## Tables of Logarithms of Numbers and of Sines and Tangents for Every Ten Seconds of the Quadrant: With Other Useful TablesHarper & brothers, 1859 - 150 pages |

### From inside the book

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Page 21

... sine of the arc DF , or the cosine of the arc AF . The

... sine of the arc DF , or the cosine of the arc AF . The

**cotangent**of an arc is the tangent of the complement of that arc . Thus DL is the tangent of the arc DF , or the**co**-**tangent**of the arc AF . The cosecant of an arc is the secant of ... Page 22

...

...

**cotangent**, and cosecan of the other . D Cotan . L Cosine · Sec . I ( 27. ) The sine , tangent , and secant of an arc are equal to the sine , tangent , and secant of its supplement . Thus FG is the sine of the arc AF , or of its sup ... Page 24

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...

**co**- sines ,**tangents**, and**cotangents**are given for every minute of the quadrant to six places of figures . ( 30. ) To find from the table the natural**sine**,**cosine**, & c . , of an arc or angle . If a**sine**is required , look for the ... Page 25

With Other Useful Tables Elias Loomis. the sine "

With Other Useful Tables Elias Loomis. the sine "

**cosine**"**tangent**of 143 ° 24 ' is 0.596225 ; of 151 ° 23 ' is 0.877844 ; of 132 ° 36 ' is 1.08749 ; "**cotangent**of 116 ° 7 ' is 0.490256 , & c . ( 31. ) If a sine is required for an arc ... Page 26

... sine or tangent . Thus the arc whose cosine is .40000 is 66 ° 25 ' 18 " ; 66 66 66

... sine or tangent . Thus the arc whose cosine is .40000 is 66 ° 25 ' 18 " ; 66 66 66

**cotangent**is 1.99468 is 26 ° 37 ' 34 " . ( 33. ) On pages 134-5 will be found a table of natural se- cants for every ten minutes of the quadrant ...### Other editions - View all

### Common terms and phrases

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

### Popular passages

Page 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.

Page 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.

Page 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.

Page 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.

Page 69 - TO THE NUMBER OF DEGREES IN THE ARC ; So IS THE AREA OF THE CIRCLE, TO THE AREA OF THE SECTOR.

Page 73 - To find the solidity of a pyramid. RULE. Multiply the area of the base by one third of the altitude.

Page 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.

Page 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.