## A manual of logarithms and practical mathematics |

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added affection altitude amount angle annuity answering approximate Arc nearly Area axis base BC sin called centre circle circular column contains correction corresponding Cosine Cotang course cubic decimal Degrees diameter Diff difference of latitude Dist distance Ditto divide equal equations feet figures formula frustum given greater half height Hence horizontal inches latitude and departure length less logarithm mean measured middle miles minutes multiply NATURAL Note observed opposite otherwise Parabolic plane polygon preceding PROBLEM Proportional radius Reciprocals REDUCING represent right-angled root secant seconds segment ship sides Sine solar Solidity solution sought spherical triangle spheroid spindle Square Square Cube Subtract Surface taken Tang tangent thermometer true V(BC versine whole Yard zone

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Page 81 - Do. specimen 4 Norway Spar 745 579 969 934 872 756 993 760 696 553 660 657 553 753 738 696 693 531 522 556 560 577 818 596 598 435 588 724 610 395 615 509 588 605 757 588 588 403 411 518 518 518 648...

Page 85 - Every spherical triangle consists of six parts, three sides, and three angles ; any three of which being given, the rest may be found. In a right-angled spherical triangle, two given parts, besides the right angle, are sufficient to determine the rest.

Page 26 - Arc expressed in Degrees, Minutes, and Seconds. RULE. — Find the sine, tangent, &c. corresponding to the given degree and minute, and also that answering to the next greater minute, multiply the difference between them by the given number of seconds, and divide the product by 60 ; then the quotient added to the sine, tangent, &c. of the given degree and minute, or subtracted from the cosine, cotangent, &c. will give the quantity required nearly.

Page 14 - Powers of the same quantity are divided by subtracting the exponent of the divisor from that of the dividend ; the remainder is the exponent of the quotient.

Page 16 - To find any root of a number by logarithms. Divide the logarithm of the number by the exponent of the root ; the quotient is the logarithm of the root.

Page 12 - The decimals of the corrections are added together to determine the nearest value of the sixth figure of the mantissa. To find the number corresponding to a given logarithm. If the given mantissa is not in the table, find the one next less, and take out the four figures corresponding to it; divide the difference between the two mantissas by the tabular difference in that part of the table, and annex the figures of the quotient to the four figures already taken out. Finally, place the...

Page 49 - ... are in the same vertical plane. This table contains the dip answering to a free unobstructed horizon, and the numbers corresponding to the height of the eye are to be subtracted from the observed altitude when taken by the fore observation, but added to it in the back observation. TABLE XII.— The Dip at different Distances from the Observer.

Page 30 - In its respective column find the nearest sine, tangent, &c. to that given ; and take the degrees from the top or bottom of the page, according as the quantity is found in a column, with the proper title at the top or bottom ; and the minute is found in the same horizontal line, in the left or right hand marginal columns, according as the quantity is found in a column titled at the top or at the bottom of the page.

Page 9 - ... 2, that is, the integral part must be 1. In the same manner, if the number consist of three integers, the integral part of its logarithm must be 2, &c., so that the index, or characteristic, is always equal to the number of integral figures in the proposed number, minus 1. (149.) It also follows, that in this system the logarithm of any number, and that of one 10 times as great...

Page 29 - To the log. arc and the above constant quantity, add two-thirds of the arithmetical complement of the log. cosine, the sum is the log. tangent of the given arc. 3. To find the arc from the sine. To the given log. sine of a small arc 5'3144251, add ^ of arith.