Elements of Plane and Spherical Trigonometry with Logarithmic and Other Mathematical Tables and Examples of Their Use and Hints on the Art of Computation |
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Página
That of Part I. is an introduction to the employment of imaginary quantities in
trigonometric developments , while that of Part II . is an introduction to the higher
forms of solid geometry . VI . To the usual list of subjects treated , has been added
1 ...
That of Part I. is an introduction to the employment of imaginary quantities in
trigonometric developments , while that of Part II . is an introduction to the higher
forms of solid geometry . VI . To the usual list of subjects treated , has been added
1 ...
Página 7
This will be clear from the following analytic deduction of the same result . Let the
smallest measure of the angle AOB be a . Then the other measures of this angle (
87 ) will be a + c , a + 2C , a +30 ... atic . Dividing these quantities by n , the ...
This will be clear from the following analytic deduction of the same result . Let the
smallest measure of the angle AOB be a . Then the other measures of this angle (
87 ) will be a + c , a + 2C , a +30 ... atic . Dividing these quantities by n , the ...
Página 38
Express the same quantities in terms of NP . 3. Express NX separately in terms of
OX and XP , and by multiplying the two values prove the geometric theorem that
NX is a mean proportional between OX and XP . 4. In a right triangle the sides ...
Express the same quantities in terms of NP . 3. Express NX separately in terms of
OX and XP , and by multiplying the two values prove the geometric theorem that
NX is a mean proportional between OX and XP . 4. In a right triangle the sides ...
Página 54
But either or both of these quantities may be negative . Whatever their signs ,
there are always two values of q , differing by 180 ° , corresponding to any given
value of tan q ( $ 31 ) . Hence the problem admits of two solutions in all cases .
But either or both of these quantities may be negative . Whatever their signs ,
there are always two values of q , differing by 180 ° , corresponding to any given
value of tan q ( $ 31 ) . Hence the problem admits of two solutions in all cases .
Página 56
From the equations p sin ( B + 8 ) = a , r sin ( B +9 ) = b , to find the values of r and
B , —the other four quantities , a , b , a , and 0 , being supposed known . Solution
. Developing the sines of B + a and B + ( 840 ) , we have r sin ß cos a tre cos ß ...
From the equations p sin ( B + 8 ) = a , r sin ( B +9 ) = b , to find the values of r and
B , —the other four quantities , a , b , a , and 0 , being supposed known . Solution
. Developing the sines of B + a and B + ( 840 ) , we have r sin ß cos a tre cos ß ...
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Términos y frases comunes
9 Prop added addition algebraic amount angle applied base called circle co-ordinates column complement computation corresponding cosec cosine Cotg decimals differences direction distance divided equal equations error example EXERCISES expression figure formula four functions geometry given gives greater Hence increase interest interpolation intersect length less limit logarithm means measure minutes multiply negative NOTE obtain opposite perpendicular plane polar polygon positive powers preceding problem projection Prop Prove quadrant quantities radius rectangular reduce relations remaining represented respective result root secant shown sides sin a cos sin a sin sine sinº Solution spherical triangle square student substituting subtract suppose Tang tangent theorem third tion triangle trigonometric unit unity values write zero
Pasajes populares
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.
Información bibliográfica
| Título | Elements of Plane and Spherical Trigonometry with Logarithmic and Other Mathematical Tables and Examples of Their Use and Hints on the Art of Computation Mathematical course, Simon Newcomb Newcomb's mathematical course |
| Autor | Simon Newcomb |
| Edición | 2 |
| Editor | H. Holt, 1882 |
| Procedencia del original | Universidad de Harvard |
| Digitalizado | 11 Ene. 2008 |
| Largo | 104 páginas |
| Exportar cita | BiBTeX EndNote RefMan |