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added angled triangle base calculation called chord circle circumference column common contains cosine course decimal departure determined diameter difference of latitude direction distance divided draw drawn earth equal equator Example expressions extend feet field figure four fourth frustum given greater half height horizon hypothenuse inches increase latter length less logarithm longitude manner measured meridian method middle miles minutes multiplied nearly negative object observed opposite parallel perpendicular plane polygon positive PROBLEM proportion pyramid quadrant quantity radius ratio regular right angled rods root rule sailing scale secant segment ship sides similar sine solidity sphere square stations subtract supposed surface survey tables taken taking tangent term theorem third triangle trigonometry whole
Page 81 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 73 - It will be sufficient to lay the edge of a rule on C, so as to be parallel to a line supposed to pass through B and D, and to mark the point of intersection G. 126. If after a field has been surveyed, and the area computed, the chain is found to be too long or too short ; the true contents may be found, upon the principle that similar figures are to each other as the squares of their homologous sides.
Page 118 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Page 21 - AND ALSO THE AREA OF THE TRIANGLE FORMED BY THE CHORD OF THE SEGMENT AND THE RADII OF THE SECTOR. THEN...
Page 29 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Page 14 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16. And this point is called the centre of the circle.
Page 98 - For, by art. 14, the decimal part of the logarithm of any number is the same, as that of the number multiplied into 10, 100, &c.
Page 79 - T8T of the axis, and the product by .7854. Ex. If the axis of a parabolic spindle be 30, and the middle diameter 17, what is the solidity ? Ans.
Page 56 - CoR. 9. From the same demonstration it likewise follows that the arc which a body, uniformly revolving in a circle by means of a given centripetal force, describes in any time is a mean proportional between the diameter of the circle and the space which the same body falling by the same given force would descend through in the same given time.