A System of Plane and Spherical Trigonometry: To which is Added a Treatise on Logarithms |
From inside the book
Results 1-5 of 10
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 33
... tangent . Therefore , lies between sin and tan 96 96 ? T 96 Hence , if the arithmetic operations be performed , the result , as far as the decimal places agree in both , may be taken for an approximate value of - ; and , π 96 therefore ...
... tangent . Therefore , lies between sin and tan 96 96 ? T 96 Hence , if the arithmetic operations be performed , the result , as far as the decimal places agree in both , may be taken for an approximate value of - ; and , π 96 therefore ...
Page 48
... tangents of angles also admit of all degrees of magnitude , therefore 2 bc A there is some angle whose tangent is sin Let S be b - c 2 this angle . .. a2 = ( b - c ) 2 { 1 + ( tan S ) 2 } .. a = ( b - c ) 2 ( sec S ) 2 c ) sec S ...
... tangents of angles also admit of all degrees of magnitude , therefore 2 bc A there is some angle whose tangent is sin Let S be b - c 2 this angle . .. a2 = ( b - c ) 2 { 1 + ( tan S ) 2 } .. a = ( b - c ) 2 ( sec S ) 2 c ) sec S ...
Page 179
... tangents at the point of inter- section . For each of these tangents being perpendicular to the radius in which the planes of the circles intersect , the angle contained by the tangents measures the inclination of the planes of the ...
... tangents at the point of inter- section . For each of these tangents being perpendicular to the radius in which the planes of the circles intersect , the angle contained by the tangents measures the inclination of the planes of the ...
Other editions - View all
Common terms and phrases
2m cos a)m 2ί π A₁ C₁ centre circle cos a)2 cos(a cosec cosec 22 cosec a)² cot 2n cot a cot cot cot decimal equal factors find what values Firstly given greater hence imaginary quantities integer loga logarithm loge m² n2 mcot Method Napier's rules nearly negative odd integer perpendicular plane angles plane triangle polar triangle pole polygon positive integer PROB PROP quadrant radius unity regular polyhedrons sec a)2 sides Similarly sin a)2 sin sin sin sin ẞ sines and cosines sın solid angle sphere spherical angle spherical polygon spherical triangle substituting subtending sum the series tangent trigonometric functions vanish xn+1 α α α β α+β 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 255 - 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.