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 60
... when its circumference touches all of the sides of the polygon . Ө 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 .
... when its circumference touches all of the sides of the polygon . Ө 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 and AC their sum : then will AC2 = AB2 + BC + 2AB × BC . = On ...
... 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 and AC their sum : then will AC2 = AB2 + BC + 2AB × BC . = On ...
Page 102
... described on a line is equal to four times the square described on half the line . PROPOSITION IX . THEOREM . The square described on the difference of two lines is equal to the sum of the squares described on the lines , dimin ished by ...
... described on a line is equal to four times the square described on half the line . PROPOSITION IX . THEOREM . The square described on the difference of two lines is equal to the sum of the squares described on the lines , dimin ished by ...
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Common terms and phrases
AB² AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence