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 Fine 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 ... |
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Page 9
... PLATE I. Figure 1. is an Angle , formed by the meeting of the Lines AB and BC . 7. If a right Line CD . Fig . 2. fall upon another Right Line AB , so as to incline to neither side , but make the Angles on each side equal , then those ...
... PLATE I. Figure 1. is an Angle , formed by the meeting of the Lines AB and BC . 7. If a right Line CD . Fig . 2. fall upon another Right Line AB , so as to incline to neither side , but make the Angles on each side equal , then those ...
Page 14
... PLATE 1. Fig . 22 . With the Dividers take the nearest distance between the Point D and the given Line AB ; with that dis- tance set one foot of the Dividers any where on the Line AB , as at E , and draw the Arch C ; through the Point D ...
... PLATE 1. Fig . 22 . With the Dividers take the nearest distance between the Point D and the given Line AB ; with that dis- tance set one foot of the Dividers any where on the Line AB , as at E , and draw the Arch C ; through the Point D ...
Page 18
... PLATE II . Fig . 37 . Draw the Line AB the length of the proposed Square ; from B erect a Perpendicular to C and make it of the same length as AB ; from A and C , with the some distance in the Dividers , describe Arches inter- secting ...
... PLATE II . Fig . 37 . Draw the Line AB the length of the proposed Square ; from B erect a Perpendicular to C and make it of the same length as AB ; from A and C , with the some distance in the Dividers , describe Arches inter- secting ...
Page 20
... PLATE II . Figure 44. it is plain from PLATE I. Fig . 7. compared with the Geometrical Definitions to which that Figure refers , that if the Hy- pothenuse AC be made Radius , and with it an Arch of a Circle be described from each end ...
... PLATE II . Figure 44. it is plain from PLATE I. Fig . 7. compared with the Geometrical Definitions to which that Figure refers , that if the Hy- pothenuse AC be made Radius , and with it an Arch of a Circle be described from each end ...
Page 30
... PLATE II . Figure 47 . In the Triangle ABC , given the Angle at B 48 ° , the Angle at C 72 ° , consequently the Angle at A 60 ° , and the Side AB 200 ; to find the Sides AC and BC . To find the Side AC . As Sine ACB , 72 ° : Side AB ...
... PLATE II . Figure 47 . In the Triangle ABC , given the Angle at B 48 ° , the Angle at C 72 ° , consequently the Angle at A 60 ° , and the Side AB 200 ; to find the Sides AC and BC . To find the Side AC . As Sine ACB , 72 ° : Side AB ...
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A System of Geometry and Trigonometry: Together with a Treatise on Surveying ... Able Flint No preview available - 2017 |
A System of Geometry and Trigonometry: Together with a Treatise on Surveying ... Able Flint No preview available - 2017 |
Popular passages
Page 26 - 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.
Page 23 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 8 - 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 25 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Page 25 - The solution of this CASE depends on the following PROPOSITION. In every Plane Triangle, As the Sum of any two Sides ; Is to their Difference ; So is the Tangent of half the Sum of the two opposite Angles ; To the Tangent of half the Difference between them. Add this half difference to half the Sum of the Angles and you will have the greater Angle ; and...
Page 8 - The radius of a circle is a line drawn from the centre to the circumference, as A, B.
Page 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.
Page 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.