Elements of Geometry and Conic Sections |
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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 contained 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 given straight line greater hyperbola hypothenuse inscribed intersect join latus rectum Let ABC lines AC major axis mean proportional measured by half meet number of sides ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN principal vertex prism PROPOSITION pyramid quadrant radii radius ratio rectangle regular polygon right angles right angles Prop right-angled triangle Scholium segment side AC similar solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices
Popular passages
Page 30 - 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.
Page 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 11 - A rhombus, is that which has all its sides equal, but its angles are not 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 20 - therefore, because in the triangles DBC, ACB, DB is equal to AC, and BC common to both, the two sides, DB, BC are equal to the two AC, CB, each to each ; and the angle DBC is equal to...
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 148 - It will be shown (p. 7,) that every section of a sphere, made by a plane, is a circle...
Page 14 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles.
Page 152 - THEOREM. The sum of the sides of a spherical polygon is less than the circumference of a great circle.