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 9
... unit of measure . 2. Since the unit of measure is of the same kind as the thing measured , there are as many kinds of units as there are species of quantity . In Geometry , there are four species of quantity , called GEOMETRICAL ...
... unit of measure . 2. Since the unit of measure is of the same kind as the thing measured , there are as many kinds of units as there are species of quantity . In Geometry , there are four species of quantity , called GEOMETRICAL ...
Page 74
... unit : then will they be propor- tional to the intercepted arcs AB and DE .. m M Z E Let the angle M be a common unit ; and suppose , for example , that this unit is contained 7 times in the angle ACB , and 4 times in the angle DOE ACB ...
... unit : then will they be propor- tional to the intercepted arcs AB and DE .. m M Z E Let the angle M be a common unit ; and suppose , for example , that this unit is contained 7 times in the angle ACB , and 4 times in the angle DOE ACB ...
Page 77
... unit . If , therefore , any angle be measured by one - half or two - thirds of a quadrant , it will be equal to one - half or two - thirds of a right angle . PROPOSITION XVIII . THEOREM . An inscribed angle is measured by half of the ...
... unit . If , therefore , any angle be measured by one - half or two - thirds of a quadrant , it will be equal to one - half or two - thirds of a right angle . PROPOSITION XVIII . THEOREM . An inscribed angle is measured by half of the ...
Page 94
... unit . The unit adopted is a square described on the linear unit , as a side . PROPOSITION I. THEOREM . Parallelograms which have equal bases and equal altitudes , are equal . Let the parallelograms ABCD and EFGH have equal bases and ...
... unit . The unit adopted is a square described on the linear unit , as a side . PROPOSITION I. THEOREM . Parallelograms which have equal bases and equal altitudes , are equal . Let the parallelograms ABCD and EFGH have equal bases and ...
Page 98
... unit , the rectangle AEGF superficial unit , and we shall have , each to be will be the ABCD : 1 :: AB × AD : 1 ; ABCD AB × AD : hence , the area of 98 GEOMETRY .
... unit , the rectangle AEGF superficial unit , and we shall have , each to be will be the ABCD : 1 :: AB × AD : 1 ; ABCD AB × AD : hence , the area of 98 GEOMETRY .
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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