A Course of Mathematics: Containing the Principles of Plane Trigonometry, Mensuration, Navigation, and Surveying : Adapted to the Method of Instruction in the American Colleges, Volumes 1-3

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Durrie and Peck, 1838 - Geometry

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Page 120 - 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 83 - 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 45 - A cone is a solid figure described by the revolution of a right angled triangle about one of the sides containing the right angle, which side remains fixed.
Page 57 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
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 63 - 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...
Page 16 - 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 124 - From half the sum of the three sides subtract each side separately ; multiply together the half sum and the three remainders, and extract the square root of the product.
Page 100 - 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 58 - 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.

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