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 164 - Then ;As the sum of the two given sides, Is to their difference ; So is the tangent of half the sum of the two unknown angles. To the tangent of half their difference...
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 52 - ... two points be very far distant, it is almost impossible to draw the line with accuracy and exactness ; a circular line may be described more easily, and more exactly, than a straight or any other line, though even then many difficulties occur, when the circle is required to be of a large radius. "And let no one consider these reflections as the effect of too scrupulous exactness, or as an unnecessary aim at precision; for, as the foundation of all our knowledge in geography, navigation, and astronomy,...
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 44 - But if the measure be taken from any point in 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 bounded by three parallel lines ; the, innermost of these is that on which the points of the compasses are to be placed, because this alone is the line which goes to the centre, and is alone, therefore, the sectoral line. We shall now proceed to give a few general instances...
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 2 - A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies.
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 34 - ... of the larger divisions, extend the other along the sixth parallel to the seventh diagonal. For, if the five larger divisions be taken for 500, seven of the first subdivisions will be 70, which upon the sixth parallel, taking in six of the second subdivisions for units, makes the whole number 576. Or, if the five larger divisions be taken for five tens, or 50, seven of the first subdivisions will be seven units, and the six second subdivisions upon the sixth parallel, will be six tenths of an...

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