Elements of Plane and Spherical Trigonometry |
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Common terms and phrases
added angle base bearing called circle Co-tangent column complement computed correction corresponding cosine course cubic decimal Degrees departure determine diameter difference difference of latitude direction distance divided draw drawn earth east entire equal equator example feet field figure four Geometry give given greater ground half height Hence horizontal hypothenuse inches latitude length less logarithm longitude manner means measured meridian method middle miles minutes Multiply natural object observed obtain opposite parallel perpendicular places plane pole position preceding Prob PROBLEM Prop proportional quadrant radius remaining represent Required right-angled RULE sailing scale secant ship side sine solidity spherical triangle square station subtract surface survey tang tangent Theorem third triangle triangle ABC vernier vertical yards
Popular passages
Page 20 - The circumference of every circle is supposed to be divided into 360 equal parts, • called degrees, each degree into 60 minutes, and each minute into 60 seconds, etc.
Page 69 - To find the volume of a pyramid, or of a cone. Multiply the area of the base by one third of the altitude.
Page 17 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 71 - ADD THE LENGTH OF THE EDGE TO TWICE THE LENGTH OF THE BASE, AND MULTIPLY THE SUM BY £ OF THE PRODUCT OF THE HEIGHT OF THE WEDGE AND THE BREADTH OF THE BASE.
Page 119 - A=gThat is, the difference between the true and the apparent level, is nearly equal to the square of the distance divided by the diameter of the earth. Ex. 1. What is the difference between the true and the apparent level, for a distance of one English mile, supposing the earth to be 7940 miles in diameter?
Page 59 - To find the area of an irregular polygon. RULE. Draw diagonals dividing the polygon into triangles, and find the sum of the areas of these triangles.
Page 45 - ... a scale of 100 rods to an inch, in which case the side AB will be represented by 4.32 inches ; or we may construct it upon a scale of 200 rods to an inch ; that is, 100 rods to a half inch, which is very conveniently done from a scale on which a half inch is divided like that described in Art.
Page 51 - 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 37 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 51 - A. sin (A + B) - sin A cos B + cos A sin B. sin (A - B) - sin A cos B - cos A sin B. cos (A + B) - cos A cos B - sin A sin B.
Bibliographic information
| Title | Elements of Plane and Spherical Trigonometry |
| Author | Elias Loomis |
| Edition | 25 |
| Publisher | Harper, 1865 |
| Original from | Harvard University |
| Digitized | 9 Oct 2007 |
| Length | 150 pages |
| Export Citation | BiBTeX EndNote RefMan |