A Treatise on Surveying and Navigation: Uniting the Theoretical, Practical, and Educational Features of These Subjects

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Ivison & Phinney, 1858 - 347 pages

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Page 56 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Page 4 - NB In the following table, in the last nine columns of each page, where the first or leading figures change from 9's to O's, points or dots are introduced instead of the O's through the rest of the line, to catch the eye, and to indicate that from thence the annexed first two figures of the Logarithm in the second column stand in the next lower line. N.
Page 32 - BY LOGARITHMS. RULE. FROM the logarithm of the dividend subtract the logarithm of the divisor, and the number answering to the remainder will be the quotient required.
Page 73 - Invettigate and give a rule for finding the area of a triangle when two sides and their included angle are given. Let ABC be the triangles, AB, BC the given sides, and B the given angle.
Page 4 - Upon this principle is constructed the thermometeric barometer, which indicates the elevation of any place above the level of the sea, by the temperature at which water boils at that elevation. By experiment it has been found that a difference in elevation, amounting to nearly 520 feet, makes a difference of one degree in the boiling point of water.
Page 74 - Applying the rule for finding the area of a triangle when the three sides are given...
Page 28 - Add 44 Hence, the logarithm of 834785 is 5.921574 the logarithm of 83.4785 is 1.921574 From this we draw the following rule to find the logarithm of any number consisting of more than four places of figures. RULE. — Take out the logarithm of the four superior places directly from the table, and take the difference between this logarithm and the next greater logarithm in the table. Multiply this difference by the inferior places in the number as a decimal, and add the result to the logarithm corresponding...
Page 168 - The pressure of the atmosphere at any place, is measured by the height of a column of mercury it sustains in the barometer tube. It is found by experiment, that air is compressible, and the amount of compression is always in proportion to the amount of the compressing force. Now, suppose the atmosphere to be divided into an indefinite number of strata, of the same thickness, and so small that the density of each stratum may be considered as uniform. Commence at an indefinite distance above the surface...
Page 25 - For it has been shown (Art. 3) that the logarithm of 1 is 0, of 10 is 1, of 100 is 2, of 1000 is 3, and so on.
Page 201 - Hence, azimuths may be reckoned from the north or sotith points of the horizon. 11. ALTITUDE. — The altitude of any object is its angular distance from the horizon, measured on a vertical circle.* Altitudes are very frequently measured at sea, several times in a day in fair weather ; but altitudes observed from the surface of the earth, or above it, require several corrections before the true altitudes can be deduced from them.

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