An introduction to the theory ... of plane and spherical trigonometry ... including the theory of navigation1839 |
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Side v
... Euclid , habituate the mind to close and demonstrative rea- soning ; and the practical parts are of extensive use in the common concerns of life . By Trigonometry we determine the magnitudes of the earth and planets , and the positions ...
... Euclid , habituate the mind to close and demonstrative rea- soning ; and the practical parts are of extensive use in the common concerns of life . By Trigonometry we determine the magnitudes of the earth and planets , and the positions ...
Side vii
... Euclid , with similar parts of the Trigonometry at the end of Legendre's Geometry . FIRST , Where the three sides of a spherical triangle are given , to find an angle . In Prop . XXVIII . of Dr. Simson's work , the process is con ...
... Euclid , with similar parts of the Trigonometry at the end of Legendre's Geometry . FIRST , Where the three sides of a spherical triangle are given , to find an angle . In Prop . XXVIII . of Dr. Simson's work , the process is con ...
Side 31
... ( Euclid 15. of IV . ) the side of a hexagon , which is the chord of 60 ° , is equal to the radius of the circumscribing circle . The sine of any arc is equal to half the chord of double that arc ; thus let BF and BH ( Plate I. Fig . 1 ...
... ( Euclid 15. of IV . ) the side of a hexagon , which is the chord of 60 ° , is equal to the radius of the circumscribing circle . The sine of any arc is equal to half the chord of double that arc ; thus let BF and BH ( Plate I. Fig . 1 ...
Side 32
... ( Euclid 47. of I. ) CB2 + BT2 = CT2 the square of the secant , CB2 + AC2 = AB2 ; therefore ABCT , that is , the chord of 90 ° is equal to the secant of 45 ° . But the sine of 45 ° is equal to half the chord of 90 ° , art . ( 98 ) , and ...
... ( Euclid 47. of I. ) CB2 + BT2 = CT2 the square of the secant , CB2 + AC2 = AB2 ; therefore ABCT , that is , the chord of 90 ° is equal to the secant of 45 ° . But the sine of 45 ° is equal to half the chord of 90 ° , art . ( 98 ) , and ...
Side 35
... Euclid III . ) the sides of the triangle will be E bisected , and also the arcs which these sides subtend . D B Now an angle at the centre of a circle is double to an angle at the cir- cumference when they stand on the same arc , ( 20 ...
... Euclid III . ) the sides of the triangle will be E bisected , and also the arcs which these sides subtend . D B Now an angle at the centre of a circle is double to an angle at the cir- cumference when they stand on the same arc , ( 20 ...
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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...
Side 23 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Side 330 - Method of correcting the apparent distance of the Moon from the Sun, or a Star, for the effects of Parallax and Refraction.