## A System of Plane and Spherical Trigonometry: To which is Added a Treatise on Logarithms |

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a₁ according addition base become called centre circle contained corresponding cos y cosec cosines determined distance dividing draw equal equation error expression factors figure formula four given giving greater hence integer join less logarithm magnitude manner measured meeting method multiplying Napier's nearly negative opposite pass perpendicular plane plane angles polar pole polygon positive PROB produced PROP quadrant quantities radius remaining result right angles roots rules shown sides Similarly sin ß sin y sine solid angle sphere spherical angle spherical triangle substituting subtending sum the series suppose surface tables tangent triangle unity values vanish variations Δα π π

### 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.