A treatise on navigation, and nautical astronomy |
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Page 3
... produced if 4 , or the difference of 6 and 2 , be added to that quantity . If 9 is to be subtracted from any quantity , and 3 added to it , this will be equivalent to subtracting 6 , or the difference of 9 and 3 from the same quantity ...
... produced if 4 , or the difference of 6 and 2 , be added to that quantity . If 9 is to be subtracted from any quantity , and 3 added to it , this will be equivalent to subtracting 6 , or the difference of 9 and 3 from the same quantity ...
Page 14
... produced to any distance . 11. Oblique Lines are those which will meet if produced . 12. A Line is a Tangent to a circle , or other curve , when the line touches the curve without cutting it , when both are produced . 13. An Angle is ...
... produced to any distance . 11. Oblique Lines are those which will meet if produced . 12. A Line is a Tangent to a circle , or other curve , when the line touches the curve without cutting it , when both are produced . 13. An Angle is ...
Page 18
... produced , meet the other . 13. If two straight lines intersect each other , they cannot both be parallel to the same straight line . POSTULATES . 1. Let it be granted that a straight line may be drawn from one point to any other point ...
... produced , meet the other . 13. If two straight lines intersect each other , they cannot both be parallel to the same straight line . POSTULATES . 1. Let it be granted that a straight line may be drawn from one point to any other point ...
Page 21
... produced , be in the direction BE . Then the angles ABD and DBE together , are equal to two right angles ; and as A B D and D B C together are also A B equal to two right angles ; if the common angle ABD D E be omitted from each sum ...
... produced , be in the direction BE . Then the angles ABD and DBE together , are equal to two right angles ; and as A B D and D B C together are also A B equal to two right angles ; if the common angle ABD D E be omitted from each sum ...
Page 22
... producing C B , and bisecting A B , it may be shewn that the angle A B G , which is equal to CBD , is greater than BA ... produced to D , then the angles A B C and CBD are together equal to two right angles ; but the angle CBD is greater ...
... producing C B , and bisecting A B , it may be shewn that the angle A B G , which is equal to CBD , is greater than BA ... produced to D , then the angles A B C and CBD are together equal to two right angles ; but the angle CBD is greater ...
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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.