## A Treatise of Practical Surveying: Which is Demonstrated from Its First Principles. Wherein Every Thing that is Useful and Curious in that Art, is Fully Considered and Explained ... The Whole Illustrated with CopperplatesP. Wogan, 1795 - 319 pages |

### From inside the book

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**is to their Difference ; as the Tangent of half the Sum of**the two unknown Angles A and C is to the Tangent of half their Difference . Fig . 11 . Produce Plate V. Produce AB , and make HB = BC 94 PLANE TRIGONOMETRY . \### Common terms and phrases

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### Popular passages

Page 13 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees; and each degree into 60 minutes, each minute into 60 seconds, and so on.

Page 88 - 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 56 - ... logarithm of that number. EXAMPLE. • Required, the logarithm of 365. Answer, 2.56229. And though most tables of logarithms run but to 10000, yet by them the log. of any number not exceeding 10,000,000 may be found, and on the contrary, the number to any such logarithm, thus : 1 Find the log. of the first four figures of the given number 2. Take that log. from the log: of the number next following, and note their difference, 3. Multiply that difference by the remaining figures of the given number...

Page 91 - In the triangle ABC, there is given AB 240, the angle A 46° 30', and BC 200, to find the angle C, being acute, the angle B, and the side AC.

Page 89 - ED. that is as the sum of the two sides AB and BC, is to their difference ; so is the tangent of half the sum of the two unknown angles A and C, to the tangent of half their difference.

Page 32 - KCML, the sum of the two parallelograms or square BCMH ; therefore the sum of the squares on AB and AC is equal to the square on BC.

Page 19 - Four quantities are said to be in proportion when the product of the extremes is equal to that of the means, thus if A multiplied by D, be equal to B multiplied by C, then A is said to be to B as C is to D. POSTULATES OR PETITIONS. 1 . That a right line may be drawn from any one given point to another. 2. That a right line may be produced or continued at pleasure. 3. That from any centre and with any radius, the circumference of a circle may be described.

Page 13 - A chord is a right line drawn from one end of an arc or arch (that is, any part of the circumference of a circle) to the other ; and is the measure of the arc. Thus the right line HG, is the measure of the arc HBG.

Page 72 - ... these three proportions, for DE we put its equal be, for AE put ab, and for AD put ac, they will become AB : ab : : AC : ас, and AB : ab : : BC : be, and AC : ac : : BC : be.

Page 285 - Then if the true and magnetic amplitudes, be both north or both south, their difference is the variation ; but if one be north and the other south, their sum is the variation ; and to know whether it be easterly or westerly, suppose the observer looking...