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 23
... rad . : : sine ( AB + BC + AC ) × sine rad . x vers , sine supp в - , or , sine AB X sine BC : rad . : vers . sine supp1 в ( AB + BC + AC ) —AC : + AC ) x sine 2 sine AB X sine BC vers . sine suppt B = X rad . 2 AC ) -AC . 2 ( AB + BC + ...
... rad . : : sine ( AB + BC + AC ) × sine rad . x vers , sine supp в - , or , sine AB X sine BC : rad . : vers . sine supp1 в ( AB + BC + AC ) —AC : + AC ) x sine 2 sine AB X sine BC vers . sine suppt B = X rad . 2 AC ) -AC . 2 ( AB + BC + ...
Page 39
... rad.::BD cosine of the angle в ( Z. 34. ) BD COS . BX BC rad . here B is acute in the first triangle , and obtuse in the second . By substitution , or , COS . Z. BX BC rad . AB2 + BC - AC2 2AB AC2 . AB2 - BC2 rad . 2BA COS . BX BC from ...
... rad.::BD cosine of the angle в ( Z. 34. ) BD COS . BX BC rad . here B is acute in the first triangle , and obtuse in the second . By substitution , or , COS . Z. BX BC rad . AB2 + BC - AC2 2AB AC2 . AB2 - BC2 rad . 2BA COS . BX BC from ...
Page 84
... rad . : am :: cosine KIL : AB , or AB = AM × Cosine △ KIL rad . • ( M ) If Am = 400 yards , and KIL = 4 ° , AB will be 399.025 yards , hence the difference between am and AB is less than 1 yard . It appears from this example , that ...
... rad . : am :: cosine KIL : AB , or AB = AM × Cosine △ KIL rad . • ( M ) If Am = 400 yards , and KIL = 4 ° , AB will be 399.025 yards , hence the difference between am and AB is less than 1 yard . It appears from this example , that ...
Page 85
... rad . : PD :: sine DPB : DB , 119 · 93 toisés . In order to cal- hence DB PD X sine DPB rad . culate BS ; PD may be used instead of PB , and cs and CB may be considered as equal to each other without sensible error . And as ( 2cs + BS ) ...
... rad . : PD :: sine DPB : DB , 119 · 93 toisés . In order to cal- hence DB PD X sine DPB rad . culate BS ; PD may be used instead of PB , and cs and CB may be considered as equal to each other without sensible error . And as ( 2cs + BS ) ...
Page 91
... rad . : ; es : cos . DBS , for the tri- BS angles BSB and DSP are right angled at s . COS . DBP X rad . Conseq . cos . SBP = , or cos . DBS COS . DBP :: COS . DBS . rad . cos . SBP . ( L ) That is , The cosine of the L of elevation ...
... rad . : ; es : cos . DBS , for the tri- BS angles BSB and DSP are right angled at s . COS . DBP X rad . Conseq . cos . SBP = , or cos . DBS COS . DBP :: COS . DBS . rad . cos . SBP . ( L ) That is , The cosine of the L of elevation ...
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.