A Treatise of Practical Surveying: Which is Demonstrated from Its First Principles ...Lewis Nichols, 1806 - 452 σελίδες |
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Αποτελέσματα 6 - 10 από τα 41.
Σελίδα 44
... triangle , ABC , the square of the hypothenuse or longest side , BC , or BCMH , is equal to the sum of the squares made on the other two sides AB and AC , that is , ABDE and ACGF ( fig . 32. ) = Through A draw AKL perpendicular to the ...
... triangle , ABC , the square of the hypothenuse or longest side , BC , or BCMH , is equal to the sum of the squares made on the other two sides AB and AC , that is , ABDE and ACGF ( fig . 32. ) = Through A draw AKL perpendicular to the ...
Σελίδα 45
... triangle ABC , the angle ACB is 60 de grees , being measured by the arc AEB ; therefore the sum of the other two angles is 120 degrees ( by cor . 1. theo . 5. ) but since AC - CB , the an- gle CAB - CBA ( by lemma preceding theo . 7 ...
... triangle ABC , the angle ACB is 60 de grees , being measured by the arc AEB ; therefore the sum of the other two angles is 120 degrees ( by cor . 1. theo . 5. ) but since AC - CB , the an- gle CAB - CBA ( by lemma preceding theo . 7 ...
Σελίδα 47
... other , so will be the sum of the small triangles in the first , to the sum of the small triangles in the second triangle ; that is AB : BD :: ABC : BDC . Plate II . Whence also the parallelograms ABCF and BDEC THEOREMS . 47.
... other , so will be the sum of the small triangles in the first , to the sum of the small triangles in the second triangle ; that is AB : BD :: ABC : BDC . Plate II . Whence also the parallelograms ABCF and BDEC THEOREMS . 47.
Σελίδα 48
... Triangles ABC , DEF , standing upon equal ba- ses AB and DE , are to each other as their alti- tudes CG and FH . fig . 2 . Let BI be perpendicular to AB and equal to CG , in which let KB - FH , and let AI and AK be drawn . The triangle ...
... Triangles ABC , DEF , standing upon equal ba- ses AB and DE , are to each other as their alti- tudes CG and FH . fig . 2 . Let BI be perpendicular to AB and equal to CG , in which let KB - FH , and let AI and AK be drawn . The triangle ...
Σελίδα 49
... triangle proportionally , must be parallel to the remaining side . Cor . 3. Hence also theo . 16. is manifest ; since the sides of the triangles ABE , ACD , being equi- angular , are proportional . THEOREM XXI . If two triangles ABC ...
... triangle proportionally , must be parallel to the remaining side . Cor . 3. Hence also theo . 16. is manifest ; since the sides of the triangles ABE , ACD , being equi- angular , are proportional . THEOREM XXI . If two triangles ABC ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
40 perches ABCD acres altitude Answer base bearing blank line centre chains and links chord circle circumferentor Co-sec Co-sine Co-tang Tang column contained cyphers decimal decimal fraction diameter difference distance line divided divisor draw drawn east edge EXAMPLE feet field-book figures fore four-pole chains half the sum height hypothenuse inches instrument Lat Dep Lat latitude line of numbers logarithm measure meridian distance multiplied needle number of degrees off-sets parallel parallelogram perpendicular piece of ground plane Plate prob PROBLEM proportion protractor quotient radius right angles right line scale of equal SCHOLIUM Secant second station sect semicircle side sights sine square root stationary distance sun's suppose survey taken tance tangent thence theo theodolite THEOREM trapezium triangle ABC trigonometry true amplitude two-pole chains vane variation whence
Δημοφιλή αποσπάσματα
Σελίδα 25 - 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.
Σελίδα 207 - ... that triangles on the same base and between the same parallels are equal...
Σελίδα 40 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 43 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Σελίδα 103 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Σελίδα 31 - Figures which consist of more than four sides are called polygons ; if the sides are all equal to each other, they are called regular polygons. They sometimes are named from the number of. their sides, as a five-sided figure is called a pentagon, one of six sides a hexagon, &"c.
Σελίδα 31 - ... they are called regular polygons. They sometimes are named from the number of their sides, as a five-sided figure is called a pentagon, one of. six sides a hexagon, &c. but if their sides are not equal to each other, then they are called irregular polygons, as an irregular pentagon, hexagon, &c.
Σελίδα 45 - The hypothenuse of a right-angled triangle may be found by having the other two sides ; thus, the square root of the sum of the squares of the base and perpendicular, will be the hypothenuse. Cor. 2. Having the hypothenuse and one side given to find the other; the square root of the difference of the squares of the hypothenuse and given side will be the required side.
Σελίδα 265 - 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°.
Σελίδα 32 - Things that are equal to one and the same thing are equal to one another." " If equals be added to equals, the wholes are equal." " If equals be taken from equals, the remainders are equal.