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 100
Page viii
... oblique- angled spherical triangles , from which several useful rules are derived . The fifth Chapter is , in substance , the same as the IVth Chapter of Book II . in the first edition , but the mode of de- monstration has been varied ...
... oblique- angled spherical triangles , from which several useful rules are derived . The fifth Chapter is , in substance , the same as the IVth Chapter of Book II . in the first edition , but the mode of de- monstration has been varied ...
Page xx
... oblique - angled triangles PRACTICAL RULES FOR THE SOLUTION OF ALL THE DIFFERENT CASES OF RIGHT - ANGLED PLANE TRIANGLES , WITH THEIR APPLI- CATION BY LOGARITHMS • 42 243 to 5 2. Practical rules for solving all the cases of oblique ...
... oblique - angled triangles PRACTICAL RULES FOR THE SOLUTION OF ALL THE DIFFERENT CASES OF RIGHT - ANGLED PLANE TRIANGLES , WITH THEIR APPLI- CATION BY LOGARITHMS • 42 243 to 5 2. Practical rules for solving all the cases of oblique ...
Page xxii
... oblique angle contained be- tween the objects , to find the horizontal angle BOOK IV . THE THEORY OF NAVIGATION . Page 366 368 371 373 CHAPTER I. Definitions and Plane sailing 376 to 380 CHAP , II . Parallel and Middle Latitude sailing ...
... oblique angle contained be- tween the objects , to find the horizontal angle BOOK IV . THE THEORY OF NAVIGATION . Page 366 368 371 373 CHAPTER I. Definitions and Plane sailing 376 to 380 CHAP , II . Parallel and Middle Latitude sailing ...
Page xxiii
... OBLIQUE - ANGLED SPHE- RICAL TRIANGLES TO ASTRONOMICAL PRO- BLEMS Prob . 7. Given the sun's declination , and the latitude of the place , to find the apparent time of day - break in the morning , and the end of twilight in the evening ...
... OBLIQUE - ANGLED SPHE- RICAL TRIANGLES TO ASTRONOMICAL PRO- BLEMS Prob . 7. Given the sun's declination , and the latitude of the place , to find the apparent time of day - break in the morning , and the end of twilight in the evening ...
Page xxiv
... oblique angles is a constant quantity 3. To find the fluxions of the several parts of a RIGHT- 308 310 313 316 317 319 323 326 332 333 • 337 344 · 344 345 Page ANGLED spherical triangle , when one of its legs xxiv CONTENTS .
... oblique angles is a constant quantity 3. To find the fluxions of the several parts of a RIGHT- 308 310 313 316 317 319 323 326 332 333 • 337 344 · 344 345 Page ANGLED spherical triangle , when one of its legs xxiv CONTENTS .
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.