A System of Geometry and Trigonometry: With a Treatise on Surveying; in which the Principles of Rectangular Surveying, Without Plotting, are Explained |
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Page 9
... but make the angles on each side equal , then those angles are called right angles ; and the line CD is said to be perpendicular to the other line . BZ Fig . 1 . Fig . 2 . D A B с Fig . 3 . 8. An obtuse angle is greater 2 GEOMETRY. ...
... but make the angles on each side equal , then those angles are called right angles ; and the line CD is said to be perpendicular to the other line . BZ Fig . 1 . Fig . 2 . D A B с Fig . 3 . 8. An obtuse angle is greater 2 GEOMETRY. ...
Page 11
... perpendicular to the radius or diameter drawn through the other end : or , it is half the chord of double the arc ; thus HL is the sine of the arc HB . Fig . 7 . 21. The sines on the same diameter in- crease in length till they come to ...
... perpendicular to the radius or diameter drawn through the other end : or , it is half the chord of double the arc ; thus HL is the sine of the arc HB . Fig . 7 . 21. The sines on the same diameter in- crease in length till they come to ...
Page 14
... perpendicular height of a tri- angle is a line drawn from one of the an- gles perpendicular to its opposite side ; thus , the dotted line AD . Fig . 14 , is the perpendicular height of the triangle ABC . B Fig . 14 . A D NOTE . This ...
... perpendicular height of a tri- angle is a line drawn from one of the an- gles perpendicular to its opposite side ; thus , the dotted line AD . Fig . 14 , is the perpendicular height of the triangle ABC . B Fig . 14 . A D NOTE . This ...
Page 15
... perpendicular height of a rhombus or rhomboi- des , is a line drawn from one of the angles to its opposite side ; thus , the dotted lines AB . Figs . 17 and 18 , represent the perpendicular heights of those figures . 46. A trapezoid is ...
... perpendicular height of a rhombus or rhomboi- des , is a line drawn from one of the angles to its opposite side ; thus , the dotted lines AB . Figs . 17 and 18 , represent the perpendicular heights of those figures . 46. A trapezoid is ...
Page 17
... perpendicular to the other . NOTE . There are other methods of erecting a perpendicu- lar , but this is the most simple . PROBLEM IV . From a given point as at C , to drop a perpendicular on a given line AB . Fig . 25 . Fig . 25 . C B F ...
... perpendicular to the other . NOTE . There are other methods of erecting a perpendicu- lar , but this is the most simple . PROBLEM IV . From a given point as at C , to drop a perpendicular on a given line AB . Fig . 25 . Fig . 25 . C B F ...
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Common terms and phrases
Acres Roods Rods bounds calculated centre chains and links closing line compass correct Cosine Sine Cotang course and distance cyphers decimal degrees departure column diameter difference Dist diurnal motion divided division double area double mean distance draw east or west equal error EXAMPLE feet FIELD BOOK figure find the area flag GEORGE GILLET given number given side given to find Gulliver's land half hypothenuse inches land LatDegDegDegDeg Distance latitude and departure learner leg BC length M.
M. M.
M. Sine measure meridian distances method multiplied NATURAL SINES north areas number of acres opposite parallelogram perpendicular PROBLEM protractor quotient radius random line remains right angled triangle rod chains RULE scale secant side BC side required south areas spruce stake station survey surveyor taken Tang tangent thence trapezium trapezoid TRIGONOMETRY width
Popular passages
Page 6 - Congress of the United States, entitled, "An Act for the encouragement of learning, by securing the copies of Maps, Charts, and Books, to the authors and proprietors of such copies, during the times therein mentioned." And also to the Act, entitled, " An Act supplementary to an Act, entitled, ' An Act for the encouragement of learning, by securing the copies of Maps, Charts, and Books, to the Authors and Proprietors of such copies during the times therein mentioned,' and extending the benefits thereof...
Page 6 - District, has deposited in this office the title of a book, the right whereof he claims as proprietor, in the words following, to wit : " THE CHILD'S BOTANY," In conformity to the act of the Congress of the United States, entitled, " An act for the encouragement of learning by securing the copies of maps, charts, and books to the authors and proprietors of such copies, during the times therein mentioned...
Page 35 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Page 9 - Definitions. 1. A point is a small dot; or, mathematically considered, is that which has no parts, being of itself indivisible. 2. A line has length but no breadth. 3. A superficies or surface, called also afea, has length and breadth, but no thickness. 4. A solid has length, breadth, and thickness. 5. A right line is the shortest that can be drawn between two points.
Page 52 - ... angles which they make with the meridian. The position of the line BC (Fig. 31.) is determined by the angle ABC, as well as by the angle S'BC. When the several courses are given, the angles which any two contiguous sides make with each other, may be known by the following rules. 1. If one course is North and the other South, one East and the other West; subtract the less from the greater. 2. If one is North and the other South, but both East or West ; add them together. 3. If both are North or...
Page 10 - Fig. 5. 14. The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Page 147 - 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 50 - ... are truly taken and performed ; if not, an error must have been committed in one of them : in such cases, make a second protraction ; if this agrees with the former, it is to be presumed the fault is in the field work ; a re-survey must then be taken.
Page 131 - NB In the following table, in the last nine columns of each page, where the first or leading figures change from 9's to O's, points or dots are introduced instead of the O's...
Page 84 - As the length of the whole line, Is to 57.3 Degrees,* So is the said distance, To the difference of Variation required. EXAMPLE. Suppose it be required to run a line which some years ago bore N. 45°. E.