## A treatise on navigation, and nautical astronomy |

### From inside the book

Page 27

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**are equal to twice as many right angles as the figure has**sides , wanting four right angles . Q. E. D. Cor . 1. All the interior angles of any quadrilateral figure are together equal to four right angles . Cor . 2. If the sum of two ...### 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.