The quadrature of the circle, the square root of two, and the right-angled triangle, by William Alexander Myers.

QUADRATURE OF THE CIRCLE. 111
The cosine, radius, and secant have also been omitted, partly for the same reason, and partly
because the radius with which they should both agree will be found carried out in the Second
Part of this book; for Case 6 they should agree like the sine and tangent with each other to 72
decimal places, and for Case 7 to 144 decimal places.
By Case 6, the tangent is 1972063063734639263984455073299118 -8 and the square which forms the unit of comparison is the square
of the tangent, which is
of the tangent, which i38890327273464518838061949606599216563 -67162016449544406781628584372454400'
Again, by Case 6, the rectangle contained by the radius and the sine
2
is and the number of sides
2788918330588564181308597538924774401 o sides
87651718961354874269698779794778624031.
1753034379227097485393975 -Multiplying these together, we have 27889 588564 859
278891833058856418130859 -5958955724806- 44 1
7538924774401 -7 * 388903272734645188380619496065992165 -44 3889032727346 -6367162016449544406781628584372454400 7 X 1
4518838061949606599216563671620164495444067816285843724544 -00 17111744000324388288747257826903655288015512872377995 -7
3898391657712387993600
3898391657712387993600 = 244453485718919832696389397527195 -07554307875531968564842627379673198284800; therefore there are
exactly 244453485718919832696389397527195075543078755319685 -64842627379673198284800 squares in the given polygon, each of
which is expressed hby 1
which is expressed 388903272734645188380619496065992165636 -7162016449544406781628584372454400'
Then, multiplying the number of squares by the value of each square,
244453485718919832696389397527195075543078753196856 -we have
388903272734645188380619496065992165636716201644954 -4842627379673198284800 44
4406781628584372454400 - 7 67 =- area of the inscribed polygon for double the number of sides.