A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and of Plane and Spherical Trigonometry, Together with a Series of Trigonometrical Tables |
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... sphe- rical triangles , on the same sphere , and on the same base , or on equal bases , and between any two parallel circles whatever of the sphere , be equal ; and , if not , whether there is not one par- ticular pair of parallel ...
... sphe- rical triangles , on the same sphere , and on the same base , or on equal bases , and between any two parallel circles whatever of the sphere , be equal ; and , if not , whether there is not one par- ticular pair of parallel ...
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... Sphe- rical Geometry is to be looked for in the doctrine of Spherical Trigonometry : and it must , further , be admitted , that it is possible to deduce the solution of spherical triangles from one general theorem , which in order to be ...
... Sphe- rical Geometry is to be looked for in the doctrine of Spherical Trigonometry : and it must , further , be admitted , that it is possible to deduce the solution of spherical triangles from one general theorem , which in order to be ...
Page ii
... sphe- rical triangles , on the same sphere , and on the same base , or on equal bases , and between any two parallel circles whatever of the sphere , be equal ; and , if not , whether there is not one par- ticular pair of parallel ...
... sphe- rical triangles , on the same sphere , and on the same base , or on equal bases , and between any two parallel circles whatever of the sphere , be equal ; and , if not , whether there is not one par- ticular pair of parallel ...
Page iii
... Sphe- rical Geometry is to be looked for in the doctrine of Spherical Trigonometry : and it must , further , be admitted , that it is possible to deduce the solution of spherical triangles from one general theorem , which in order to be ...
... Sphe- rical Geometry is to be looked for in the doctrine of Spherical Trigonometry : and it must , further , be admitted , that it is possible to deduce the solution of spherical triangles from one general theorem , which in order to be ...
Page 36
... sphe- rical distance of a pole of the one , from a pole of the other , measures also the spherical angle contained by their circumferences . For , if two straight lines be drawn at right angles to the common section of the circles , one ...
... sphe- rical distance of a pole of the one , from a pole of the other , measures also the spherical angle contained by their circumferences . For , if two straight lines be drawn at right angles to the common section of the circles , one ...
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Common terms and phrases
angle opposite base bisect circle EFH circumference co-tangent common section cosine describe a circle describe Art diameter drawn equal and parallel equal arches equal circles equal spheres equal to FE equations Euclid's Elements Find Art fore four right angles given angle given arch given circle given great circle given point given sphere given triangle greater hypotenuse Introd join Art less measure meet oblique angles opposite angle parallel circles perpendicular plane triangle polar distance polar triangle pole Problem PROP proposition quadrantal triangle radius rical triangle right angles right-angled spherical triangle SCHOLIUM semi-circumference shewn side BC sin S sin sine sphe sphere's center sphere's surface spherical angle spherical distance Spherical Geometry spherical polygon spherical tri Spherical Trigonometry straight line tangent Theorem three angles three sides touch the circle triangle ABC trigonometrical functions wherefore
Popular passages
Page 53 - 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 46 - 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 53 - 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 53 - 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 132 - 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 50 - 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.