Surveying and Navigation, with a Preliminary Treatise on Trigonometry and MensurationVan Antwerp, Braggs & Company, 1864 - 490 páginas |
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Página 28
... cosec . 4. The solution of triangles is accomplished by the aid of these functions , since they enable us to ascertain the relations which exist between the sides and angles of triangles . 5. The primary origin will be taken as the ...
... cosec . 4. The solution of triangles is accomplished by the aid of these functions , since they enable us to ascertain the relations which exist between the sides and angles of triangles . 5. The primary origin will be taken as the ...
Página 40
... cosec 0 ° + ∞ , cosec 90 ° +1 , cosec 180 ° = + ∞ , cosec 270 ° = - 1 , cosec 360 ° : ∞o . To aid the memory , and for convenience of reference , we give the following tabular summaries : 47. Signs of the Circular Functions ...
... cosec 0 ° + ∞ , cosec 90 ° +1 , cosec 180 ° = + ∞ , cosec 270 ° = - 1 , cosec 360 ° : ∞o . To aid the memory , and for convenience of reference , we give the following tabular summaries : 47. Signs of the Circular Functions ...
Página 49
... cosec P , sec P cosec B ; ... ( 9 ) and ( 10 ) become , h h p cosec P ( 11 ) cosec P and ( 12 ) p b h cosec B h cosec B b 11. Either side adjacent to the right angle is equal to the hypotenuse divided by the co - secant of the angle ...
... cosec P , sec P cosec B ; ... ( 9 ) and ( 10 ) become , h h p cosec P ( 11 ) cosec P and ( 12 ) p b h cosec B h cosec B b 11. Either side adjacent to the right angle is equal to the hypotenuse divided by the co - secant of the angle ...
Página 50
... cosec P cosec P ( 11 ) ( 12 ) p Rh Rh b cosec B cosec B b ( 1 ) Applying logarithms to these formulas , we have : = log p logh log sin P log blog hlog sin --- 10 . B 10 . ( 2 ) log sin P = 10 + log p log h log sin B10 + log blog h ...
... cosec P cosec P ( 11 ) ( 12 ) p Rh Rh b cosec B cosec B b ( 1 ) Applying logarithms to these formulas , we have : = log p logh log sin P log blog hlog sin --- 10 . B 10 . ( 2 ) log sin P = 10 + log p log h log sin B10 + log blog h ...
Página 51
... cosec P. + log h ― log cosec B. Š ( 12 ) log cosec P = 10 + log log cosec B h log p . = = 10 + log h log b . 65. Case I. Given the hypotenuse and one acute angle , required the B B. น remaining parts . 1. Given h = 365 . = P 33 ° 12 ...
... cosec P. + log h ― log cosec B. Š ( 12 ) log cosec P = 10 + log log cosec B h log p . = = 10 + log h log b . 65. Case I. Given the hypotenuse and one acute angle , required the B B. น remaining parts . 1. Given h = 365 . = P 33 ° 12 ...
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Términos y frases comunes
a. c. log ABCD adjacent angles adjacent sides altitude angle is equal arc increases base line C₁ chains clamp co-sine compass cosec Cotang denote departure diameter difference of level divided east escribed circles Examples feet field notes Find the angle find the area formulas frustum given side height hence horizontal hypotenuse included angle increases from 90 instrument intersection latitude links dist logarithm longitude M.
M. Cosine M.
M. Sine mantissa meander miles minus needle negative number corresponding offsets opposite angle parallel sailing parallelogram perpendicular plane plane sailing positive quarter section corner radius rhumb line right angle sailing secant ship side adjacent sin A sin solar compass spherical triangle stake standard parallel station survey surveyor Tang tangent telescope trapezoid variation vernier versed-sine vertex vertical Willamette Meridian
Pasajes populares
Página 110 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Página 34 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.
Página 258 - All the corners marked in the surveys, returned by the surveyor general, or by the surveyor of the lands south of the state of Tennessee, respectively, shall be established as the proper corners of sections, or subdivisions of sections, which they were intended to designate ; and the corners of half and quarter sections, not marked on said surveys, shall be placed as nearly as possible equidistant from those two corners which stand on the same line.
Página 22 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 19 - To Divide One Number by Another, Subtract the logarithm of the divisor from the logarithm of the dividend, and obtain the antilogarithm of the difference.
Página 144 - Any angle is greater than the difference between 180° and the sum of the other two angles.
Página 124 - That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles.
Página 65 - 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.
Página 145 - 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 162 - Now, since the areas of similar polygons are to each other as the squares of their homologous sides...