A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and of Plane and Spherical Trigonometry, Together with a Series of Trigonometrical Tables
J. Mawman, 1816 - Geometry - 294 pages
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applied arch base bisect called chords circumference common section complement consequently construction contained conversely cosine describe describe a circle diameter distance draw drawn equal equal circles equations evident express extremity fall figure fore Forms four functions given arch given circle given point given sphere greater half Hence hypotenuse hypothesis Introd isosceles join known less lesser circle manifest manner means measure meet method parallel pass perpendicular plane polar distance pole Problem produced PROP proposed proposition proved quadrant radius remaining respectively right angles segments semi-circumference shewn sine solution solved species sphere's center sphere's surface spherical angle spherical triangle straight line supposed tangent Theorem third three angles three sides touch touch the circle triangle ABC wherefore
Page 58 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Page 50 - BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles, to which the equal sides are opposite, shall be equal, each to each, viz.
Page iii - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.
Page 43 - Theorem. If two spherical triangles on the same sphere, or on equal spheres, are equilateral with respect to each other, they are also equiangular with respect to each other.
Page 60 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 58 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
Page iii - A diameter of a circle is a straight line drawn through the center and terminated both ways by the circumference, as AC in Fig.
Page 146 - If two triangles have two sides and the included angle in the one equal to two sides and the included angle in the other, each to each, the two triangles will be equal.
Page 38 - THEOREM. The sum of the sides of a spherical polygon is less than the circumference of a great circle.
Page 54 - If two angles of a triangle be equal to one another, the sides also which subtend the equal angles shall be equal to one another.