THE LIBER ASSUMPTORUM 
103 
Lastly, we may mention the elegant theorem about the 
area of the Salinon (presumably ‘salt-cellar’) in Prop. 14. 
ACB is a semicircle on AB as diameter, AD, EB are equal 
lengths measured from A and B on AB. Semicircles are 
drawn with AD, EB as diameters on the side towards G, and 
c 
a semicircle with DE as diameter is drawn on the other side of 
AB. CF is the perpendicular to AB through 0, the centre 
of the semicircles ACB, DFE. Then is the area bounded by 
all the semicircles (the Salinon) equal to the circle on CF 
as diameter. 
The Arabians, through whom the Book of Lemmas has 
reached us, attributed to Archimedes other works (1) on the 
Circle, (2) on the Heptagon in a Circle, (3) on Circles touch 
ing one another, (4) on Parallel Lines, (5) on Triangles, (6) on 
the properties of right-angled triangles, (7) a book of Data, 
(8) De clepsydris: statements which we are not in a position 
to check. But the author of a book on the finding of chords 
in a circle, 1 Abu’l Raihan Muh. al-Biruni, quotes some alterna 
tive proofs as coming from the first of these works. 
(S) Formula for area of triangle. 
More important, however, is the mention in this same work 
of Archimedes as the discoverer of two propositions hitherto 
attributed to Heron, the first being the problem of finding 
the perpendiculars of a triangle when the sides are given, and 
the second the famous formula for the area of a triangle in 
terms of the sides, 
V{s (s — a) (s—b){s — c)}. 
1 See Bibliotheca mathematica, xi 3 , pp. 11-78.