF have two sides and the included angle of the one equal to two sides and the included angle . of ...
... drawn , making the angle CAG equal to the angle D ( Post . 7 ) ; make AG equal to -DE , and draw GC . Then will the triangles AGC and DEF have two sides and the included angle of the one equal to two sides and the included angle . of ...
Page 31
... drawn from the vertex of an isosceles triangle . to the middle of the base , bisects the vertical angle , and is per ... draw DC . Then , in the triangles ABC , DBC , we have the side BD equal to AC , by construction , the side BC common ...
... drawn from the vertex of an isosceles triangle . to the middle of the base , bisects the vertical angle , and is per ... draw DC . Then , in the triangles ABC , DBC , we have the side BD equal to AC , by construction , the side BC common ...
Page 32
... draw CD , making the angle BCD equal to the angle B ( Post . 7 ) : then , in the triangle DCB , we have the angles DCB and DBC equal : hence , the opposite sides DB and DC are equal ( P. XII . ) . In the triangle ACD , we bave ( P. VII ...
... draw CD , making the angle BCD equal to the angle B ( Post . 7 ) : then , in the triangle DCB , we have the angles DCB and DBC equal : hence , the opposite sides DB and DC are equal ( P. XII . ) . In the triangle ACD , we bave ( P. VII ...
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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