A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ; Adapted to the Use of Students ; Extracted Mostly from Similar Works of Ludlam, Playfair, Vince, and Bonnycastle |
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Page iii
... Formulæ 75 SPHERICAL TRIGONOMETRY . Introduction 77 Spherical Trigonometry 82 Formulæ for the Solution of Spherical Triangles Napier's Rules of the Circular Parts 100 103 Quadrantal Spherical Triangles 106 Affections and Properties of ...
... Formulæ 75 SPHERICAL TRIGONOMETRY . Introduction 77 Spherical Trigonometry 82 Formulæ for the Solution of Spherical Triangles Napier's Rules of the Circular Parts 100 103 Quadrantal Spherical Triangles 106 Affections and Properties of ...
Page x
... formulæ can be easily obtained ; and in the present state of science every treatise upon trigonometry should comprise some portion of trigonometrical analysis . " British Review for March 1811 . The definitions and preliminary ...
... formulæ can be easily obtained ; and in the present state of science every treatise upon trigonometry should comprise some portion of trigonometrical analysis . " British Review for March 1811 . The definitions and preliminary ...
Page 74
... formulæ , which have been demonstrated in the first and third sections , are oftem em- ployed in mathematical inquiries , it will be useful to collect them into a table , with some others which are deduced from them by simple processes ...
... formulæ , which have been demonstrated in the first and third sections , are oftem em- ployed in mathematical inquiries , it will be useful to collect them into a table , with some others which are deduced from them by simple processes ...
Page 75
... ( a + b ) = 2 Cot . a = tan . a γε sine a r cos . a sine a Cosec . a = = r sine ( a + b ) _ r2 ( tan . a + tan . b ) cos . ( a + b ) r2 + tan a tan . b r * sine ( a + b ) sine ( PLANE TRIGONOMETRY . 75 Table of Trigonometrical Formulæ.
... ( a + b ) = 2 Cot . a = tan . a γε sine a r cos . a sine a Cosec . a = = r sine ( a + b ) _ r2 ( tan . a + tan . b ) cos . ( a + b ) r2 + tan a tan . b r * sine ( a + b ) sine ( PLANE TRIGONOMETRY . 75 Table of Trigonometrical Formulæ.
Page 87
... formulæ for the solution of oblique - angled triangles , by drawing a perp . from the vertical angle upon the opposite side , if we suppose the perp . to fall within the triangle , and the sides and angles to be less than 90 ° , the ...
... formulæ for the solution of oblique - angled triangles , by drawing a perp . from the vertical angle upon the opposite side , if we suppose the perp . to fall within the triangle , and the sides and angles to be less than 90 ° , the ...
Common terms and phrases
90 degrees adjacent angle AHDL algebra analogy angle ABC angle ACB Answer arc AC arc or angle base centre chord circle comp complement cosecant cosine cotangent Euclid's Elements find the angles find the rest formulæ geometry Given the side greater than 90 half the sum half their difference height Hence hypothenuse AC included angle less than 90 logarithmic sines mathematics measured mechanical philosophy negative opposite angle perp perpendicular plane triangle plane trigonometry PROP propositions quadrant AH quantity right-angled spherical triangle right-angled triangle Scholium secant side AB side AC sides and angles sine a sine sine and cosine sines and tangents solution spherical angle spherical triangle ABC spherical trigonometry supplement tables tangent of half theorems third side three angles three sides triangle are given trigono versed sine yards
Popular passages
Page 12 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page ix - 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 23 - Then multiply the second and third terms together, and divide the product by the first term: the quotient will be the fourth term, or answer.
Page 13 - In any triangle, twice the rectangle contained by any two sides is to the difference between the sum of the squares of those sides, and the square of the base, as the radius to the cosine of the angle included by the two sides. Let ABC be any triangle, 2AB.BC is to the difference between AB2+BC2 and AC2 as radius to cos.
Page 87 - The cosine of half the sum of two sides of a spherical triangle is to the cosine of half their difference as the cotangent of half the included angle is to the tangent of half the sum of the other two angles. The sine of half the sum of two sides of a spherical...
Page 74 - The sum of any two sides is greater than the third side, and their difference is less than the third side.