Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 60
... its circumference touches all of the sides of the polygon . OOD хо о POSTULATE . A circumference can be described from any point as a centre , and with any radius . PROPOSITION I. THEOREM . Any diameter divides the circle , 60 GEOMETRY .
... its circumference touches all of the sides of the polygon . OOD хо о POSTULATE . A circumference can be described from any point as a centre , and with any radius . PROPOSITION I. THEOREM . Any diameter divides the circle , 60 GEOMETRY .
Page 77
... described from the vertex of any angle , as a cen- tre , and with a fixed radius , the arc intercepted between the sides of the angle may be taken as the measure of the angle . In Geometry , the right angle which is measured by a ...
... described from the vertex of any angle , as a cen- tre , and with a fixed radius , the arc intercepted between the sides of the angle may be taken as the measure of the angle . In Geometry , the right angle which is measured by a ...
Page 94
... 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 equal altitudes : then will the ...
... 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 equal altitudes : then will the ...
Page 101
... described on the sum of two lines is equal to the sum of the squares described on the lines , increased by twice the rectangle of the lines . Let AB and BC be two lines , E H D and AC their sum : then will F AC2 = AB2 + BC2 + 2AB × BC ...
... described on the sum of two lines is equal to the sum of the squares described on the lines , increased by twice the rectangle of the lines . Let AB and BC be two lines , E H D and AC their sum : then will F AC2 = AB2 + BC2 + 2AB × BC ...
Page 102
... described on a line is described on half the line . will also be equal : hence , the equal to four times the square PROPOSITION IX . THEOREM . The square described on the difference of two lines is equal to the sum of the squares described ...
... described on a line is described on half the line . will also be equal : hence , the equal to four times the square PROPOSITION IX . THEOREM . The square described on the difference of two lines is equal to the sum of the squares described ...
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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