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praise and the angels, through fear of Him ! He sends the 
thunderbolts to strike therewith whomever He pleases, even 
while they are disputing concerning God ; indeed, He is 
of immense power ! His name is Cayeeala Tacamamu 
Daburim Buaburim Jawburim Masseevayaramu. O God ! 
in Salvation ; if it is the will of God.” 
Mr. Wilkinson also laid before the meeting the following 
Geometrical Theorems. 
If from the angular points of any triangle, ABC, lines be 
drawn making the same constant angles with the adjacent 
sides, four triangles, AjBjQ, A 2 B 2 C 2 , A 3 B 3 C 3 , A 1 B 1 C 4 , will 
be formed which possess the following properties : — 
1. The triangles A^C^ A 2 B 2 C 2 , A 3 B 3 C 3 , A 4 B,C 4 , are all 
similar amongst themselves and to the triangle ABC. 
2. If circles be described about the triangles A 2 C A, B 2 A B, 
C 2 B C, they will all pass through a common point P. 
3. Circles described about the triangles A 3 B A, B 3 C B, 
C 3 A C, will all intersect in another common point P. 
4. If 0 15 0 2 , 0 3 , be the centres of the circles in (2) ; and 
0 4 , 0 5 , O c , the centres of those in (3) ; then the triangles 
0,0 3 0 3 , 0,0 3 0 G are similar to each other and to the original 
triangle ABC. 
5. The triangles OjOaOs, 0 4 0,0 G , are coaxial, since their 
vertices lie two and two on the radials O 0 15 O 0 2 , O 0 3 ; 
they are therefore also copolar, or the intersections of their 
opposite sides range in the same straight line. 
6. The triangle 0 4 0 2 0 3 :=the triangle O 4 O 5 O 0 ; for 
16 ABCx 0 1 0 ! 0 3 =16 A B C x 0 ( 0 5 0g — a~lr + a~ c 2 
+ b 2 c 3 . 
7. If r x , r 2 , r 3 ; r i} r 5 , r 6 , be the radii of the circles in (2) 
and (3) respectively, and R = the radius of the circle circum- 
scribing ABC; then R 3 = r x r 2 rz = r 4 r 6 r fi . 
8. Let f g, h, be the intersections of A C 3 , C A 2 ; A B 3 , 
AB,; C B 3 , BC 2 ; then the lines A//, B /, C g, will all 
intersect in the same point P a . 
