A Treatise on Practical Surveying: Which is Demonstrated from Its First Principles. Wherein Everything that is Useful and Curious in that Art, is Fully Considered and ExplainedF. Lucas and Joseph Cushing, 1818 - 478 páginas |
Dentro del libro
Resultados 6-10 de 67
Página 33
... thus , as A is to B , so is C to D ; but when three quantities A , B , C , are proportional , the middle quantity is repeated , and they are written A : B :: B : C. GEOMETRICAL THEOREMS . THEOREM I. IF F a right line GEOMETRY . 33.
... thus , as A is to B , so is C to D ; but when three quantities A , B , C , are proportional , the middle quantity is repeated , and they are written A : B :: B : C. GEOMETRICAL THEOREMS . THEOREM I. IF F a right line GEOMETRY . 33.
Página 34
... right line falls on another , as A B , or EB , does on C D , ( fig . 20. ) it either makes with it two right angles , or two angles equal to two right angles . B 20 . E D 1. If AB be perpendicular to CD , then ( by def . 11. ) the ...
... right line falls on another , as A B , or EB , does on C D , ( fig . 20. ) it either makes with it two right angles , or two angles equal to two right angles . B 20 . E D 1. If AB be perpendicular to CD , then ( by def . 11. ) the ...
Página 35
... right line cross another ( as C does BD ) the opposite angles ade by those lines , will be equal to ach other ; that is , AEB to CED nd BEC to AED . fig . 21 . B A fig . 24 . C D By theorem 1. BEC + CED = 2 right angles . and CED + DEA ...
... right line cross another ( as C does BD ) the opposite angles ade by those lines , will be equal to ach other ; that is , AEB to CED nd BEC to AED . fig . 21 . B A fig . 24 . C D By theorem 1. BEC + CED = 2 right angles . and CED + DEA ...
Página 36
... right angles , and AEF + CFE are equal to two right angles . 1. Since AB is parallel to CD , they may be consi- dered as one broad line , crossed by another line , as GH ; ( then by the last theo . ) GEB - CFH , and AEG = HFD . 2. Also ...
... right angles , and AEF + CFE are equal to two right angles . 1. Since AB is parallel to CD , they may be consi- dered as one broad line , crossed by another line , as GH ; ( then by the last theo . ) GEB - CFH , and AEG = HFD . 2. Also ...
Página 39
... line , there be drawn right lines to the extremities of the given one , they with it will form an isosceles triangle , THEOREM VII . fg . 25 . The angle BCD at the centre of a circle ABED is double the angle BAD at the circumference ...
... line , there be drawn right lines to the extremities of the given one , they with it will form an isosceles triangle , THEOREM VII . fg . 25 . The angle BCD at the centre of a circle ABED is double the angle BAD at the circumference ...
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A Treatise of Practical Surveying: Which is Demonstrated From Its First ... Robert Gibson Sin vista previa disponible - 2021 |
Términos y frases comunes
40 perches ABCD acres altitude Answer base bearing blank line centre chains and links chord circle circumferentor Co-secant Secant Co-sine Co-tang column compass complement contained cyphers decimal decimal fraction Dep Lat difference Dist divided divisor draw east edge EXAMPLE feet field-book figures four-pole chains half the sum height Hence hypothenuse inches instrument Lat Dep latitude length logarithm measure meridian distance multiplied needle number of degrees object off-sets parallel parallelogram perpendicular piece of ground plane pole polygon Portmarnock PROB proportion protractor quotient radius right angles right line scale of equal SCHOLIUM second station sect semicircle side sights sine square root stationary distance stationary line sun's suppose survey taken Tang thence theo theodolite THEOREM thro triangle ABC trigonometry true azimuth two-pole chains vane variation
Pasajes populares
Página 42 - 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.
Página 99 - ... on a side, denotes its length to be given in feet, yards, perches, or miles, &c. and this mark", either in an angle or on a side, denotes the angle or side to be required. ; From these proportions it may be observed ; that to find a side, when the angles and one side are given, any side may be made the radius; and to find an angle, one of the given sides must be made the radius. So that in the 1st, 2d, and 3d cases, any side as well required as given may be made the radius, and in the first statings...
Página 46 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Página 93 - 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.
Página 114 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Página 4 - POMEROY, of the said District, hath deposited in this Office the title of a Book, the right whereof he claims as Proprietor, in the words following, to wit : . . "Biography of the Signers to the Declaration of Independence.
Página 48 - 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.
Página 115 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Página 175 - ... the two cardinal points of your compass the point of the needle lies between (the north, south, east, and west being called the four cardinal points, and are graved on the bottom of the box), putting down those points together by their initial letters, and thereto annexing the number of degrees, counting from the north or south, as before, thus ; if the point of your needle lies between the north and east, north and west, south and east, or south and west points in the bottom of the box, then...
Página 282 - But if one corner cannot be seen from the other, run the line according to the given bearing, and observe the nearest distance between the line so run and the corner: then...