A Treatise of Practical Surveying: Which is Demonstrated from Its First Principles ... |
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Page 38
... b , by making the angle a cd- dcb ( by postulate 4. ) then because ac - bc , and cd common , ( by the last ) the triangle adc - dcb ; and therefore the angle ab . Q. E. D. Plate 1 . Cor . Hence if from any point 38 GEOMETRICAL.
... b , by making the angle a cd- dcb ( by postulate 4. ) then because ac - bc , and cd common , ( by the last ) the triangle adc - dcb ; and therefore the angle ab . Q. E. D. Plate 1 . Cor . Hence if from any point 38 GEOMETRICAL.
Page 39
... Hence if from any point in a perpendi- cular which bisects a given line , there be drawn right lines to the ... Hence an angle at the circumference is measured by half the arc it subtends or stands on . Cor . 2. Hence all angles at the ...
... Hence if from any point in a perpendi- cular which bisects a given line , there be drawn right lines to the ... Hence an angle at the circumference is measured by half the arc it subtends or stands on . Cor . 2. Hence all angles at the ...
Page 40
... Hence an angle in a segment greater than a semicircle is less than a right angle ; thus ADB is measured by half the arc AB , but as the arc AB is less than a semicircle , therefore half the arc AB , or the angle ADB is less than half a ...
... Hence an angle in a segment greater than a semicircle is less than a right angle ; thus ADB is measured by half the arc AB , but as the arc AB is less than a semicircle , therefore half the arc AB , or the angle ADB is less than half a ...
Page 41
... Hence it follows , that any line bisecting a chord at right angles , is a diameter ; for a line drawn from the centre perpendicular to a chord , bisects that chord at right angles ; therefore , con- versely , a line bisecting a chord at ...
... Hence it follows , that any line bisecting a chord at right angles , is a diameter ; for a line drawn from the centre perpendicular to a chord , bisects that chord at right angles ; therefore , con- versely , a line bisecting a chord at ...
Page 43
... Hence the quadrilateral figure ABCD is a parallelogram , and the diagonal BD bisects the same , inasmuch as the triangle ABD - BCD , as now proved . Cor . 2. Hence also the triangle ABD on the same base AB , and between the same ...
... Hence the quadrilateral figure ABCD is a parallelogram , and the diagonal BD bisects the same , inasmuch as the triangle ABD - BCD , as now proved . Cor . 2. Hence also the triangle ABD on the same base AB , and between the same ...
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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.