## A Treatise on Land-surveying: Comprising the Theory Developed from Five Elementary PrinciplesD. Appleton & Company, 1878 - 508 pages |

### From inside the book

Results 1-5 of 56

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**cosine**. Subtract this product from the reserved product , and take the square root of the remainder . It will be the area of the quadrilateral . When the four sides , and the angle of intersection of the diagonals of the quadria teral ... Page 168

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**cosine**, of any angle Multiply the given angle by two ; find , in the Table , the chord of this double angle ; and half of this chord will be the natural sine required For , the chord of any angle is equal to twice the sine of half the ... Page 170

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**cosine**of the bearing by the length of the course ; and to find the Departure of any course , multiply the natural sine of the bearing by the length of the course . If the course be Northerly , the Latitude will be North , and will be ... Page 171

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**cosines**, tangents , & c . , are here named , they mean the natu ral sines & c . , of an arc described with a radius equal to one , or to the unit by which the sines , & c . , are measured . facilitate these calculations , which are of ... Page 195

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**cosine**of the Hour angle before or after the culmination . Reduce the space to time ; correct for sidereal acceleration ( 3m . 56s . for 24 hours ) and subtract the result from the time of the star's passing the meridian on that day ...### Other editions - View all

A Treatise On Land-surveying: Comprising The Theory Developed From Five ... W. M. Gillespie No preview available - 2022 |

### Common terms and phrases

ABCD acres alidade base line Bearing calculated centre CHAPTER chord circle compass complete quadrilateral convenient corner Cosine Cotang course cross-hairs desired desired line determined diagonal difference direction distance divided division draw drawn East equal feet field Field-notes figure fixed gamboge given line given point half horizontal inaccessible inch instrument intersection Latitudes and Departures length line of sight Longitude MAGNETIC BEARING marked measured Meridian method needle North object observed obtained offsets paper parallel pass perpendicular plane plat plate plumb-line preceding precisely prolonged protractor quadrilateral radius reading right angles scale screws side similar triangles Sine South square chains stake station straight line subtract survey surveyor Table Tang Tangent telescope Theodolite Theorem tion township Transit trapezoid Trigonometry turn Variation Vernier Vernier scale vertical West whence

### Popular passages

Page 153 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 365 - ... in all cases where the exterior lines of the townships thus to be subdivided into sections or half sections, shall exceed, or shall not extend six miles, the excess or deficiency shall be specially noted, and added to or deducted from the western or northern ranges of sections or half sections in such township, according as the error may be in running the lines from east to west, or from south to north...

Page 405 - Since similar triangles are to each other as the squares of their homologous sides...

Page 370 - President may prescribe, to cause the lands thus situated to be surveyed in tracts of two acres in width, fronting on any river, bayou, lake, or watercourse, and running back the depth of forty acres...

Page 372 - The precise relative position of islands, in a township made fractional by the river in which the same are situated, is to be determined trigonometrically. Sighting to a flag or other fixed object on the island, from a special and carefully measured base line, connected with the surveyed lines, on or near the river bank, you are to form...

Page 375 - Whenever bearing trees are not found, mounds of earth, or stone, are to be raised around posts on which the corners are to be marked in the manner aforesaid. Wherever a mound of earth is adopted, the same will present a conical shape; but at its base, on the earth's surface, a quadrangular trench will be dug; by the

Page 366 - ... (either of which would indicate an important error in the surveying,) the lines must be retraced, even if found necessary to remeasure the meridional boundaries of the township, (especially the western boundary,) so as to discover and correct the error ; in doing which, the true corners must be established and marked, and the false ones destroyed and obliterated to prevent confusion in future ; and all the facts must be distinctly

Page 372 - A sufficient number of other trees standing within 50 links of the line, on either side of it, are to be blazed on two sides diagonally, or quartering toward the line, in order to render the line conspicuous, and readily to be traced, the blazes to be opposite each other, coinciding in direction with the line where the trees stand very near it, and to approach nearer each other the farther the line passes from the blazed trees. Due care must ever be taken to have the lines so well marked as to be...

Page 44 - Multiply the sum of the parallel sides by the perpendicular distance between them, and half the product will be the area.

Page 138 - Bearing and length of a line are named collectively the Course. To take the Bearing of any line, set the compass exactly over any point of it by a plumb-line suspended from beneath the centre of the compass, or, approximately, by dropping a stone. Level the compass by bringing the air bubbles to the middle of the level tubes.