Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United StatesA.S. Barnes & Company, 1869 - 455 páginas |
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Página vii
... Circumference of a Circle , To find the Diameter of a Circle , To find the length of an Arc , 116 116 ... 117 Area of a Circle , 117 Area of a Sector , Area of a Segment , 118 118 Area of a Circular Ring , 119 ... ... Area of the ...
... Circumference of a Circle , To find the Diameter of a Circle , To find the length of an Arc , 116 116 ... 117 Area of a Circle , 117 Area of a Sector , Area of a Segment , 118 118 Area of a Circular Ring , 119 ... ... Area of the ...
Página 59
... circumference . 3. A DIAMETER is a straight line drawn through the centre and terminating in the circumference . All radii of the same circle are equal . All diameters are also equal , and each is double the radius . an 4. An ARC is any ...
... circumference . 3. A DIAMETER is a straight line drawn through the centre and terminating in the circumference . All radii of the same circle are equal . All diameters are also equal , and each is double the radius . an 4. An ARC is any ...
Página 60
... circumference , and whose sides are chords . 9. An INSCRIBED POLYGON is a poly- gon whose vertices are in the circumfer- ence , and whose sides are chords . 10. A SECANT is a straight line which cuts the circumference in two points . 11 ...
... circumference , and whose sides are chords . 9. An INSCRIBED POLYGON is a poly- gon whose vertices are in the circumfer- ence , and whose sides are chords . 10. A SECANT is a straight line which cuts the circumference in two points . 11 ...
Página 61
... circumference , into two equal parts . Let AEBF be a circle , and AB any diameter : then will it divide the circle and its circumference into two equal parts . A F For , let AFB be applied to AEB , the diameter AB remaining common ; E ...
... circumference , into two equal parts . Let AEBF be a circle , and AB any diameter : then will it divide the circle and its circumference into two equal parts . A F For , let AFB be applied to AEB , the diameter AB remaining common ; E ...
Página 62
... circumference in more thar two points . Let AEBF be a circumference , and АВ a straight line : then AB cannot meet the circumference in more than two points . For , suppose that they could meet in three points . We should then have ...
... circumference in more thar two points . Let AEBF be a circumference , and АВ a straight line : then AB cannot meet the circumference in more than two points . For , suppose that they could meet in three points . We should then have ...
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Términos y frases comunes
ABCD altitude apothem Applying logarithms centre chord circle circumference circumscribed complement 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 log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right-angled triangle Scholium segment semi-circumference side BC similar sine 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 vertices volume whence write the following
Pasajes populares
Página 85 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Página 28 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.
Página 104 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Página 90 - To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles A and B by the lines AO and BO, meeting at the point 0.
Página 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 58 - ABM'" ; that is, the functions of — a are the same as the functions of 360° — a. From an inspection of the figure, we shall discover the following relations, viz. : sin (— a) = — sin a ; cos (— a) = cos a ; tan (—a) = — tan a ; cot (— a) = — cot a ; sec ( - a) = sec a ; cosec ( — a) = — cosec a.
Página 243 - AD c, have two sides, and the included angle of the one equal to two sides and the included angle of the other, each \ to each, and are equal in all their parts...
Página 154 - Similar arcs are to each other as their radii; and similar sectors are to each other as the squares of their radii.
Página 57 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Página 16 - A DIAGONAL of a polygon is a line joining the vertices of two angles, not consecutive.