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 σελίδες
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ABED axis base becomes bisect C.sin Calculation called centre circle common section complement computed cone consequently construction contained cosine cotan cutting describe diameter difference distance draw drawn ellipse equal equation evidently extremes follows formed given greater half Hence hyperbola intersection join known less logarithms meet oblique opposite original circle parallel pass perpendicular plane of projection pole positive primitive circle produced projecting point proposed Q. E. D. Art quadrant radius ratio respectively Result right angles right line secant semitangent sides similar sine sphere spherical triangle suppose surface tangent tion touch triangle whence wherefore
Σελίδα 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.
Σελίδα 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.
Σελίδα 95 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Σελίδα 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.
Σελίδα 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.
Σελίδα 36 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Σελίδα 97 - The cotangent of half the sum of the angles at the base, Is to the tangent of half their difference...
Σελίδα 82 - If two triangles have two angles of the one respectively equal to two angles of the other, the third angles are equal.
Σελίδα 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...