A Treatise of Practical Surveying: Which is Demonstrated from Its First Principles ... |
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Page 36
... theo . ) GEB = CFH , and AEG = HFD . 2. Also GEB = AEF , and CFH - EFD ; but GEB = CFH ( by part 1. of this theo . ) therefore AEF = EFD . The same way we prove FEB = EFC . 3. AEF = EFD ; ( by the last part of this theo . ) but AEF ...
... theo . ) GEB = CFH , and AEG = HFD . 2. Also GEB = AEF , and CFH - EFD ; but GEB = CFH ( by part 1. of this theo . ) therefore AEF = EFD . The same way we prove FEB = EFC . 3. AEF = EFD ; ( by the last part of this theo . ) but AEF ...
Page 37
... theo . ) and again , since AC cuts the same parallels , the angle ACE A ( by part 2. of the last . ) Therefore ECD + ACE ACD = B + A . Q. E. D. = THEOREM V. In any triangle ABC , all the three angles taken together are equal to two ...
... theo . ) and again , since AC cuts the same parallels , the angle ACE A ( by part 2. of the last . ) Therefore ECD + ACE ACD = B + A . Q. E. D. = THEOREM V. In any triangle ABC , all the three angles taken together are equal to two ...
Page 39
... theo . 4. ) but since AC - CD being radii of the same circle , it is plain ( by the preceding lemma ) that the angles subtended by them will be also equal , and that their sum is double to either of them , that is , DAC + ADC is double ...
... theo . 4. ) but since AC - CD being radii of the same circle , it is plain ( by the preceding lemma ) that the angles subtended by them will be also equal , and that their sum is double to either of them , that is , DAC + ADC is double ...
Page 40
... theo . 5. ) then have we AC , CD , and the angle ACD in one triangle ; severally equal to CB , CD , and the angle BCD in the other : therefore by theo . 6. ) A = DB . Q. E. D. Plate I. Cor . Hence it follows , that any 40 GEOMETRICAL.
... theo . 5. ) then have we AC , CD , and the angle ACD in one triangle ; severally equal to CB , CD , and the angle BCD in the other : therefore by theo . 6. ) A = DB . Q. E. D. Plate I. Cor . Hence it follows , that any 40 GEOMETRICAL.
Page 41
... theo . 6. ) AFFB ; but in the same circle , equal lines are chords of equal arcs , since they measure them : ( by def . 19. ) whence the arc AF FB , and so AFB is bisected in F , by the line CF. = Cor . Hence the sine of an arc is half ...
... theo . 6. ) AFFB ; but in the same circle , equal lines are chords of equal arcs , since they measure them : ( by def . 19. ) whence the arc AF FB , and so AFB is bisected in F , by the line CF. = Cor . Hence the sine of an arc is half ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 207 - ... that triangles on the same base and between the same parallels are equal...
Page 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.
Page 43 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Page 103 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Page 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.
Page 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.
Page 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.
Page 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°.
Page 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.