Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Books Books
" 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. "
Elements of Geometry, Theoretical and Practical: Including Constructions of ... - Page 99
by Eugenius Nulty - 1836 - 220 pages
Full view - About this book

A Course of Mathematics: Designed for the Use of the Officers ..., Volumes 1-2

Isaac Dalby - Mathematics - 1807 - 968 pages
...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.):...
Full view - About this book

Mathematics: Compiled from the Best Authors, and Intended to be ..., Volume 1

Samuel Webber - Mathematics - 1808 - 466 pages
...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,...
Full view - About this book

An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...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...
Full view - About this book

A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 446 pages
...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...
Full view - About this book

A Treatise on Plane and Spherical Trigonometry

Robert Woodhouse - Plane trigonometry - 1819 - 300 pages
...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...
Full view - About this book

Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - Astronomy - 1822 - 516 pages
...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,...
Full view - About this book

Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - Astronomy - 1822 - 508 pages
...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...
Full view - About this book

The Elements of Analytical Geometry ...

John Radford Young - Geometry, Analytic - 1835 - 298 pages
...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...
Full view - About this book

The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...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,...
Full view - About this book

A collection of examples in pure and mixed mathematics, with hints and ...

Alfred Wrigley - 1845 - 222 pages
...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....
Full view - About this book




  1. My library
  2. Help
  3. Advanced Book Search
  4. Download EPUB
  5. Download PDF