## A Treatise on Plane and Spherical Trigonometry: Including the Construction of the Auxiliary Tables; a Concise Tract on the Conic Sections, and the Principles of Spherical Projection |

### Other editions - View all

### Common terms and phrases

ABDP angled spherical triangle bisect C.cos c.sin centre common section Comp AC cone conical surface consequently construction cosē cosec cosine cotan directrix distance drawn ECē ecliptic EDē ellipse equal equation given angle greater axis Hence hyperbola hypothenuse join latus rectum less circle Let ABC line of measures logarithms meet opposite ordinate original circle parabola parallel perpendicular plane of projection primitive circle projected circle projected pole projecting point Q. E. D. ART Q. E. D. Cor quadrant radius right angled spherical right ascension right line secant semicircle semitangent sides similar triangles sine sphere spherical angle tan AC tangent tangent of half touches the circle triangle ABC vertex vertical angle whence wherefore

### Popular passages

Page 32 - 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 39 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.

Page 95 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.

Page 98 - In a right angled spherical triangle, the rectangle under the radius and the sine of the middle part, is equal to the rectangle under the tangents of the adjacent parts ; or', to the rectangle under the cosines of the opposite parts.

Page 40 - Def. 10. 1.) If then CE is made radius, GE is the tangent of GCE, (Art. 84.) that is, the tangent of half the sum of the angles opposite to AB and AC. If from the greater of the two angles ACB and ABC, there be taken ACD their half sum ; the remaining angle ECB will be their half difference.

Page 36 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.

Page 97 - The cotangent of half the sum of the angles at the base, Is to the tangent of half their difference...

Page 82 - If two triangles have two angles of the one respectively equal to two angles of the other, the third angles are equal.

Page 84 - ... such, that the sides of the one are the supplements of the arches which measure the angles of the other. Let ABC be a spherical triangle ; and from the points A, B, and C as poles, let the great circles FE, ED, DF be described...

Page 82 - If two angles of a spherical triangle are equal, the sides opposite these angles are equal and the triangle is isosceles. In the spherical triangle ABC, let the angle B equal the angle C. To prove that AC = AB. Proof. Let the A A'B'C