A treatise on navigation, and nautical astronomyBaldwin, Cradock, and Joy, 1824 - 551 Seiten |
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Seite 67
... sine of an arc is a perpendicular let fall from one of its extremities upon the diameter which passes through the other extremity . Cor . 7. The versed sine of an arc is that portion of the diameter intercepted between the sine and the ...
... sine of an arc is a perpendicular let fall from one of its extremities upon the diameter which passes through the other extremity . Cor . 7. The versed sine of an arc is that portion of the diameter intercepted between the sine and the ...
Seite 68
... sine do . Vers . A B. Suversed sine do . Suvers . A B. Coversed sine do . Covers . A B. From the above definitions we deduce the following obvious con- sequences : viz . 1st , When an arc is evanescent , or becomes nothing , its sine ...
... sine do . Vers . A B. Suversed sine do . Suvers . A B. Coversed sine do . Covers . A B. From the above definitions we deduce the following obvious con- sequences : viz . 1st , When an arc is evanescent , or becomes nothing , its sine ...
Seite 69
... sine , tangent , & c . of an arc , which is the measure of any given angle , as ABC , is to the sine , tangent , & c . of any other arc , by which the same angle A B C may be measured , as the radius of the first arc to the radius of ...
... sine , tangent , & c . of an arc , which is the measure of any given angle , as ABC , is to the sine , tangent , & c . of any other arc , by which the same angle A B C may be measured , as the radius of the first arc to the radius of ...
Seite 71
... sine of 30 ° , the versed sine of 60 ° , and the cosine of 60 ° are each equal to half the radius ; and the secant of 60 ° is equal to the diameter , or to double the radius . G Let D be the centre of a circle , A B an arc of 60 ° , and ...
... sine of 30 ° , the versed sine of 60 ° , and the cosine of 60 ° are each equal to half the radius ; and the secant of 60 ° is equal to the diameter , or to double the radius . G Let D be the centre of a circle , A B an arc of 60 ° , and ...
Seite 75
... sine of the sum of two arcs , is to the sum of their sines , so is the difference of their sines to the sine of their difference . By an analogous process we deduce the following expression from the third and fourth of Formula 1 . cos A ...
... sine of the sum of two arcs , is to the sum of their sines , so is the difference of their sines to the sine of their difference . By an analogous process we deduce the following expression from the third and fourth of Formula 1 . cos A ...
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Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 18 - LET it be granted that a straight line may be drawn from any one point to any other point.
Seite 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.
Seite 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...
Seite 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.
Seite 114 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Seite 63 - If from a point without a circle two straight lines be drawn, one of which...
Seite 147 - Mathematical o>jgraphy.) the arc of the equator, intercepted between the first meridian...
Seite 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.
Seite 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.
Seite 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.