Elements of Geometry and Trigonometry |
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Page 42
... inscribed figure is one , of which all the angles have their vertices in the circumference . The circle is then said ... polygon is circumscribed about a circle , when all its sides are tangents to the circumference : in the same case , the ...
... inscribed figure is one , of which all the angles have their vertices in the circumference . The circle is then said ... polygon is circumscribed about a circle , when all its sides are tangents to the circumference : in the same case , the ...
Page 110
Adrien Marie Legendre. PROPOSITION II . THEOREM . Any regular polygon may be inscribed in a circle , and circum- scribed about one . Let ABCDE & c . be a regular poly- gon : describe a circle through the three points A , B , C , the ...
Adrien Marie Legendre. PROPOSITION II . THEOREM . Any regular polygon may be inscribed in a circle , and circum- scribed about one . Let ABCDE & c . be a regular poly- gon : describe a circle through the three points A , B , C , the ...
Page 111
Adrien Marie Legendre. Scholium 2. To inscribe a regu- lar polygon of a ... polygon . PROPOSITION III . PROBLEM . To inscribe a square in a given circle ... inscribed square is to the radius , square root of 2 , is to unity . as the ...
Adrien Marie Legendre. Scholium 2. To inscribe a regu- lar polygon of a ... polygon . PROPOSITION III . PROBLEM . To inscribe a square in a given circle ... inscribed square is to the radius , square root of 2 , is to unity . as the ...
Page 112
... inscribed hexagon is equal to the radius . Hence to inscribe a regular ... inscribed , the equilateral triangle ACE may be formed by joining the vertices of ... polygon of fifteen sides . Divide the radius AO in extreme and mean ratio at ...
... inscribed hexagon is equal to the radius . Hence to inscribe a regular ... inscribed , the equilateral triangle ACE may be formed by joining the vertices of ... polygon of fifteen sides . Divide the radius AO in extreme and mean ratio at ...
Page 113
... . It is further evident , that any of the inscribed polygons will be less than the inscribed polygon of double the number of sides , since a part is less than the whole . H PROPOSITION VI . PROBLEM . A regular inscribed polygon being BOOK V ...
... . It is further evident , that any of the inscribed polygons will be less than the inscribed polygon of double the number of sides , since a part is less than the whole . H PROPOSITION VI . PROBLEM . A regular inscribed polygon being BOOK V ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex