Tables of Logarithms of Numbers and of Sines and Tangents for Every Ten Seconds of the Quadrant: With Other Useful TablesHarper & brothers, 1859 - 150 páginas |
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Página 21
... angle by A , COS . cot . A = sine ( 90 ° —A ) . A = tang . ( 90 ° —A ) . cosec . A sec . ( 90 ° -A ) . Since , in a right - angled triangle , either of the acute angles is the complement of the other , the sine , PLANE TRIGONOMETRY . 21.
... angle by A , COS . cot . A = sine ( 90 ° —A ) . A = tang . ( 90 ° —A ) . cosec . A sec . ( 90 ° -A ) . Since , in a right - angled triangle , either of the acute angles is the complement of the other , the sine , PLANE TRIGONOMETRY . 21.
Página 22
... tang . A. R sin . A cos . A Whence tang . A = 2. CG :: CF : CA : CI ; that is , cos . A : R :: R : sec . A. Whence sec . A : R2 cos . A ' 3 GF : CG :: CD : DL ; that is , sin . A : cos . A :: R : cot . A. Whence cot . A : R cos . A sin ...
... tang . A. R sin . A cos . A Whence tang . A = 2. CG :: CF : CA : CI ; that is , cos . A : R :: R : sec . A. Whence sec . A : R2 cos . A ' 3 GF : CG :: CD : DL ; that is , sin . A : cos . A :: R : cot . A. Whence cot . A : R cos . A sin ...
Página 32
... angled at A , then will R : CA :: tang . C : AB :: sec . C : CB . From the point C as a center , with a radius equal to the radius of the tables , B F E D A describe the arc DE , and from the point D 32 TRIGONOMETRY .
... angled at A , then will R : CA :: tang . C : AB :: sec . C : CB . From the point C as a center , with a radius equal to the radius of the tables , B F E D A describe the arc DE , and from the point D 32 TRIGONOMETRY .
Página 33
... tang . C : AB . CD : CA :: CF : CB , R : CA : sec . C : CB . ( 43. ) In every plane triangle there are six parts : three sides and three angles . Of these , any three being given , provided one of them is a side , the others may be ...
... tang . C : AB . CD : CA :: CF : CB , R : CA : sec . C : CB . ( 43. ) In every plane triangle there are six parts : three sides and three angles . Of these , any three being given , provided one of them is a side , the others may be ...
Página 37
... tang . A + B : tang . 2 A - B 2 Produce AC to D , making CD equal to CB , and join DB . Take CE equal to CA , draw AE , and produce it to F. Then AD is the sum of CB and CA , and BE is their difference . D The sum of the two angles CAE ...
... tang . A + B : tang . 2 A - B 2 Produce AC to D , making CD equal to CB , and join DB . Take CE equal to CA , draw AE , and produce it to F. Then AD is the sum of CB and CA , and BE is their difference . D The sum of the two angles CAE ...
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Términos y frases comunes
9 I I altitude angle of elevation arithm base chains circle Co-sine Co-tangent complement computed correction cosecant course and distance decimal diameter diff difference of latitude difference of longitude Dist divided equal equator fifth figure find the angles find the area find the Logarithm frustum given number given the angle height Hence horizontal plane hypothenuse inches latitude and departure length LO LO LO logarithmic sine measured meridian middle latitude miles minutes Multiply natural number nautical miles parallel parallel sailing perpendicular places plane sailing Prob Prop proportional quadrant radius Required the logarithmic right-angled spherical triangle right-angled triangle Sandy Hook secant ship sails side AC spherical triangle ABC SPHERICAL TRIGONOMETRY station subtract surface tabular number tang Tangent telescope theodolite Theorem vernier vertical Vulgar Fraction wyll yards zoids ΙΙ ΙΟ
Pasajes populares
Página 20 - The circumference of every circle is supposed to be divided into 360 equal parts, • called degrees, each degree into 60 minutes, and each minute into 60 seconds, etc.
Página 163 - In any spherical triangle, the sines of the sides are proportional to the sines of the opposite angles. In the case of right-angled spherical triangles, this proposition has already been demonstrated.
Página 69 - FIND the area of the sector having the same arc with the segment, by the last problem. Find also the area of the triangle, formed by the chord of the segment and the two radii of the sector.
Página 54 - 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 69 - TO THE NUMBER OF DEGREES IN THE ARC ; So IS THE AREA OF THE CIRCLE, TO THE AREA OF THE SECTOR.
Página 73 - To find the solidity of a pyramid. RULE. Multiply the area of the base by one third of the altitude.
Página vi - The characteristic of the logarithm of ANY NUMBER GREATER THAN UNITY, is one less than the number of integral figures in the given number.
Página 184 - If a heavy sphere, whose diameter is 4 inches, be let fall into a conical glass, full of water, whose diameter is 5, and altitude 6 inches ; it is required to determine how much water will run over ? AHS.