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, 1804 - 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 30 . 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 30 . 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 the Leg BC as found ...
... 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 the Leg BC as found ...
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 |
Pasajes populares
Página 28 - 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 27 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Página 6 - The Circumference of every circle is supposed to be divided into 360 equal parts, called Degrees ; and each degree into 60 Minutes, each minute into 60 Seconds, and so on.
Página 24 - In this case the" hypothenuse may be found by the square root without finding the angles ; according to the following PROPOSITION. IN EVERY RIGHT ANGLED TRIANGLE, THE SUM OF THE SQUARES OF THE TWO LEGS IS EQUAL TO THE SQUARE OF THE HYPOTHENUSE. In the above EXAMPLE, the square of AB 78.7 is 6193.69, the square of BC 89 is 7921 ; these added make 14114,69 the square root of which is nearest 119.
Página 40 - 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 33 - To find the area of a trapezoid. RULE. Multiply half the sum of the two parallel sides by the perpendicular distance between them : the product will be the area.
Página 6 - Therefore all radii of the same circle are equal. 13. The diameter of a circle is a right line drawn from one side of the circumference to the other, passing through the centre ; and it divides the circle into two equal parts, called semicircles ; as AB or DE.
Página 40 - 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 23 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.