Problem 654: Salinon

Exercise your brain. Archimedes wrote the "Book of Lemmas" more than 2200 years ago. Solve the proposition #14 (high school level) and lift up your geometry skills.

Click the figure below to see the complete problem 654

Continue reading at:

gogeometry.com/ArchBooLem14.htm

## Tuesday, December 16, 2008

### Archimedes' Book of Lemmas, Proposition #14

Labels:
Archimedes,
area,
book of lemmas,
circle,
diameter,
perpendicular,
salinon

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Let AC = BD = 2p, CD = 2q

ReplyDeleteSo EF = OE + OF = OA + q = 2p + q + q = 2p +2q

Let(XY)denote area of semicircle on XY as diameter

Salmon area

=(AB)-(AC)-(DB)+(CD)]

=[Pi/2][(2p+q)^2 - p^2 - p^2 + q^2]

=[Pi/2][2p^2 + 4pq +2q^2]

=Pi(p + q)^2

=Area of circle on EF as diameter