# 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 ...

Oliver D. Cooke, 1804 - 168 sider

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### Innhold

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### Populćre avsnitt

Side iv - IDE, of the said District, hath deposited in this office, the title of a book, the right whereof he claims as proprietor, in the words following, to wit : " Inductive Grammar, designed for beginners. By an Instructer." In conformity to the act of the Congress of the United States...
Side 34 - 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.
Side 33 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Side 12 - 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.
Side 30 - 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.
Side 48 - 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.
Side 41 - 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.
Side 12 - 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.
Side 48 - 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.
Side 29 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.