The Complete Mathematical and General Navigation Tables: Including Every Table Required with the Nautical Almanc in Finding the Latitude and Longitude: with an Explanation of Their Construction, Use, and Application to Navigation and Nautical Astronomy, Trigonometry, Dialling, Gunnery, EtcSimpkin, Marshall, & Company, 1838 |
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Página 4
... Hence it is manifest that altitudes taken by the fore observation must be diminished by the angle of horizontal depression , and that in back observations the altitudes must be increased by the value of that angle . The absolute value ...
... Hence it is manifest that altitudes taken by the fore observation must be diminished by the angle of horizontal depression , and that in back observations the altitudes must be increased by the value of that angle . The absolute value ...
Página 9
... hence by trigonometry , As the angle at the moon , A M E = 57'30 " Log . sine ar . comp . 1.776626 Is to the earth's semidiameter = A E = 3958 . 75 miles , Log . 3.597558 So is radius • · • 90 : · • Log . sine 10.000000 To moon's ...
... hence by trigonometry , As the angle at the moon , A M E = 57'30 " Log . sine ar . comp . 1.776626 Is to the earth's semidiameter = A E = 3958 . 75 miles , Log . 3.597558 So is radius • · • 90 : · • Log . sine 10.000000 To moon's ...
Página 34
... Hence , by plane trigono- metry : - = As moon's horizontal parallax 57:15 " , sine comp . arith . Is to the earth's semidiameter - 3958 . 75 , logarithm So is radius . • • 1.7785185 3.5975581 90 degrees - sine 10.0000000 · To the moon's ...
... Hence , by plane trigono- metry : - = As moon's horizontal parallax 57:15 " , sine comp . arith . Is to the earth's semidiameter - 3958 . 75 , logarithm So is radius . • • 1.7785185 3.5975581 90 degrees - sine 10.0000000 · To the moon's ...
Página 54
... hence the sine of 30 degrees is . 5000000000 , and its cosine . 8660254037 . Again , In the triangle FN B , the perpendicular FN is given = .5000000000 , and the base CB - CN = NB . 1339745963 , to find the hypothenuse BF : but half the ...
... hence the sine of 30 degrees is . 5000000000 , and its cosine . 8660254037 . Again , In the triangle FN B , the perpendicular FN is given = .5000000000 , and the base CB - CN = NB . 1339745963 , to find the hypothenuse BF : but half the ...
Página 64
... hence the log . of 3. 1622777 is .5 . Second , The log . of 1 is 0 , and the log . of 3. 1622777 is .5 ; therefore 0 + 5 + 2 = 25 is the arithmetical mean , · and 1 x 3.1622777 = 1.7782794 the geometrical mean : hence the log . of ...
... hence the log . of 3. 1622777 is .5 . Second , The log . of 1 is 0 , and the log . of 3. 1622777 is .5 ; therefore 0 + 5 + 2 = 25 is the arithmetical mean , · and 1 x 3.1622777 = 1.7782794 the geometrical mean : hence the log . of ...
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Términos y frases comunes
90 degrees add the log angle of meeting answering approximate auxiliary angle celestial object co-secant co-sine co-tangent co-versed sine comp computed Constant log Corr correction course and distance decimal fraction departure Diff difference of latitude difference of longitude distance sailed earth equal equator Example find the Angle find the Difference fixed star given angle Given arch given log given side hence hypothenuse A C leg AC mean solar merid meridian meridional difference middle latitude miles minutes moon's apparent altitude moon's horizontal parallax multiplied natural number natural sine natural versed sine Nautical Almanac noon observation perpendicular B C plane PROBLEM prop proportional log quadrant radius reduced refraction right angled right ascension right-hand rising and setting secant semidiameter ship side A B side BC sidereal day spherical distance spherical triangle star's subtracted Table tabular tangent trigonometry true altitude tude versed sine supplement
Pasajes populares
Página 59 - Also, between the mean, thus found, .and the nearest extreme, find another geometrical mean, in the same manner ; and so on, till you are arrived within the proposed limit of the number whose logarithm is sought.
Página 206 - For the purpose of measuring angles, the circumference is divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; each minute into 60 equal parts called seconds.
Página 258 - If two triangles have two angles of the one equal to two angles...
Página 59 - ... progression, to which those indices belong. Thus, the indices 2 and 3, being added together, make 5 ; and the numbers 4 and 8, or the terms corresponding to those indices, being multiplied together, make 32, which is the number answering to the index 5.
Página 59 - And, if the logarithm of any number be divided by the index of its root, the quotient will be equal to the logarithm of that root. Thus the index or logarithm of 64 is 6 ; and, if this number be divided by 2, the quotient will be = 3, which is the logarithm of 8, or the square root of 64.
Página 152 - RULE. Divide as in whole numbers, and from the right hand of the quotient point off as many places for decimals as the decimal places in the dividend exceed those in the divisor.
Página 153 - When there happens to be a remainder after the division ; or when the decimal places in the divisor are more than those in the dividend ; then ciphers may be annexed to the dividend, and the quotient carried on as far as required.
Página 154 - REDUCTION OF DECIMALS. CASE I. . To reduce a Vulgar Fraction to a Decimal Fraction of equal value.
Página 177 - II. The sine of the middle part is equal to the product of the cosines of the opposite parts.
Página 243 - II. the difference of latitude and departure corresponding to each course and distance, and set them in their respective columns : then the difference between the sums of the northings and southings will be the difference of latitude made good, of the same name with the greater ; and the difference between the sums of the eastings and westings will be the departure made good, of the same name with the greater quantity.