## An Introduction to the Theory and Practice of Plain and Spherical Trigonometry: And the Stereographic Projection of the Sphere : Including the Theory of Navigation ... |

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acute adjacent adjacent angle altitude ambiguous angle cab angle opposite Answer azimuth base centre co-tangent compasses complement construction Corollary cosec cosine cot AC degrees diameter distance draw ecliptic equation Euclid find the angle formula given angle given side greater Greenwich half the sum height Hence hypoth less line of numbers log sine logarithm longitude mean arc measure meridian moon's Nautical Almanac observed obtuse opposite angle parallax parallel perpendicular Plate pole PRACTICAL EXAMPLES primitive PROPOSITION quadrant Rad x sine rad2 radius Required right ascension right-angled spherical triangle right-angled triangle scale of chords SCHOLIUM secant semi-tangents side AC side opposite sine2 SOLUTION species sphere spherical angle spherical triangle abc straight line subtract sun's declination supplement tang tangent of half three angles three sides toßnd Trigonometry versed sine vertical angle ас вс ев

### Popular passages

Page 25 - 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 6 - 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 i - An INTRODUCTION to the THEORY and PRACTICE of PLANE and SPHERICAL TRIGONOMETRY, and the Stereographic Projection of the Sphere, including the Theory of Navigation ; comprehending a variety of Rules, Formulae, &c.

Page 32 - The CO-SINE of an arc is the sine of the complement of that arc as L.

Page 111 - 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 35 - 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 140 - 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 262 - 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 32 - 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 31 - 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.