A Course of Mathematics: Containing the Principles of Plane Trigonometry, Mensuration, Navigation, and Surveying : Adapted to the Method of Instruction in the American Colleges, 第 1〜3 巻
Durrie and Peck, 1838
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added angled triangle base calculation called chord circle circumference column common complement 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 Note object observed opposite parallel perpendicular plane polygon portion 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
83 ページ - 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.
57 ページ - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
73 ページ - 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.
63 ページ - When a quantity is greater than any other of the same class, it is called a maximum. A multitude of straight lines, of different lengths, may be drawn within a circle. But among them all, the diameter is a maximum. Of all sines of angles, which can be drawn in a circle, the sine of 90° is a maximum. When a quantity is less than any other of the same class, it is called a minimum. Thus, of all straight lines drawn from a given point to a given straight line, that which is perpendicular to the given...
16 ページ - 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.
100 ページ - 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.
58 ページ - 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.