## 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 ... |

### Dentro del libro

Resultados 1-5 de 5

Página 12

The measure of an Angle is the Arch of a Circle

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

The measure of an Angle is the Arch of a Circle

**contained**between the two Lineswhich 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 ... Página 39

When two sides of a Triangle and their

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 madeby 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 ...

Página 47

... of Scale and Di. viders . In the preceding ExamPLE , suppose the Field divided

into three Triangles . See Fig . 53. In the Triangle EAB , the Sides EA and AB are

known from the FIELD Book , and their

... of Scale and Di. viders . In the preceding ExamPLE , suppose the Field divided

into three Triangles . See Fig . 53. In the Triangle EAB , the Sides EA and AB are

known from the FIELD Book , and their

**contained**Angle is known from ... Página 68

But the space osxw will be

70w8 , which was

manner , it will be seen that the North Areas

taken ...

But the space osxw will be

**contained**in the next South Area ; and the space70w8 , which was

**contained**in the two ... By examining the whole Figure , in thismanner , it will be seen that the North Areas

**contain**all without the Field that istaken ...

Página 74

As in this Triangle two Sides and their

be found by Prob . IX . Rule 4 . Page 39 . Having found the Area of this Triangle ,

proceed to find CN according to PROB . II . Page 71 , as follows : As the Area of ...

As in this Triangle two Sides and their

**contained**Angle are given , the Area maybe found by Prob . IX . Rule 4 . Page 39 . Having found the Area of this Triangle ,

proceed to find CN according to PROB . II . Page 71 , as follows : As the Area of ...

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SYSTEM OF GEOMETRY & TRIGONOME Abel 1765-1825 Flint,George Gillet,Frederick a. P. (Frederick Augu Barnard Sin vista previa disponible - 2016 |

SYSTEM OF GEOMETRY & TRIGONOME Abel 1765-1825 Flint,George Gillet,Frederick a. P. (Frederick Augu Barnard Sin vista previa disponible - 2016 |

### Términos y frases comunes

according accurately added Angle Angled Triangle Arch Base Bearing calculated called 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 known Land Left Leg BC length less Line Links Logarithms manner measuring method Minutes multiply Natural Sines Needle North North Areas Note observe opposite parallel particular Perpendicular PLATE Plot Point practice preceding PROBLEM Product Proportion protract Quotient Radius Remainder represent Right Angled 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

### 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.