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 Seiten |
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Seite 38
... known , the Area may be found Arithmetically , as fol- lows : Add together the three Sides ; from half their Sum subtract each side , noting down the Remainders ; mul- tiply the half Sum by one of those Remainders , and that Product by ...
... known , the Area may be found Arithmetically , as fol- lows : Add together the three Sides ; from half their Sum subtract each side , noting down the Remainders ; mul- tiply the half Sum by one of those Remainders , and that Product by ...
Seite 40
... known , the Area of the two Triangles , into which the Tra- pezium is divided , may be calculated Arithmetically , accorde ing to PROB . IX . Rule 3 . PROBLEM XII . To find the Area of a Figure con- taining more than Four Sides . RULE ...
... known , the Area of the two Triangles , into which the Tra- pezium is divided , may be calculated Arithmetically , accorde ing to PROB . IX . Rule 3 . PROBLEM XII . To find the Area of a Figure con- taining more than Four Sides . RULE ...
Seite 45
... known from the Field Book , the Area of the Field may be cal- culated Arithmetically , by finding the Area of each Triangle , according to PROB . IX . Rule 3 ; and then adding the whole together . This method , though it may require ...
... known from the Field Book , the Area of the Field may be cal- culated Arithmetically , by finding the Area of each Triangle , according to PROB . IX . Rule 3 ; and then adding the whole together . This method , though it may require ...
Seite 47
... known from the FIELD Book , and their contained Angle is known from the Bearing of the Sides . The other Angles and the Side EB may be found by OBLIQUE TRIGONOMETRY , CASE III ; and then there will be the three Sides to find the Area ...
... known from the FIELD Book , and their contained Angle is known from the Bearing of the Sides . The other Angles and the Side EB may be found by OBLIQUE TRIGONOMETRY , CASE III ; and then there will be the three Sides to find the Area ...
Seite 53
... known , two Sides and their contained Angle are given in each of the Triangles into which the Plot is divided ; the Area may , therefore , be readily calculated by the Rule above referred to . Note . As in the operation , the Logarithm ...
... known , two Sides and their contained Angle are given in each of the Triangles into which the Plot is divided ; the Area may , therefore , be readily calculated by the Rule above referred to . Note . As in the operation , the Logarithm ...
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System of Geometry and Trigonometry: Together with a Treatise on Surveying ... Abel Flint Keine Leseprobe verfügbar - 2017 |
System of Geometry and Trigonometry: Together With a Treatise on Surveying ... Abel Flint Keine Leseprobe verfügbar - 2017 |
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Seite 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.
Seite 27 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 23 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.