## Course of Civil Engineering: Comprising Plane Trigonometry, Surveying, and Levelling. With Their Application to the Construction of Common Roads, Railways, Canals ...S.J. Machen, 1842 |

### From inside the book

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Page 14

... . On these lines all proportions are solved ; and when four numbers are proportionals , the ratio sub- sisting between the two first terms is equal to that between the two last : that is , the

... . On these lines all proportions are solved ; and when four numbers are proportionals , the ratio sub- sisting between the two first terms is equal to that between the two last : that is , the

**quotient**14 GUNTER'S SCALE . Page 15

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**quotient**of the first term by the second , is equal to the**quotient**of the third term by the fourth . Therefore , from the nature of logarithms , the difference between the first and second terms , on the scale , is equal to the ... Page 16

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**quotient**. Divide 60 by 5 ; extend the compasses from 5 to 1 , and the same will reach from 60 to 12 , the**quotient**. To find a mean proportional between two given numbers , as suppose between 7 and 28 : extend the compasses from 7 to ... Page 19

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**quotients**in division , are obtained by means of addition and sub- traction only . Or , Logarithms are a series of numbers in arith- metical progression , corresponding to another series in geometrical progression , the arithmetical ... Page 21

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**quotient**is the root required . To extract the cube root of any number , we divide the log . of the number by 3 , and the number answering to the**quotient**is the root required . Thus , to extract the square root of 10000 , or ( 10000 ) ...### Other editions - View all

Course of Civil Engineering: Comprising Plane Trigonometry, Surveying, and ... John Gregory No preview available - 2015 |

Course of Civil Engineering: Comprising Plane Trigonometry, Surveying, and ... John Gregory No preview available - 2018 |

### Common terms and phrases

accuracy acres angles of elevation angular ascertain base line bisect boundary calculation centre chain chord circumferentor compass cosecant Cosine Sine Cotang Cotang Sine Cosine deducted diameter difference direction distance divided divisions equal error extend feet field-book figure given height Hence horizontal instrument length line of numbers line of sines line of tangents logarithmic mark measure the angles meridian method minutes multiplied N.cos natural sine needle object offsets Ordnance Survey parallel parallel ruler parish perches perpendicular plane triangle plotted poles position Prop protractor quotient radius right angles right-angled triangle roods scale secant sextant sin N.cos N Sine Cosine Tang Sine Cotang Tang spherical angles spherical excess spherical triangle station line surveyor tables taken telescope theodolite three angles took the angle Townlands trapezium triangle ABC trigonometrical survey variation versed sine yards

### Popular passages

Page vii - into 360 equal parts, called degrees ; each degree being divided into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds, &c.

Page 36 - the angle opposite to that other given side is always acute. But when the given side opposite to the given angle, is less than the other given side, then the angle opposite that other given side may be either acute or obtuse, and

Page 145 - The number of changes shows how many times ten chains the line contains, to which the follower adds the arrows he holds in his hand, and the number of links of another chain over to the mark or end of the line.

Page 38 - sum of the other two, as their difference is to the difference of the segments of the base, made by a perpendicular

Page 79 - Suppose that in carrying on an extensive survey, the distance between two spires, A and B, has been found equal to 6594 yards, and that C and D are two eminences conveniently situated for extending the triangles, but not admitting of the determination of their distance by actual admeasurement ; to ascertain it, therefore,

Page 206 - materially from the arcs which they subtend. Let the three angles of the spherical triangle be represented by A, B, C ; and their opposite sides by a, b, c ; and let a', b', c', represent the chords of these sides, which chords are supposed not to differ

Page 38 - of half the perimeter above those sides, as the square of the radius is to the square of the sine of half the angle included by

Page 68 - of the bottom of the object, equal 27°, and of its top 19°. Required the height of the object, and the distance of the mark from its bottom. Here,

Page 3 - 0, 10, 20, 30, &c. ; each of these large divisions represents 10 degrees of the equator, or 600 miles. The first of these divisions is sometimes divided into 40 equal parts, each representing 15 miles. The

Page 146 - with the cross, by fixing it by trials on such parts of the line as that through one pair of the sights both ends of the line may appear, and through the other pair you