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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Page 20
... Polar Distance of that circle . ( 35. ) DEF . The fourth part of the circumference of a great circle , in a sphere , is called a Quadrant . PROP . VIII . ( 36. ) Theorem . The polar distance of a great circle , in a sphere , is a ...
... Polar Distance of that circle . ( 35. ) DEF . The fourth part of the circumference of a great circle , in a sphere , is called a Quadrant . PROP . VIII . ( 36. ) Theorem . The polar distance of a great circle , in a sphere , is a ...
Page 21
... distance of G R H B L K p a quadrant , from any two points , A and B , in the circum- ference of the great circle ABD , that is , let the arches of great circles PA and PB be quadrants ... polar distances Art . 38. ] 21 SPHERICAL GEOMETRY .
... distance of G R H B L K p a quadrant , from any two points , A and B , in the circum- ference of the great circle ABD , that is , let the arches of great circles PA and PB be quadrants ... polar distances Art . 38. ] 21 SPHERICAL GEOMETRY .
Page 22
... polar distances are equal , because ( Art . 36. ) each of them is a quadrant . But , let EH and Al be two lesser circles in the sphere EAH and , first , let the circle EH be equal to P G H E F M A p AI : the polar distance of EH is ...
... polar distances are equal , because ( Art . 36. ) each of them is a quadrant . But , let EH and Al be two lesser circles in the sphere EAH and , first , let the circle EH be equal to P G H E F M A p AI : the polar distance of EH is ...
Page 68
... polar triangle of any given isosceles spherical triangle . Or , the proof of the proposition very readily follows , from Art . 40 , if arches of circles be first described from each extremity of the base , as a pole , at a distance ...
... polar triangle of any given isosceles spherical triangle . Or , the proof of the proposition very readily follows , from Art . 40 , if arches of circles be first described from each extremity of the base , as a pole , at a distance ...
Page 97
... distance , from the pole P , than the polar distance PC . G in the sphere's surface , to the circumference of a Art . 141. ] 97 SPHERICAL GEOMETRY .
... distance , from the pole P , than the polar distance PC . G in the sphere's surface , to the circumference of a Art . 141. ] 97 SPHERICAL GEOMETRY .
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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.