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 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 , 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 line . NOTE . In making references , the following abbreviations are employed , viz . ‹ A. for Axiom ...
... 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 line . NOTE . In making references , the following abbreviations are employed , viz . ‹ A. for Axiom ...
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 the ...
... 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 the ...
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 have ( 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 have ( P. VII ...
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence