Elements of Geometry and Trigonometry |
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Page 24
... cosine , tang , or cotang , as the case may be ; the number there found is the logarithm required . log sin 19 ° 55 ' log tan 19 ° 55 ' Thus , 9.532312 9.559097 45 ° , look for the degrees at for the minutes in the right If the angle is ...
... cosine , tang , or cotang , as the case may be ; the number there found is the logarithm required . log sin 19 ° 55 ' log tan 19 ° 55 ' Thus , 9.532312 9.559097 45 ° , look for the degrees at for the minutes in the right If the angle is ...
Page 25
... cosine of 53 ° 40 ′ 40 ′′ . OPERATION . log cos 53 ° 40 ' 9.772675 Tabular difference 2.86 No. of seconds 40 Product 114.40 to be subtracted 114 log cos 53 ° 40 ′ 40 ′′ 9.772561 If the arc is greater than 90 ° , we find the required ...
... cosine of 53 ° 40 ′ 40 ′′ . OPERATION . log cos 53 ° 40 ' 9.772675 Tabular difference 2.86 No. of seconds 40 Product 114.40 to be subtracted 114 log cos 53 ° 40 ′ 40 ′′ 9.772561 If the arc is greater than 90 ° , we find the required ...
Page 26
... cosine or a cotangent . 1. Find the arc sine 9.422248 . Given logarithm Next less in table . EXAMPLES . corresponding to the logarithmic OPERATION . 9.422248 9.421857 • 15 ° 19 ′ Tabular difference 7.68 ) 391.00 ( 51 " , to be added ...
... cosine or a cotangent . 1. Find the arc sine 9.422248 . Given logarithm Next less in table . EXAMPLES . corresponding to the logarithmic OPERATION . 9.422248 9.421857 • 15 ° 19 ′ Tabular difference 7.68 ) 391.00 ( 51 " , to be added ...
Page 27
... cosine 9.944599 . Ans . 28 ° 19 ′ 45 " . SOLUTION OF RIGHT - ANGLED TRIANGLES . 37. In what follows , we shall designate the three angles of every triangle , by the capital letters A , B , and C , A denoting the right angle ; and the ...
... cosine 9.944599 . Ans . 28 ° 19 ′ 45 " . SOLUTION OF RIGHT - ANGLED TRIANGLES . 37. In what follows , we shall designate the three angles of every triangle , by the capital letters A , B , and C , A denoting the right angle ; and the ...
Page 28
... cosine of the angle at the base . 3. The perpendicular is equal to the base into the tan- gent of the angle at the base . 4. The sine of the angle at the base is equal to the perpendicular divided by the hypothenuse . 5. The cosine of ...
... cosine of the angle at the base . 3. The perpendicular is equal to the base into the tan- gent of the angle at the base . 4. The sine of the angle at the base is equal to the perpendicular divided by the hypothenuse . 5. The cosine of ...
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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
AB² ABCD AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm 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 polygon right-angled triangle Scholium secant segment semi-circumference side BC similar Sine slant height sphere spherical angle spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prisms upper base vertex vertices 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...