An Introduction to the Theory and Practice of Plain and Spherical Trigonometry: And the Stereographic Projection of the Sphere : Including the Theory of Navigation ...Longman, Rees, Orme, Brown, and Green, 1826 - 442 pages |
From inside the book
Results 1-5 of 33
Page
... Euclid , habituate the mind to close and demonstrative reason- ing ; and the practical parts are of extensive use in the com- mon concerns of life . By Trigonometry we determine the magnitudes of the earth and planets , and the ...
... Euclid , habituate the mind to close and demonstrative reason- ing ; and the practical parts are of extensive use in the com- mon concerns of life . By Trigonometry we determine the magnitudes of the earth and planets , and the ...
Page iii
... Euclid , habituate the mind to close and demonstrative reason- ing ; and the practical parts are of extensive use in the com- mon concerns of life . By Trigonometry we determine the magnitudes of the earth and planets , and the ...
... Euclid , habituate the mind to close and demonstrative reason- ing ; and the practical parts are of extensive use in the com- mon concerns of life . By Trigonometry we determine the magnitudes of the earth and planets , and the ...
Page v
... 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 ...
Page 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 RF 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 RF and BH ( Plate I. Fig . 1 ...
Page 32
... ( Euclid 47. of I. ) CB 2+ BT2 = CT 2 the square of the secant , CB2 + AC2 = AB2 ; therefore AB = CT , 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 ° ( K. 31. and Note ) ...
... ( Euclid 47. of I. ) CB 2+ BT2 = CT 2 the square of the secant , CB2 + AC2 = AB2 ; therefore AB = CT , 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 ° ( K. 31. and Note ) ...
Common terms and phrases
acute angle CAB Answer apparent altitude azimuth base centre circle co-tangent compasses complement construction cosec cosine degrees diff difference of latitude difference of longitude draw ecliptic equator Euclid find the angle formulæ given side greater Greenwich Hence horizon horizontal parallax hypoth hypothenuse less line of numbers line of sines log sine measured meridian miles moon's N.sine N.cos natural number Naut Nautical Almanac noon North oblique observed obtuse opposite angle parallax parallel perpendicular plane sailing Plate pole prime vertical PROPOSITION quadrant Rad x sine rad2 radius rhumb line right angles right ascension right-angled spherical triangle RULE scale of chords SCHOLIUM secant side AC sine A sine sine BC Sine Co-sine sphere spherical angle spherical triangle ABC Spherical Trigonometry star star's subtract sun's declination supplement tables tang tangent of half three angles three sides Trigonometry true altitude versed sine
Popular passages
Page 21 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Page 2 - And if the given number be a proper vulgar fraction ; subtract the logarithm of the denominator from the logarithm of the numerator, and the remainder will be the logarithm sought ; which, being that of a decimal fraction, must always have a negative index.
Page 28 - The CO-SINE of an arc is the sine of the complement of that arc as L.
Page 107 - 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.
Page 31 - 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.
Page 136 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 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.
Page 28 - The SECANT of an arc, is a straight line drawn from the center, through one end of the arc, and extended to the tangent which is drawn from the other end.
Page 27 - 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.