Elements of Plane and Spherical Trigonometry with Logarithmic and Other Mathematical Tables and Examples of Their Use and Hints on the Art of ComputationH. Holt, 1882 - 104 páginas |
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Página 113
... triangle , measure the respective face - angles MOP , POQ , QOM of the trihedral angle . Therefore the six parts of the trihedral angle are represented PAGE FUNDAMENTAL PRINCIPLES Preliminary notions, 113 Fundamental equations, 116 Polar ...
... triangle , measure the respective face - angles MOP , POQ , QOM of the trihedral angle . Therefore the six parts of the trihedral angle are represented PAGE FUNDAMENTAL PRINCIPLES Preliminary notions, 113 Fundamental equations, 116 Polar ...
Página 120
... polar triangle of the other . It is shown in geometry that the relation of a triangle to its . polar triangle is reciprocal ; that is , if X and Y are two triangles , and Y is the polar triangle of X , then X is the polar triangle of Y ...
... polar triangle of the other . It is shown in geometry that the relation of a triangle to its . polar triangle is reciprocal ; that is , if X and Y are two triangles , and Y is the polar triangle of X , then X is the polar triangle of Y ...
Página 121
... polar triangles to every given triangle . To avoid doubt which triangle is to be chosen , we take for each vertex of the polar triangle that pole of each side of the given triangle which is on the side toward the triangle . R C B For ...
... polar triangles to every given triangle . To avoid doubt which triangle is to be chosen , we take for each vertex of the polar triangle that pole of each side of the given triangle which is on the side toward the triangle . R C B For ...
Página 122
... triangle , and thus obtain equations between these parts . Let us put a ' , b ' , c ' , A ' , B ' , C ' , the sides and opposite angles of the polar triangle . Since the general equations ( 1 ) are true for every triangle , they are ...
... triangle , and thus obtain equations between these parts . Let us put a ' , b ' , c ' , A ' , B ' , C ' , the sides and opposite angles of the polar triangle . Since the general equations ( 1 ) are true for every triangle , they are ...
Página 123
Simon Newcomb. of the polar triangle gives a much shorter and more elegant mode of deducing them . 103. In the solution of spherical triangles we require for- mulæ which shall express any three parts in terms of the remaining three ; the ...
Simon Newcomb. of the polar triangle gives a much shorter and more elegant mode of deducing them . 103. In the solution of spherical triangles we require for- mulæ which shall express any three parts in terms of the remaining three ; the ...
Outras edições - Ver tudo
Elements of Plane and Spherical Trigonometry with Logarithmic and Other ... Simon Newcomb Pré-visualização indisponível - 2016 |
Elements of Plane and Spherical Trigonometry: With Logarithmic and Other ... Simon Newcomb Pré-visualização indisponível - 2018 |
Elements of Plane and Spherical Trigonometry: With Logarithmic and Other ... Simon Newcomb Pré-visualização indisponível - 2017 |
Palavras e frases frequentes
9 Prop algebraic sign angle AOB angle corresponding angle XOM applied arithmetical complement circle circumference co-log co-ordinates coefficients column computation cos² cos³ cosec cosine cotangent Cotg differences distance divided Entering the table equal equations error example EXERCISES expression find log find the values formula fourth quadrant geometry gives greater Hence interpolation intersect latitude length line OX log cot measure metres minutes nth roots perpendicular places of decimals polar triangle polygon preceding problem projection quantities radius revolving right angle right triangle roots of unity secant sides sin a cos sin a sin sin² sine N sines and cosines spherical triangle spherical trigonometry square substituting subtract suppose Tang theorem third quadrant tions trigono trigonometric functions trihedral angle unit write wwww zero ΙΟ
Passagens conhecidas
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 4 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Página 66 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.
Página 70 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Página 34 - To find the trigonometric functions corresponding to an angle between 45° and 90°, we take the degrees at the bottom of the page and the minutes in the right-hand column. The values of the...
Página 139 - 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 132 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts. II. The sine of the middle part is equal to the product of the cosines of the opposite parts.
Página 44 - To express the sine and cosine of the sum of two angles in terms of the sines and cosines of the angles.
Página 73 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Página 53 - Conventionally the period is divided into 24 hours, each hour into 60 minutes, and each minute into 60 seconds.