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 ... |
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Seite 12
The measure of an Angle is the Arch of a Circle contained between the two Lines
which form the Angle , the angular Point being the Centre ; thus the Angle HCB .
Fig . 7. is measured by the Arch BH ; and is said to contain so many Degrees as ...
The measure of an Angle is the Arch of a Circle contained between the two Lines
which form the Angle , the angular Point being the Centre ; thus the Angle HCB .
Fig . 7. is measured by the Arch BH ; and is said to contain so many Degrees as ...
Seite 18
Likewise, Rectangular Surveying; Or, an Accurate Method of Calculating the Area
of Any Field Arithmetically, Without Abel Flint. Suppose the Side BC 98 ; the
Angle at B 45 ° 15 ' , the Angle at D 108 ° 30 ' , consequently the other Angle 26 °
15 ...
Likewise, Rectangular Surveying; Or, an Accurate Method of Calculating the Area
of Any Field Arithmetically, Without Abel Flint. Suppose the Side BC 98 ; the
Angle at B 45 ° 15 ' , the Angle at D 108 ° 30 ' , consequently the other Angle 26 °
15 ...
Seite 30
CASE I. The Angles and one Side given , to find the other Sides , 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 .
CASE I. The Angles and one Side given , to find the other Sides , 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 .
Seite 31
To find the Angle ACB . As Side BC , 200 2.30103 Angle at A 46 ° 30 ' : Sine BAC
, 46 ° 30 ' 9.86056 C 60 30 :: Side AB , 240 2.38021 107.00 12.24077 2.30103
Sum of the three Angles 180 ° . Sum of two 107 : Sine ACB , 60 ° 30 ' 9.93974 ...
To find the Angle ACB . As Side BC , 200 2.30103 Angle at A 46 ° 30 ' : Sine BAC
, 46 ° 30 ' 9.86056 C 60 30 :: Side AB , 240 2.38021 107.00 12.24077 2.30103
Sum of the three Angles 180 ° . Sum of two 107 : Sine ACB , 60 ° 30 ' 9.93974 ...
Seite 39
When two sides of a Triangle and their contained Angle , that is , the Angle made
by those Sides , are given , the Area may be found as follows : Add together the
Logarithms of the two Sides and the Logarithmic Sine of the Angle ; from their ...
When two sides of a Triangle and their contained Angle , that is , the Angle made
by those Sides , are given , the Area may be found as follows : Add together the
Logarithms of the two Sides and the Logarithmic Sine of the Angle ; from their ...
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SYSTEM OF GEOMETRY & TRIGONOME Abel 1765-1825 Flint,George Gillet,Frederick a. P. (Frederick Augu Barnard Keine Leseprobe verfügbar - 2016 |
SYSTEM OF GEOMETRY & TRIGONOME Abel 1765-1825 Flint,George Gillet,Frederick a. P. (Frederick Augu Barnard Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
according accurately added Angle Arch Base Bearing calculated called Chains Circle Co-Sine Sine Compass contained Course Decimals describe Diagonal Difference directions Dist Distance divided double draw drawn Elongation equal EXAMPLE Field FIELD BOOK Figure find the Angle find the Area four fourth give given greater half hand Hypothenuse Land Left Leg BC length less Line Links Logarithms manner measuring method Minutes multiply Natural Sines Needle North North Areas Note number of Degrees observe opposite parallel particular Perpendicular PLATE Plot Point practice preceding PROBLEM Product Proportion protract Quotient Radius Remainder represent Right Angled Rods Roods Rule Secant Co-Secant seen Side Sine Co-Sine Sine Sine Sine Square Square Root Star Station subtract Surveying Surveyor Table Tang Tangent Co-Secant Secant third Trapezoid Triangle TRIGONOMETRY true whole
Beliebte Passagen
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.
Bibliografische Informationen
| Titel | 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 ... |
| Autor/in | Abel Flint |
| Zusammengestellt von | Abel Flint |
| Verlag | Oliver D. Cooke, 1804 |
| Original von | University of Michigan |
| Digitalisiert | 29. Mai 2007 |
| Länge | 168 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |