A treatise on navigation, and nautical astronomy |
From inside the book
Results 1-5 of 75
Page 9
... corresponding root of the given quantity ; and if a root of any quantity be given , that quan- tity will be obtained by the corresponding power of the given quantity . 1. Given x + 4 = 18 to find x ALGEBRAICAL CALCULATION . 9.
... corresponding root of the given quantity ; and if a root of any quantity be given , that quan- tity will be obtained by the corresponding power of the given quantity . 1. Given x + 4 = 18 to find x ALGEBRAICAL CALCULATION . 9.
Page 10
... corresponding geometrical one . The common system of logarithms , or that which is most used , and most useful in common calculations , has 10 for its root ; and the logarithm of any number in that system , is that power of 10 which is ...
... corresponding geometrical one . The common system of logarithms , or that which is most used , and most useful in common calculations , has 10 for its root ; and the logarithm of any number in that system , is that power of 10 which is ...
Page 17
... corresponding sides about the angles of each figure , proportional . 62. The Perimeter of a figure is the sum of all its sides . 63. A Problem is an operation proposed to be performed . 64. A Theorem is a truth which it is proposed to ...
... corresponding sides about the angles of each figure , proportional . 62. The Perimeter of a figure is the sum of all its sides . 63. A Problem is an operation proposed to be performed . 64. A Theorem is a truth which it is proposed to ...
Page 19
... corresponding parts of the other ; namely , the side A B to the side D E , the angle A to the angle D , and the angle B to the angle E. Q. E. D. THEOREM II . In any two triangles A B C , D E F , if the angle A be equal to the angle D ...
... corresponding parts of the other ; namely , the side A B to the side D E , the angle A to the angle D , and the angle B to the angle E. Q. E. D. THEOREM II . In any two triangles A B C , D E F , if the angle A be equal to the angle D ...
Page 21
... corresponding portions of the circumference of the circle , described by the other extremity of the revolving line , make together , the whole circumference . If , therefore , the circumference of a circle be assumed as the measure of ...
... corresponding portions of the circumference of the circle , described by the other extremity of the revolving line , make together , the whole circumference . If , therefore , the circumference of a circle be assumed as the measure of ...
Other editions - View all
Common terms and phrases
angled spherical triangle Answer apparent altitude Atlantic Ocean bisected Cape celestial object centre chronometer circle column compass computed correction Cosec Cosine Cotang course and distance declination diff lat diff long Difference of Latitude difference of longitude Dist equal equator EXAMPLES FOR EXERCISE Given A B greater Greenwich Hence horizontal parallax Indian Archipelago Indian Ocean Island Latitude and Departure latitude and longitude logarithm longitude Lunar Distance meridian distance miles moon moon's Nautical Almanac noon observed opposite Pacific Ocean parallax parallel parallel sailing parallelogram perpendicular plane sailing polar distance pole quadrant radius rectangle rhumb line right angled spherical right ascension Secant semidiameter sides squares of A C subtract Suvers Suversed Sines Table Tang tangent Theo THEOREM triangle A B C true altitude true distance Vers
Popular passages
Page 18 - LET it be granted that a straight line may be drawn from any one point to any other point.
Page 17 - When equals are taken from unequals, the remainders are unequal. 6. Things which are double of the same thing, or equal things, are equal to each other.
Page 86 - III.), is a circle. If the plane pass through the centre, then, as every point in the surface of the sphere is equidistant from its centre, the section is a plane figure, every point of whose periphery is equidistant from a certain point within it, and the figure is therefore a circle. But if the plane do not pass through...
Page 26 - Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 114 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Page 63 - If from a point without a circle two straight lines be drawn, one of which...
Page 147 - Mathematical o>jgraphy.) the arc of the equator, intercepted between the first meridian...
Page 64 - If from any point without a circle straight lines be drawn touching it, the angle contained by the tangents is double the angle contained by the straight line joining the points of contact and the diameter drawn through one of them.
Page 139 - Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex ; construct the triangle.
Page 86 - ... half a right angle, as the tangent of half the sum of the angles, at the base of the triangle to the tangent of half their difference.