Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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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 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 be ...
... unit : then will they be propor- tional to the intercepted arcs AB and DE . M 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 be ...
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 will be the superficial unit , and we shall have , ABCD : 1 :: AB × AD 1 ; ABCD AB × AD : hence , the area of 98 GEOMETRY .
... unit , the rectangle AEGF will be the superficial unit , and we shall have , ABCD : 1 :: AB × AD 1 ; ABCD AB × AD : hence , the area of 98 GEOMETRY .
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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