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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Page 28
... feet long , having one of the edges divided into inches and tenths , and seve- ral triangles with their hypothenuse in different pro- portions to their respective perpendiculars . Thus , if you would make it answer for a scale of twenty ...
... feet long , having one of the edges divided into inches and tenths , and seve- ral triangles with their hypothenuse in different pro- portions to their respective perpendiculars . Thus , if you would make it answer for a scale of twenty ...
Page 31
... feet , & c . each part on the scale answering to one foot , one yard , & c . and the plan will be larger or smaller , as the scale contains a smaller or a greater number of parts in an inch . Hence a variety of scales is useful to lay ...
... feet , & c . each part on the scale answering to one foot , one yard , & c . and the plan will be larger or smaller , as the scale contains a smaller or a greater number of parts in an inch . Hence a variety of scales is useful to lay ...
Page 32
... feet and inches , the first primary division is often duodecimally divided by an upper line ; therefore , to lay down any number of feet and inches , as for instance , eight feet eight inches , extend the compasses from eight of the ...
... feet and inches , the first primary division is often duodecimally divided by an upper line ; therefore , to lay down any number of feet and inches , as for instance , eight feet eight inches , extend the compasses from eight of the ...
Page 35
... feet upwards till one of them fall into the point where the diagonal from the nearest tenth cuts the same parallel as is cut by the other on the vertical line ; then one foot shews the chain , and the other the hundredth parts or odd ...
... feet upwards till one of them fall into the point where the diagonal from the nearest tenth cuts the same parallel as is cut by the other on the vertical line ; then one foot shews the chain , and the other the hundredth parts or odd ...
Page 40
... feet long , when opened to its greatest extent . In describing the lines usually placed on this instrument , I refer to those commonly laid down on the best six - inch brass sectors . But as the principles are the same in all , and the ...
... feet long , when opened to its greatest extent . In describing the lines usually placed on this instrument , I refer to those commonly laid down on the best six - inch brass sectors . But as the principles are the same in all , and the ...
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Geometrical and Graphical Essays, Containing, a General Description of the ... Sir William Jones,George Adams No preview available - 2015 |
Common terms and phrases
acres adjusted altitude avoirdupois axis beam compasses Bisect brass centre chains chord circle circumference circumferentor contained describe diameter difference direction ditto divided divisions draw a line edge error feet field book figure fixed foot girt given line given point gives ground height horizon glass horizontal inches instrument intersection length limb mark measure meridian method minutes move moveable needle nonius object observation offsets pantographer parallelogram perpendicular plane plate 9 plotting pole polygon PROBLEM proportion protractor quadrant radius right angles right ascension right line ruler scale of equal screw secant sector sextant shew shewn side sight sine slide slider socket spirit level square staff star station line straight line subtracted sun's survey taken tance tangent telescope theodolite tion toises transverse distance transverse measure trapezium triangle vanishing point vertical
Popular passages
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...