A System of Geometry and Trigonometry: Together with a Treatise on Surveying : Teaching Various Ways of Taking the Survey of a Field : Also to Protract the Same and Find the Area : Likewise, Rectangular Surveying, Or, an Accurate Method of Calculating the Area of Any Field Arithmetically, Without the Necessity of Plotting it : to the Whole are Added Several Mathematical Tables, with a Particular Explanation and the Manner of Using Them : Compiled from Various AuthorsOliver D. Cooke, 1808 - 168 páginas |
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Página 22
... preceding PROPOSITIONS and RULES being duly attended to , the solution of the following CASES of Rectangular Trigonometry will be easy . CASE I. The Angles and Hypothenuse given to find the Legs . Fig . 39 . In the Triangle ABC , given ...
... preceding PROPOSITIONS and RULES being duly attended to , the solution of the following CASES of Rectangular Trigonometry will be easy . CASE I. The Angles and Hypothenuse given to find the Legs . Fig . 39 . In the Triangle ABC , given ...
Página 24
... preceding figure may be called one more than it is , viz . 2. And whenever in any Product , & c . there are more places of Decimals than you wish to work with , if the one at the Right Hand of the last which you wish to retain is more ...
... preceding figure may be called one more than it is , viz . 2. And whenever in any Product , & c . there are more places of Decimals than you wish to work with , if the one at the Right Hand of the last which you wish to retain is more ...
Página 26
... preceding CASES . It is SO . By Natural Sines . The Angle opposite the given Leg may be found by the following Proportion : As the Hypothenuse ; Is to Unity or 1 ; So is the given leg ; To the Nat . Sine of its opposite Angle . Or ...
... preceding CASES . It is SO . By Natural Sines . The Angle opposite the given Leg may be found by the following Proportion : As the Hypothenuse ; Is to Unity or 1 ; So is the given leg ; To the Nat . Sine of its opposite Angle . Or ...
Página 27
... preceding EXAMPLE ; The Square of the Leg AB 40 is 1600 ; this subtracted from the Square of the Hypothenuse 50 which is 2500 , leaves 900 , the Square of the Leg BC , the Square Root of which is 30 , the length of Leg BC as found by ...
... preceding EXAMPLE ; The Square of the Leg AB 40 is 1600 ; this subtracted from the Square of the Hypothenuse 50 which is 2500 , leaves 900 , the Square of the Leg BC , the Square Root of which is 30 , the length of Leg BC as found by ...
Página 28
... The Hypothenuse being found by the Square Root , the Angles may be found by Nat . Sines , according to Hyp . Leg . BC . Nat . Sine 119 the preceding CASE . 28 TRIGONOMETRY . The Angles being found, the Hypothenuse may be ...
... The Hypothenuse being found by the Square Root , the Angles may be found by Nat . Sines , according to Hyp . Leg . BC . Nat . Sine 119 the preceding CASE . 28 TRIGONOMETRY . The Angles being found, the Hypothenuse may be ...
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System of Geometry and Trigonometry: Together with a Treatise on Surveying ... Abel Flint Sin vista previa disponible - 2017 |
System of Geometry and Trigonometry: Together With a Treatise on Surveying ... Abel Flint Sin vista previa disponible - 2017 |
Términos y frases comunes
Angle opposite Bearing and Distance C.Tang Chord Circle Circumference Co-Sine Sine Compass contained Angle Decimals Degrees and Minutes Dep Lat Diagonal Difference Dist divided Doub Double Area double the Area draw a Line Draw the Line EXAMPLE FIELD BOOK find the Angles find the Area find the Leg given Leg given number given Side Lat Dep Latitude and Departure Leg AB Leg BC length Loga Logarithmic Sine measuring Meridian multiply Natural Sines North Areas Note number of Acres number of Degrees Offset opposite Angle Parallelogram PLATE Plot PROB PROBLEM protract Quotient Radius Remainder Rhombus Right Angled Triangle RULE Secant Co-Secant Side BC Sine Co-Sine Tangent Sine Sine Sine South Areas Square Chains Square Links Square Root stationary Lines subtract survey a Field Surveyor Table of Logarithms Table of Natural Tangent Co-Secant Secant Tangent or Secant Trapezium Trapezoid Triangle ABC TRIGONOMETRY
Pasajes populares
Página 10 - 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, etc.
Página 31 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Página 32 - As the base or sum of the segments Is to the sum of the other two sides, So is the difference of those sides To the difference of the segments of the base.
Página 10 - The Radius of a circle is a line drawn from the centre to the circumference.
Página 78 - Go to any part of the premises where any two adjacent corners are known ; and if one can be seen from the other, take their bearing ; which, compared with that of the same line in the former survey, shows the difference. 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...
Página 44 - Field work and protraction are truly taken and performed ; if not, an error must have been committed in one of them : In such cases make a second protraction ; if this agrees with the former, it is to be presumed the fault is in the Field work ; a re- survey must then be taken.
Página 14 - Figures which consist of more than four sides' are called polygons; if the sides are equal to each other they are called regular polygons, and are sometimes named from the number of their sides, as pentagon, or hexagon, a figure of five or six sides, &c.; if the sides are unequal, they are called irregular polygons.
Página 44 - Let his attention first be directed to the map, and inform him that the top is north, the bottom south, the right hand east, and the left hand west.
Página 27 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Página 39 - To find the area of a trapezoid. RULE. — Multiply half the sum of the parallel sides by the altitude, and the product is the area.