# A Practical Application of the Principles of Geometry to the Mensuration of Superficies and Solids: Being the Third Part of a Course of Mathematics, Adapted to the Method of Instruction in the American Colleges

Oliver Steele, printer, 1815 - Measurement - 96 pages

### Popular passages

Page 68 - 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 41 - A right cone is a solid described by the revolution of a right angled triangle about one of the sides which contain the right angle.
Page 71 - 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 105 - 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 12 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 49 - ... at the head of the column, take the degrees at the top of the table, and the minutes on the left; but if the title be at the foot of the column, take the degrees at the bottom, and the minutes on the right.
Page 20 - THEN, IF THE SEGMENT BE LESS THAN A SEMI-CIRCLE, SUBTRACT THE AREA OF THE TRIANGLE FROM THE AREA OF THE SECTOR.
Page 46 - Jidd together the areas of the two ends, and the square root of the product of these areas ; and multiply the sum by \ of the perpendicular height.