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 sider
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A treatise on plane and spherical trigonometry: including the construction ...
Uten tilgangsbegrensning - 1860
A Treatise on Plane and Spherical Trigonometry: Including the Construction ...
Uten tilgangsbegrensning - 1844
ABDP angled spherical triangle base bisect c.cos c.sin centre circle Art common section complement cone conical surface consequently construction cosine cotan directrix distance drawn ecliptic ellipse equal equation given angle greater axis Hence hyperbola hypothenuse intersection join latus rectum less circle Let ABC line of measures logarithms meet opposite ordinate original circle parabola parallel perpendicular plane of projection plane passing 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
Side 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.
Side 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.
Side 95 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Side 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.
Side 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.
Side 36 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Side 97 - The cotangent of half the sum of the angles at the base, Is to the tangent of half their difference...
Side 82 - If two triangles have two angles of the one respectively equal to two angles of the other, the third angles are equal.
Side 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...