## 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

Results 1-5 of 9

Page 229

...

...

**spherical**triangle PZP ; PZ , BZ , D and PB are given , to find the**angle**PZB , the measure of which is the arc SO =**angle**SDO . Z S B P 0 sin . PZB = √ sin . + ( PB + PZ ...**angles**, taken with the sextants, to true horizontal**angles**. Page 254

...

...

**spherical**trigonometry . 1. A**spherical**triangle , whose sides are very small when compared with the radius of the**sphere**, being proposed : if from each of its**angles**you subtract one third of the excess of the sum of its three**angles**... Page 255

... angles are

... angles are

**spherical angles**; therefore C = 53 ° 58 ′ 35 ′′ .75 - .36 " 53 ° 58 ′ 35 ′′ .39 . Now with this , as an included angle , and the two sides given above , find the angles and the third side of a plane triangle by the rules ... Page 256

...

...

**angles**one - third of the**spherical**excess , a complete solution will be given to the**spherical**triangle .**Angles**of**spherical**triangle . C + d = 53 ° 58 ′ 35 ′′ .75 B + d = 68 24 44.99 A + d = 57 36 40.33 180 00 1.07 Sides of ... Page 257

...

...

**angles**of every**spherical**triangle being greater than 180 ° , the sum of every three observed**angles**of every triangle on the surface of the earth , ought to exceed 180 ° . To find this excess , which is called the**spherical**excess ...### 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

acres angles of elevation ascertain base line bisect boundary calculation centre chain chord circumferentor compasses cosecant Cosine Sine Cotang Cotang Sine Cosine deducted degrees diameter difference direction distance divided divisions equal error extend feet field-book figure ground 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 N.sin N.cos natural number natural sine needle number answering object offsets parallel ruler parish perches perpendicular plane triangle plotted Prop protractor quotient radius right angles right-angled triangle roods scale secant sextant side AC Sine Cosine Tang Sine Cotang Tang spherical angles spherical excess spherical triangle station line surveyor taken theodolite three angles Tithe Commissioners took the angle Torfou Townlands trapezium triangle ABC trigonometrical survey versed sine vertical yards

### Popular passages

Page ix - 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 38 - 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 147 - 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 40 - sum of the other two, as their difference is to the difference of the segments of the base, made by a perpendicular

Page 81 - 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 40 - 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 70 - 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 5 - 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 148 - 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