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

Ivison & Phinney, 1858 - Navigation - 347 pages
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Page 2 - 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...
Page 54 - 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 - 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 30 - 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 72 - Applying the rule for finding the area of a triangle when the three sides are given...
Page 200 - Earth's centre ; or, it is the angle under which the semidiameter of the Earth would appear, as seen from the object. The true place of a celestial body, is that point of the heavens in which it would be seen by an eye placed at the centre of the Earth.
Page 141 - ... it falls ? Ex. 2. The three sides of a triangle are 5, 12, and 13. If two-thirds of this triangle be cut off by a line drawn parallel to the longest side, it is required to find the length of the dividing line, and the distance of its two extremities from the extremities of the longest side. Ex. 3. It is required to find the length and position of the shortest possible line, which shall divide, into two equal parts, a triangle whose sides are 25, 24, and 7 respectively. Ex. 4. The sides of a...
Page 70 - PROBLEM III. To find the area of a Rhombus. RULE. Multiply the length by the perpendicular breadth, and the product will be the area.* 1. What is the area of a rhombus, whose side is 16 feet, and perpendicular breadth 10 feet ? Ans. 16 X 10 = 1 60 feet, the area.
Page 14 - AC, they are, therefore, parallel, (B. I, Th. 7, Cor. 1). PROBLEM VII. To divide a given line into any number of equal parts. Let AB represent the given line, and let it be required to divide it into any number of equal parts, say five. From one end of the line A, draw AD, indefinite in both length and position. Take...
Page 2 - 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.