## A Treatise on Plane and Spherical Trigonometry |

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2bc 2bc 2nir 2sin arc AP called centre CHAPTER chord circle complement compute the sines cos-B cos.A cos.B cos.c cos.l cos.p cosec diameter equal equation EQUILATERAL POLYGONS Euclid expressed feet find the angle Find the area Find the number find the sine formulas given angle given side Hence inscribed log.a log.b log.c logarithmic multiple negative number of sides Oblique-angled perpendicular plane polar triangle pole polygon quadrant quadrilateral radius regular polygon regular polyhedrons right angle right-angled triangle secant sides and angles similarly sin.a sin.B sin.c sin.m sin.o sin.p sin.y sine and cosine sm.A sm.B solid angle sphere spherical polygon spherical triangle SPHERICAL TRIGONOMETRY subtend tan.A tan.C tangent theorem three angles three sides triangle in terms trigonometrical ratios values whence

### Popular passages

Page 114 - 4. Every section of a sphere made by a plane is a circle. Let AMB be the section made by

Page 91 - The square of the side of a pentagon inscribed in a circle is equal to the sum of the squares of the sides of a regular hexagon and decagon inscribed in the same circle.

Page 125 - For since the sum of the angles of a spherical triangle is greater than two right angles,

Page 91 - (8.) The area of a regular hexagon inscribed in a circle is a mean proportional between the areas of an inscribed and circumscribed

Page 116 - 9. A spherical triangle is a portion of the surface of a sphere contained by three arcs of three great circles,

Page 54 - or the area of a triangle is equal to half the product of any two sides multiplied by the sine of the angle included by

Page 116 - The sum of the three sides of a spherical triangle is less than the circumference of a great circle. For

Page 146 - the area of a spherical triangle is proportional to the excess of the sum of its angles above two right angles. This is

Page 8 - The interior angles of a rectilinear figure are in arithmetic progression; the least angle is 120°, and the common difference 5°. Required the number of sides.

Page 91 - Three equal circles touch each other ; show that the space between them is nearly equal to the square described upon a fifth part of the diameter; find the area when the circles are unequal and the radii as the numbers