Geometrical and Graphical Essays: Containing a General Description of the Mathematical Instruments Used in Geometry, Civil and Military Surveying, Levelling, and Perspective; with Many New Practical Problems, Illustrated by Thirty-four Copper Plates

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C. Baldwin for, and sold by W. and S. Jones, 1813 - Geometry - 534 pages

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Page 50 - ... tangents, will be the centre sought. In the secant. The transverse distance of 0 and 0, or the. beginning of the secants, near the centre of the sector, will be the radius sought. Given the radius and any line representing a sine, tangent, or secant, to find the degrees corresponding to that line.
Page 42 - The value of the divisions on most of the lines is determined by the figures adjacent to them ; these proceed by tens, which constitute the divisions of the first order, and are numbered accordingly ; but the value of the divisions on the line of lines, that are distinguished by figures, is entirely arbitrary, and may represent any value that is given to them ; hence the figures 1, 2, 3, 4, &c. may denote either 10, 20, 30, 40, or 100, 200, 300, 400, and so on.
Page 44 - When a measure is taken on any of the sectoral lines beginning at the centre, it is called a lateral distance ; but when a measure is taken from any point on one line to its corresponding point on the line of the same denomination on the other leg, it is called a transverse or parallel distance. The divisions of each sectoral line are contained within three parallel lines, the innermost...
Page 41 - The scales, or lines graduated upon the faces of the instrument, and which are to be used as sectoral lines, proceed from the centre, and are, 1. Two scales of equal parts, one on each leg, marked LIN. or L. Each of these scales, from the great extensiveness of its use, is called the line of lines.
Page 2 - A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies.
Page 3 - ... When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it. 11. An obtuse angle is that which is greater than a right angle. 12. An acute angle is that which is less than a right angle. 13. A term or boundary is the extremity of any thing.
Page 40 - ... or practice. The real inventor of this valuable instrument is unknown ; yet of so much merit has the invention appeared, that it was claimed by Galileo, and disputed by nations. This instrument derives its name from the tenth definition of the third book of Euclid, where he defines the sector of a circle. It is formed of two equal rules called legs ; these legs are moveable about the centre of a joint, and will, consequently, by their different openings, represent every possible variety of plane...
Page 44 - ... equal to one another, but unequal to the angle made by all the other pairs of lines. The solution of questions on the sector is said to be simple, when the work is begun and ended upon the same pair of lines ; compound, when the operation is begun upon one pair of lines and finished upon another. In a compound solution the two pairs of lines used must make equal angles at the...
Page 14 - ... steel. The difference in the texture and pores of the two metals causes the parts to adhere less together, diminishes the wear, and promotes uniformity in their motion. The truth of the work is ascertained by the smoothness and equality of the motion at the joint, for all shake and irregularity is a certain sign of imperfection. The points should be of steel, so tempered as neither to be easily bent or blunted ; not too fine and tapering, and yet meeting closely when the compasses are shut. As...
Page 52 - ... along this edge, we draw a line from one point to the other, which, for common purposes, is sufficiently exact ; but, where great accuracy is required, it will be found extremely difficult to lay the rule equally with respect to both the points, so as not to be nearer to one point than the other. It is difficult also so to carry the needle, or pen, that it shall neither incline more to one side than the other of the rule ; and thirdly, it is very difficult to find a rule that shall be perfectly...

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