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

J. Ernst, 1853 - History - 101 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 - If a perpendicular be let fall from any angle of a triangle to its opposite side or base, this base is to the sum of the other two sides, as the difference of the sides is to the difference of the segments of the base.
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 30 - DIVISION 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 71 - B =r83° 25' 14". 100. Problem. To find the area of a triangle when two sides and their included angle are given.
Page 141 - 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 triangle are 6, 8, and 10 : it is required to cut off nine-sixteenths of it, by a line that shall pass through the centre of its inscribed circle.
Page 17 - B to describe a segment of a circle, to contain a given angle C. At the ends of the given line make angles DAB, DBA, each equal to the given angle C. Then draw AE, BE perpendicular to AD, BD ; and with the centre E, and radius EA or EB, describe a circle ; so shall AFB be the segment required, as any angle F made in it will be equal to the given angle C.
Page 72 - Applying the rule for finding the area of a triangle when the three sides are given...
Page 207 - ... the latitude. EXAMPLES. 1. On a certain day, the meridian* altitude of the sun's lower limb was observed to be 31° 44', bearing south. At that time its declination was 7° 25' 8" south, semi-diameter 16' 9", index error +2' 12", height of the eye 17 feet.
Page 14 - Through a given point to draw a line parallel to a given line.