Plane trigonometry, by S.L. Loney.

CHAPTER XVII.

TRIGONOMETRICAL RATIOS OF SMALL ANGLES. AREA OF
A CIRCLE. DIP OF THE HORIZON.
227. IF 0 be the number of radians in any angle,
which is less than a right angle, then sin 0, 0 and tan 0 are
in ascending order of magnitude.
Let TOP be any angle which is less than a right
angle.
With centre 0 and any radius OP
describe an arc PAP' meeting OT P
in A.
Draw PN perpendicular to OA 0 \ T
and produce it to meet the arc of the.. N '
circle in P'.
Draw the tangent PT at P to
meet OA in T and join TP'.
The triangles PON and P'ON are
equal in all respects, so that PN= NP' and
arc PA = arc AP'.
Also the triangles TOP and TOP' are equal in all
respects, so that

IT '= TV.