Elements of Surveying, and Navigation: With a Description of the Instruments and the Necessary Tables |
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Page 8
... subtraction of logarithms corresponds to the di- vision of their numbers . 4. Let us examine further the equations 10 ° = 1 101 = 10 102 = 100 103 = 1000 & c . & c . It is plain that the logarithm of 1 is 0 , and that the loga- rithms ...
... subtraction of logarithms corresponds to the di- vision of their numbers . 4. Let us examine further the equations 10 ° = 1 101 = 10 102 = 100 103 = 1000 & c . & c . It is plain that the logarithm of 1 is 0 , and that the loga- rithms ...
Page 13
... subtract this less logarithm from the given logarithm , and having annexed any number of ciphers to the remainder , divide it by the dif- ference taken from the column D , and annex the quotient to the number answering to the less ...
... subtract this less logarithm from the given logarithm , and having annexed any number of ciphers to the remainder , divide it by the dif- ference taken from the column D , and annex the quotient to the number answering to the less ...
Page 15
... subtract the logarithm of the divisor , the remainder will be the logarithm of the quotient . This additional ... subtraction from the decimal part of the logarithm . Or , if the charac- teristic of the logarithm of the dividend is ...
... subtract the logarithm of the divisor , the remainder will be the logarithm of the quotient . This additional ... subtraction from the decimal part of the logarithm . Or , if the charac- teristic of the logarithm of the dividend is ...
Page 16
... subtracting the left hand figure from 9 , then proceeding to the right , subtract each figure from 9 till we reach the last significant figure , which must be taken from 10 : this will be the same as taking the logarithm from 10 ...
... subtracting the left hand figure from 9 , then proceeding to the right , subtract each figure from 9 till we reach the last significant figure , which must be taken from 10 : this will be the same as taking the logarithm from 10 ...
Page 17
... subtracting 10 , will be the logarithm of the quotient . EXAMPLES . 1. Divide 327.5 by 22.07 . log 327.5 log 22.07 2.515211 ar . comp . 8.656198 Quotient • 14.839 1.171409 • 2. Divide 0.7438 by 12.9476 . log 0.7438 · log 12.9476 ar ...
... subtracting 10 , will be the logarithm of the quotient . EXAMPLES . 1. Divide 327.5 by 22.07 . log 327.5 log 22.07 2.515211 ar . comp . 8.656198 Quotient • 14.839 1.171409 • 2. Divide 0.7438 by 12.9476 . log 0.7438 · log 12.9476 ar ...
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Elements of Surveying, and Navigation: With a Description of the Instruments ... Charles Davies No preview available - 2016 |
Elements of Surveying, and Navigation: With a Description of the Instruments ... Charles Davies No preview available - 2016 |
Common terms and phrases
axis azimuth back-sights base line bearing called centre clamp-screw coincide column comp compass corresponding course curve decimal degrees determined diff difference of latitude difference of level difference of longitude direction divided double meridian distance draw east error example extremity feet field notes figure given line given point ground half hence horizontal distance horizontal plane hypothenuse inches instrument intersection LatDegDegDegDeg Distance latitude and departure length line of collimation logarithm marked measure method middle latitude miles multiplied needle opposite station paper parallel Parallel Sailing parture passing perpendicular plane of reference Plane Sailing plane triangle protractor radius right angles right-angled triangle sails scale of equal secant ship side sights similar triangles spider's lines square chains staff subtract surface survey tance Tang tangent theodolite Trigonometry vernier plate yards
Popular passages
Page 49 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
Page 41 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
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 19 - 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...