## 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

A B C added altitude Answer apparent altitude base called Cape centre circle Coast column compass computed contained correction corresponding Cosec Cosine Cotang course declination departure difference Difference of Latitude Dist distance divided drawn England equal equator EXAMPLES figure given greater Greenwich half Hence horizontal hour Indian Island Isles join latitude less logarithm longitude mean measured meet meridian middle miles moon nearly noon object observed opposite Pacific Ocean parallax parallel passing perpendicular plane pole PROBLEM produced proportion quantity radius rectangle remainder right angles right ascension sail Secant ship sides sine squares star subtract Suvers Table taken Tang tangent Theo THEOREM triangle true Vers ΟΝ

### 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.