A System of Plane and Spherical Trigonometry: To which is Added a Treatise on Logarithms |
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Page xi
... two great circles 185 ... To draw a tangent to any point in the surface of a SECTION II . ON SPHERICAL TRIANGLES . ART . PAGE. 27 . sphere . .......... ............. ib . circle , circumference diameter a constant number . CONTENTS . xi.
... two great circles 185 ... To draw a tangent to any point in the surface of a SECTION II . ON SPHERICAL TRIANGLES . ART . PAGE. 27 . sphere . .......... ............. ib . circle , circumference diameter a constant number . CONTENTS . xi.
Page 9
... tangent of an arc is the right line drawn from one extremity of the arc touching the circle , and ter- minated by the radius produced through the other extremity . DEF . VIII . The cotangent of an arc is the tangent of the complement of ...
... tangent of an arc is the right line drawn from one extremity of the arc touching the circle , and ter- minated by the radius produced through the other extremity . DEF . VIII . The cotangent of an arc is the tangent of the complement of ...
Page 10
... tangent , at cotangent , от secant , Ot cosecant , AN an AP versed sine , coversed sine , chord . 23. The words sine , cosine , & c . are thus abbreviated , sin , cos , & c . and the letter f is used as a general symbol for any of the ...
... tangent , at cotangent , от secant , Ot cosecant , AN an AP versed sine , coversed sine , chord . 23. The words sine , cosine , & c . are thus abbreviated , sin , cos , & c . and the letter f is used as a general symbol for any of the ...
Page 14
... tangent of the arc subtending A , therefore : a tan A = Also tan ( 90 ° - A ) = tan B AC BC b .. cot A = a AB 33. COR . Sec A C = = AC cosec A = sec B = AB = BC C a 34. PROB . Any formula consisting of trigonometric func- tions of an ...
... tangent of the arc subtending A , therefore : a tan A = Also tan ( 90 ° - A ) = tan B AC BC b .. cot A = a AB 33. COR . Sec A C = = AC cosec A = sec B = AB = BC C a 34. PROB . Any formula consisting of trigonometric func- tions of an ...
Page 19
To which is Added a Treatise on Logarithms Richard Wilson. Sine . Cosine . Tangent . Cotangent . Secant . Cosecant . Versine . Coversine . Chord . 1st Quad . P1N , ON , A , T , A2t1 от Ot AN , A2n AP 2nd . P2N ON 2 AT2 A2t2 OT2 Ot2 AN ...
To which is Added a Treatise on Logarithms Richard Wilson. Sine . Cosine . Tangent . Cotangent . Secant . Cosecant . Versine . Coversine . Chord . 1st Quad . P1N , ON , A , T , A2t1 от Ot AN , A2n AP 2nd . P2N ON 2 AT2 A2t2 OT2 Ot2 AN ...
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Common terms and phrases
2ί π A₁ base C₁ centre chord circle cos a)2 cos(a cosec cosec a)² cot 2n cot a cot cot cot decimal equal factors find what values Firstly four right angles given greater or less hence imaginary quantities integer less than 90 loga logarithm loge m² n2 mcot Napier's rules nearly negative odd integer perpendicular plane angles polar triangle pole polygon positive integer PROB PROP quadrant radius unity regular polyhedrons sec a)2 Similarly sin a)2 sin sin sin sin ẞ sın solid angle sphere spherical angle spherical polygon spherical triangle substituting subtending sum the series surface tangent trigonometric functions vanish α α α β α+β α₁ αξ Δα ηβ ίπ Μπ π α π π π+α
Popular passages
Page 197 - IF two triangles have two sides of the one equal to two sides of the other, each to each ; and have likewise the angles contained by those sides equal to one another ; they shall likewise have their bases, or third sides, equal ; and the two triangles shall be equal ; and their other angles shall be equal, each to each, viz.
Page 179 - The diameter of a sphere is any straight line which passes through the centre, and is terminated both ways by the superficies of the sphere.
Page 190 - The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle; produce the sides AB, AU, till they meet again in D.
Page 191 - THEOREM. The sum of the sides of a spherical polygon is less than the circumference of a great circle.
Page 181 - ... poles. 751. COR. 2. All great circles of a sphere are equal. 752. COR. 3. Every great circle bisects the sphere. For the two parts into which the sphere is divided can be .so placed that they .will coincide; otherwise there would be points on the surface unequally distant from the centre. 753. COR. 4. Two great circles bisect each other. For the intersection of their planes passes through the centre, and is, therefore, a diameter of each circle. 754.
Page 252 - A solid angle is that which is made by the meeting of more than two plane angles, which are not in the same plane, in one point. X. ' The tenth definition is omitted for reasons given in the notes.
Page 189 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 181 - An arc of a great circle may be drawn through any two points on the surface of a sphere.
Page 45 - Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Page 9 - The Versed Sine of an arc, is the part of the diameter intercepted between the arc and its sine.