Elements of Geometry and Trigonometry |
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Page 19
... cosine of an arc is the sine of the complement of the arc . Thus , NM is the cosine of AM , and NM ' is the cosine of AM ' . These lines are respectively equal to OP and OP ' . It is evident , from the equal triangles of the PLANE ...
... cosine of an arc is the sine of the complement of the arc . Thus , NM is the cosine of AM , and NM ' is the cosine of AM ' . These lines are respectively equal to OP and OP ' . It is evident , from the equal triangles of the PLANE ...
Page 20
... cosine of an arc is equal to the cosine of its supple- ment . 28. The tangent of an arc is the perpendicular to the radius at one extremity of the arc , limited by the prolon- gation of the diameter through the other extremity Thus , AT ...
... cosine of an arc is equal to the cosine of its supple- ment . 28. The tangent of an arc is the perpendicular to the radius at one extremity of the arc , limited by the prolon- gation of the diameter through the other extremity Thus , AT ...
Page 21
... cosine , tangent , and cotangent of the angle AOM , well as of the arc AM . 30. It is often convenient to use some other radius than 1 ; in such case , the functions of the arc , to the radius 1 , may be reduced to corresponding ...
... cosine , tangent , and cotangent of the angle AOM , well as of the arc AM . 30. It is often convenient to use some other radius than 1 ; in such case , the functions of the arc , to the radius 1 , may be reduced to corresponding ...
Page 22
... COSINE , TANGENT , OR COTANGENT , is the sine , cosine , tangent , or cotangent of an arc whose radius is 1 . A TABLE OF NATURAL SINES is a table by means of which the natural sine , cosine , tangent , or cotangent of any arc , may be ...
... COSINE , TANGENT , OR COTANGENT , is the sine , cosine , tangent , or cotangent of an arc whose radius is 1 . A TABLE OF NATURAL SINES is a table by means of which the natural sine , cosine , tangent , or cotangent of any arc , may be ...
Page 23
... cosine and the cotangent of an arc are , respectively , the sine and the tangent of the complement of that are ( Arts . 26 and 28 ) : hence , the columns designated sine and tang , at the top of the page , are designated cosine and ...
... cosine and the cotangent of an arc are , respectively , the sine and the tangent of the complement of that are ( Arts . 26 and 28 ) : hence , the columns designated sine and tang , at the top of the page , are designated cosine and ...
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Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |
Common terms and phrases
ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cos²a 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 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 semi-circumference 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 volume whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 100 - The area of a triangle is equal to half the product of its base by its altitude.
Page 99 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 59 - A chord is a straight line joining the extremities of an arc.
Page 124 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 43 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 52 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 123 - Similar triangles are to each other as the squares of their homologous sides.
Page 182 - The upper end of the frustum of a pyramid or cone is called the upper base...