# 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

H. Orr, 1844 - 228 СЕКъДЕР

### тИ КщМЕ ОИ ВЯчСТЕР -сЩМТАНГ ЙЯИТИЙчР

дЕМ ЕМТОПъСАЛЕ ЙЯИТИЙщР СТИР СУМчХЕИР ТОПОХЕСъЕР.

### пЕЯИЕВЭЛЕМА

 еМЭТГТА 1 3 еМЭТГТА 2 31 еМЭТГТА 3 52 еМЭТГТА 4 78 еМЭТГТА 5 80
 еМЭТГТА 6 117 еМЭТГТА 7 129 еМЭТГТА 8 165 еМЭТГТА 9 167 еМЭТГТА 10 222

### дГЛОЖИКч АПОСПэСЛАТА

сЕКъДА 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.
сЕКъДА 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.
сЕКъДА 95 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
сЕКъДА 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.
сЕКъДА 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.
сЕКъДА 36 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
сЕКъДА 115 - The straight line joining the vertex and the centre of the base is called the axis of the cone.
сЕКъДА 97 - The cotangent of half the sum of the angles at the base, Is to the tangent of half their difference...
сЕКъДА 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
сЕКъДА 82 - If two triangles have two angles of the one respectively equal to two angles of the other, the third angles are equal.