An introduction to the theory ... of plane and spherical trigonometry ... including the theory of navigation1839 |
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Σελίδα vii
... given , to find an angle . In Prop . XXVIII . of Dr. Simson's work , the process is con- ducted from principles purely Geometrical , and the demon- stration is long and tedious ; whereas in Legendre's Geometry , article LXXVIII , page ...
... given , to find an angle . In Prop . XXVIII . of Dr. Simson's work , the process is con- ducted from principles purely Geometrical , and the demon- stration is long and tedious ; whereas in Legendre's Geometry , article LXXVIII , page ...
Σελίδα xxii
... given point in a given line , or to make a right angle CHAPTER I. 2. To draw a straight line perpendicular to a given straight line from a given point without it · 24 24 26 26 27 27 · • 27 3. To make an angle of any proposed number of ...
... given point in a given line , or to make a right angle CHAPTER I. 2. To draw a straight line perpendicular to a given straight line from a given point without it · 24 24 26 26 27 27 · • 27 3. To make an angle of any proposed number of ...
Σελίδα xxiv
... Given the time under any known meridian , to find the corresponding time at Greenwich 4. Given the time at Greenwich , to find the correspond- ing time under any known meridian 5. To reduce the declination of the sun , as given in the ...
... Given the time under any known meridian , to find the corresponding time at Greenwich 4. Given the time at Greenwich , to find the correspond- ing time under any known meridian 5. To reduce the declination of the sun , as given in the ...
Σελίδα xxv
... given place on a given day 9. To find the apparent time at which the moon or planet culminates , or passes the meridian of a given place on a given day · · • 274 10. Given the observed altitude of a fixed star , to find its true ...
... given place on a given day 9. To find the apparent time at which the moon or planet culminates , or passes the meridian of a given place on a given day · · • 274 10. Given the observed altitude of a fixed star , to find its true ...
Σελίδα xxvi
... given , to find its right ascension and declin- ation , et contra • • • 304 • 306 • 310 11. The right ascensions and declinations of two stars , or the latitudes and longitudes of two stars being given , to find their distance 12. The ...
... given , to find its right ascension and declin- ation , et contra • • • 304 • 306 • 310 11. The right ascensions and declinations of two stars , or the latitudes and longitudes of two stars being given , to find their distance 12. The ...
Συχνά εμφανιζόμενοι όροι και φράσεις
acute altitude angle CAB arc BF base centre complement construction cosec cosine cotangent degrees diff difference of latitude distance division draw ecliptic equator Euclid extent will reach find the angle formulæ given angle given side greater Greenwich half the sum Hence horizon hypoth less line of numbers line of sines logarithm logarithmic sine mean arc measure meridian moon's natural number Nautical Almanac observed obtuse opposite angles parallax parallel perpendicular plane sailing Plate pole primitive PROPOSITION quadrant rad2 radius rhumb line right angles right ascension right-angled plane triangle right-angled spherical triangle right-angled triangle RULE scale of chords scale of equal SCHOLIUM secant semi-tangents side AC side opposite sin² sphere spherical angle spherical triangle ABC spherical trigonometry straight line subtract supplement Tang tangent of half three angles three sides Trigonometry versed sine
Δημοφιλή αποσπάσματα
Σελίδα 109 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Σελίδα 141 - Consequently, a line drawn from the vertex of an isosceles triangle to the middle of the base, bisects the vertical angle, and is perpendicular to the base.
Σελίδα 33 - An angle at the circumference of a circle is measured by half the arc that subtends it. Let BAC be an angle at the circumference : it has for its measure half the arc "BC, which subtends it.
Σελίδα 29 - The sine, or right sine, of an arc, is the line drawn from one extremity of the arc, perpendicular to the diameter passing through the other extremity. Thus, BF is the sine of the arc AB, or of the arc BDE.
Σελίδα 258 - The HORIZON is a great circle which separates the visible half of the heavens from the invisible ; the earth being considered as a point in the centre of the sphere of the fixed stars.
Σελίδα 116 - C = sin. A sin. B sin. C; dividing both sides of this equation by cos. A cos. B cos. C, we have sin. A sin. B sin. C _ sin.
Σελίδα 362 - Now it is plain, that if any great circle of the sphere (as 1, 2, 3.) be divided into any number of equal parts, and through the points of division...
Σελίδα 23 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Σελίδα 330 - Method of correcting the apparent distance of the Moon from the Sun, or a Star, for the effects of Parallax and Refraction.