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adjusted angle axis base line bearing calculated called centre column compass corresponding Cosine Cotang course curve decimal departure describe determined difference direction distance divided double draw drawn east enter equal error example extremity feet field figure given gives greater ground half hence horizontal plane inches intersection known land latitude length less limb logarithm longitude manner marked means measure meridian method middle miles minutes notes object opposite parallel passing perpendicular piece position PROBLEM proportional radius remains REMARK represent right angles sailing scale screws ship side sights Sine square staff station subtract suppose surface survey taken Tang tangent telescope third triangle true turn unit vertical yards
Page 49 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
Page 73 - Being on a horizontal plane, and wanting to ascertain the height of a tower, standing on the top of an inaccessible hill, there were measured, the angle of elevation of the top of the hill 40°, and of the top of the tower 51° ; then measuring in a direct line 180 feet farther from the hill, the angle of elevation of the top of the tower Cway 33° 45' ; required the height of the tower.
Page 34 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Page 35 - The secant of an arc is the line drawn from the centre of the circle through one extremity of the arc, and limited by the tangent passing through the other extremity. Thus, OC is the secant of the arc AB.
Page 17 - NB The minutes in the left-hand column of each page, increasing downwards, belong to the degrees at the top ; and those increasing upwards, in the right.hand column, belong to the degrees below.
Page 19 - Two lines are said to be parallel, when being situated in the same plane, they cannot meet, how far soever, either way, both of them be produced. 13. A plane figure is a plane terminated on all sides by lines, either straight or curved. If the lines are straight, the space they enclose is called a rectilineal figure, or polygon, and the lines themselves, taken together, form the contour, or perimeter of the polygon. 14. The polygon of three sides, the simplest of all, is called a triangle; that of...
Page 132 - The line so determined makes, with the true meridian, an angle equal to the azimuth of the polestar; and from this line the variation of the needle is readily determined, even without tracing the true meridian on the ground. Place the compass upon this line, turn the sights in the direction of it, and note the angle shown by the needle. Now, if the elongation, at the time of observation, was west, and the north end of the needle is on the west side of the line, the azimuth, plus the angle shown by...
Page 34 - Mathematics which treats of the solution of plane triangles. In every plane triangle there are six parts : three sides and three angles. When three of these parts are given, one being a side, the remaining parts may be found by computation.
Page 21 - AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals, the sums will be unequal. 5. If equals be taken from unequals, the remainders will be unequal. 6. Things which are double...