A Compleat Treatise of Practical Navigation Demonstrated from It's First Principles: Together with All the Necessary Tables. To which are Added, the Useful Theorems of Mensuration, Surveying, and Gauging; with Their Application to Practice. Written for the Use of the Academy in Tower-Street

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J. Brotherton, 1734 - Navigation - 414 pages
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Page 4 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, etc.
Page 4 - A diameter of a circle is a straight line drawn through the center and terminated both ways by the circumference, as AC in Fig.
Page 4 - B is an arc, and a right line drawn from one end of an arc to the other is called a chord.
Page 37 - ... 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, 6 and 1 , 5 and 6, or 6 and 5.
Page 59 - IN a plain triangle, the fum of any two fides is to their difference, as the tangent of half the fum of the angles at the bafe, to the tangent of half their difference.
Page 57 - In any triangle, the sides are proportional to the sines of the opposite angles, ie. t abc sin A sin B sin C...
Page 22 - 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 14 - AED, is equal to two right angles ; that is, the sum of the angles...
Page 14 - Thro' C, let CE be drawn parallel to AB ; then since BD cuts the two parallel lines BA, CE ; the angle ECD = B, (by part 3, of the last theo.) and again, since AC cuts the same parallels, the angle ACE = A (by part 2. of the last.) Therefore ECD + ACE = ACD =1 B + AQED THEOREM V. In any triangle ABC, all the three angles taken together are equal to two right angles, viz.
Page 71 - IT is well known, that the longitude of any place is an arch, of the equator, intercepted between the firft meridian and the meridian of that place ; and that this arch is proportional to the quantity of time that the fun requires to move from the one meridian to the other ; which is at the rate of 24 hours for 360 degrees; one hour for 15 degrees; one minute of time for.

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