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acute angle add the log adopted Appendix Azimuth centre chord circle passing Circle Sailing circle which passes circle's arc circle's track circumference construction Course Lat curve cutting point determined diameter diff difference Dist draw drawn Earth English Channel equal Equator Art Equator Lat equator line equatorial track exterior angle extremities geographical Long geographical longitude given Lat given latitudes given places globe Helena Hemisphere higher latitude hypotenuse Inclin Index points Inters Intrs Latitude of Vertex leg opposite Maximum Lat meridian Miles opposite sides Panama parallel perpendicular plane triangle points of intersection Polar Tracks poles polygon Port Jackson portion radius reckoned regular polygon represented required point Rhumb Course right-angled spherical triangle shews ship ship's place small circle smaller latitude solution sphere spherical angle spherical Course spherical distance steering straight line sum reject supplement surface Tables tangents thelntrs tudes wherefore whole degrees
Page 36 - ... acute angle contained by that straight line, and another drawn from the point in which the first line meets the plane, to the point in which a perpendicular to the plane drawn from any point of the first line above the plane, meets the same plane.
Page 33 - A sphere is a solid figure described by the revolution of a semicircle about its diameter, which remains unmoved.
Page 35 - It will be seen (Prop. 2) that all circles, whether great or small, have two poles. 5. A spherical triangle is the portion of the surface of a sphere included by the arcs of three great circles.
Page 33 - Legendre's definition of the circumference of a circle as " a curved line, all the points of which are equally distant from an interior point, called the centre...
Page 38 - During an Eclipse of the Moon, the shadow of the Earth thrown on the moon is, in all positions of the Earth, circular.
Page 73 - I.) ; hence the sum of all the angles, both interior and exterior, is equal to twice as many right angles as there are sides to the polygon. But the sum of the interior angles alone, less four right angles, is equal to the same sum (Prop.
Page 61 - One latitude, course, and distance given, to find the. difference of latitude and difference of longitude. A. ship in the latitude of 42° 30' N., and longitude of 58° 51
Page 31 - NEW TABLES to facilitate the Practice of Great Circle Sailing, together with an Application of the Theory of the great Circle on the Globe to the sailing, and an Appendix, containing some mathematical demonstrations. Accompanied by a scale of great circles on a blank chart, to determine without calculation the great circle which passes through two given places, and to show the places at which the spherical courses expressed in fourths of the...
Page 34 - ... the perpendicular let fall from the centre O to the cutting plane ABD. 6. Great and small circles on a sphere. a. Definitions. The section in which a sphere is cut by a plane is called a Great Circle when the plane passes through the centre of the sphere ; the section is called a Small Circle when the cutting plane does not pass through the centre of the sphere. Thus, on a terrestrial globe the meridians and equator are great circles ; the parallels of latitude are small circles. The Axis of...