Elements of Geometry and Conic Sections |
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Page 148
... sphere , is a point in the surface equally distant from every point in the circumference of this circle . It will be shown ( Prop . V. ) , that every circle , whether great or small , has two poles . 6. A spherical triangle is a part of ...
... sphere , is a point in the surface equally distant from every point in the circumference of this circle . It will be shown ( Prop . V. ) , that every circle , whether great or small , has two poles . 6. A spherical triangle is a part of ...
Page 151
Elias Loomis. PROPOSITION II . THEOREM . Any two sides of a spherical triangle are greater than the third . Let ABC be a spherical triangle ; any two sides as , AB , BC , are together greater A than the third side AC . B Let D be the ...
Elias Loomis. PROPOSITION II . THEOREM . Any two sides of a spherical triangle are greater than the third . Let ABC be a spherical triangle ; any two sides as , AB , BC , are together greater A than the third side AC . B Let D be the ...
Page 155
... spherical triangles may be compared with each other by means of arcs of great circles described from their vertices ... triangle , as poles , arcs of great circles are described , a second triangle is formed , whose vertices are poles of ...
... spherical triangles may be compared with each other by means of arcs of great circles described from their vertices ... triangle , as poles , arcs of great circles are described , a second triangle is formed , whose vertices are poles of ...
Page 156
... spherical triangle , are the supplements of the arcs which measure the angles of its polar triangle ; and con- versely . Let DEF be a spherical triangle , ABC its polar triangle ; then will the side EF be the supplement of the arc which ...
... spherical triangle , are the supplements of the arcs which measure the angles of its polar triangle ; and con- versely . Let DEF be a spherical triangle , ABC its polar triangle ; then will the side EF be the supplement of the arc which ...
Page 157
... spherical triangle . The arcs which measure the angles A , B , and C , together with the three sides of the polar triangle , are equal to three semicircumferences ( Prop . ÎX ) . But the three sides of the polar triangle are less than ...
... spherical triangle . The arcs which measure the angles A , B , and C , together with the three sides of the polar triangle , are equal to three semicircumferences ( Prop . ÎX ) . But the three sides of the polar triangle are less than ...
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Common terms and phrases
ABCD AC is equal allel altitude angle ABC angle ACB angle BAC base BCDEF bisected chord circle circumference cone convex surface curve described diagonals diameter draw ellipse equal angles equal to AC equally distant equiangular equilateral equivalent exterior angle foci four right angles frustum given angle given point greater hyperbola hypothenuse inscribed intersect join latus rectum Let ABC lines AC Loomis major axis mean proportional measured by half meet number of sides ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN prism Professor of Mathematics PROPOSITION pyramid radii radius ratio rectangle regular polygon right angles Prop Scholium segment side AC similar similar triangles slant height solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices
Popular passages
Page 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 17 - If two triangles have two sides, and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal, their third sides will be equal, and their other angles will be equal, each to each.
Page 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Page 63 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the' rectangle contained by the parts.
Page 18 - 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 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Page 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Page 15 - Wherefore, when a straight line, &c. QED PROP. XIV. THEOR. If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Page 44 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.