 | Isaac Dalby - 1807 - 968 σελίδες
...circle. Carol. 9. Hence also, BO bisects GA, and the angle GBA. 139. THEOREM. The square on the side DB of a regular pentagon inscribed in a circle, is equal to the square on the radius CB, and the square on DA the tide of the decago* taken together (Euclid, B. 13. Pr. 10.):... | |
 | Samuel Webber - 1808 - 466 σελίδες
...x A o; but A?2=Ao2+oy2=tAo3, hence Ay 22 and consequently, Ar = AB is the side of the pentagon. As the square of the side of a regular pentagon, inscribed in a circle, is equal to the sum of the squares of the radius and of the side of a regular decagon, inscribed in the same circle,... | |
 | Daniel Cresswell - 1817 - 454 σελίδες
...the circumference of a circle may be divided into any given number of equal parts. PROP. XV. (xvn.) The square of the side of a regular pentagon, inscribed in a given circle, is equal to the square of the side of a regular decagon, together with square of the... | |
 | Daniel Cresswell - 1819 - 446 σελίδες
...sides being taken in order from any one of them assumed as the first. • « PROP. XVII. 29. THEOREM. The square of the side of a regular pentagon, inscribed in a giren circle, is equal to the square of the side of a regular decagon, together with the square of... | |
 | Robert Woodhouse - 1819 - 300 σελίδες
...equilateral pentagon and decagon, inscribed in a circle. Hence, the square of the side of an equilateral pentagon inscribed in a circle, is equal to the square of the radius plus the square of the side of an equilateral decagon inscribed in the same circle. Having now... | |
 | Rev. John Allen - 1822 - 516 σελίδες
...and therefore (Schol. 6. 4 and Def. 7. 4), of a regular decagon inscribed in the circle. Cor. 2. — The square of the side of a regular pentagon inscribed in a circle, is equal to the squares of the radius and side of a regular decagon inscribed in the same. Inscribe in the circle BDG,... | |
 | Rev. John Allen - 1822 - 508 σελίδες
...construction, AB one of the sides of the inscribed hexagon, is equal to the radius AG (Constr.). Cor. 2.—The square of the side of a regular pentagon, inscribed in a circle, is equal to the squares, of the sides of a regular hexagon, and regular decagon, inscribed in the same circle. For... | |
 | John Radford Young - 1835 - 298 σελίδες
...substitution, if— r2 + ir2 (6 — I =2r2 — 2rv/(r2 — 4r4 — 4oV+a4 .-, by the last problem ; Hence the square of the side of a regular pentagon inscribed...circle, is equal to the square of the side of a regular decagon, together with the square of the radius. PROBLEM XIX. To find the side of an equilateral triangle... | |
 | Euclid, James Thomson - 1837 - 410 σελίδες
...will be completed by inscribing nine other chords in the circle each equal to BF. PROP. XXI. THEOR. THE square of the side of a regular pentagon inscribed in a circle, is equal to the squares of the sides of a regular hexagon and regular decagon, inscribed in the same circle. Let AF,... | |
 | Alfred Wrigley - 1845 - 222 σελίδες
...ratio between the areas of an equilateral triangle and a square inscribed in the same circle. 172. The square of the side of a regular pentagon inscribed in a circle is equal to the sum of the squares of the sides of a regular hexagon and a decagon inscribed in the same circle. 173.... | |
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THE square of the side of a regular pentagon inscribed in a circle, is equal to the squares of the sides of a regular hexagon and regular decagon, inscribed in the same circle. 
