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 * angle between extended middle finger tips tangent circle-square
intersections
   is actually 100 degrees; navel at center of circle is 1 1/2 times higher
than
   1/14 of man's height; angle between raised legs at calf muscle is actually
60
   degrees as measured from the center of the square; also, angle between
raised
   legs at center of ball of foot is 60 degrees as measured from center of
circle;

 * the line segment between center of circle and center of square is the
opposite
   side of a right triangle, with adjacent side the horizontal circle radius,
and
   hypotenuse from the center of the square to the end of that same circle
radius,
   the angle of which is 80 degrees; the center of square is 2 cubits above
floor
   line, and its base is tangent to the base of circle at the vertical
centerline;
   thus solving for "y": y/(y + 2) = tan 10; y = ~0.428148 cubits; 4 cubits/14
is
   ~0.285714, for a ratio of ~1.49852; very nearly 1 1/2 times higher than
"1/14";

 * circle radius 2 + y = ~2.428148 cubits; circle diameter 2y + 4 = ~4.856296
cu-
   bits; circle area (2 + y)^2 * pi = ~18.522525 square cubits; top of circle
is
   2y = ~0.856296 cubits above square, segment chord 4 * sqrt(2y) = ~3.701451
cu-
   bits, central angle is 2 * arctan (2 * sqrt(2y)/(2 - y)) = ~99.316396
degrees
   (inside edge extended middle finger tips); 1 finger is 1/24 cubit =
~0.041667
   cubits; 1 palm is 1/6 cubit = ~0.166667 cubits; 1 foot 4/6 = ~0.666667
cubits;

 * simplifying the value of "y", y/(y+2)=tan(10): y = 2sin(10)/(
os(10)-sin(10));
   circle chord at top of square = 8sqrt(sin(10)/(cos(10)-sin(10))) =
~3.701451;
   2arcTan((cos(10)-sin(10))sqrt(sin(10)/(cos(10)-sin(10)))/(cos
10)/2-sin(10)))
   is central angle of top circle sector ~99.316396 degrees; top circle sector
   area = pi(2sin(10)/(cos(10)-sin(10))+2)^2arcTan((cos(10)-sin(
0))sqrt(sin(10)
   /(cos(10)-sin(10)))/(cos(10)/2-sin(10)))/180 = ~5.109973 square cubits; top
   circle segment area = pi(2sin(10)/(cos(10)-sin(10))+2)^2arcTan((cos(10)-sin
   (10))sqrt(sin(10)/(cos(10)-sin(10)))/(cos(10)/2-sin(10)))/180+(8sin(10)/(cos
   (10)-sin(10))-8)sqrt(sin(10)/(cos(10)-sin(10))) = ~2.200907 square cubits;

 * circle chord at side of square = 2sqrt((2sin(10)/(cos(10)-sin(10))+2)^2-4) =
   ~2.753836; central angle of side circle sector = 2arcTan(sqrt((2sin(10)/(cos
   (10)-sin(10))+2)^2-4)/2) = ~69.091629 degrees; side circle sector area = pi
   (2sin(10)/(cos(10)-sin(10))+2)^2arcTan(sqrt((2sin(10)/(cos(10)-sin(10))+2)^2
   -4)/2)/180 = ~3.554865 square cubits; area of side circle segment = pi(2sin
   (10)/(cos(10)-sin(10))+2)^2arcTan(sqrt((2sin(10)/(cos(10)-sin(10))+2)^2-4)/
   2)/180-2sqrt((2sin(10)/(cos(10)-sin(10))+2)^2-4) = ~0.801029 square cubits;

 * circle chord at bottom of square = 4 cubits; central angle of bottom circle
   sector = 2arcTan(2/sqrt((2sin(10)/(cos(10)-sin(10))+2)^2-4)) = ~110.908371
   degrees; bottom circle sector area = pi(2sin(10)/(cos(10)-sin(10))+2)^2arc
   Tan(2/sqrt((2sin(10)/(cos(10)-sin(10))+2)^2-4))/180 = ~5.706397 square cu-
   bits; bottom circle segment area = pi(2sin(10)/(cos(10)-sin(10))+2)^2arcTan
   (2/sqrt((2sin(10)/(cos(10)-sin(10))+2)^2-4))/180-2sqrt((2sin(10)/(cos(10)-
   sin(10))+2)^2-4) = ~2.952562 square cubits;

 * area of bottom square corner outside circle = -pi(2sin(10)/(cos(10)-sin(10))
   +2)^2arcTan(2/sqrt((2sin(10)/(cos(10)-sin(10))+2)^2-4))/360-sqrt((2sin(10)/
   (cos(10)-sin(10))+2)^2-4)+4sin(10)/(cos(10)-sin(10))+4 = ~0.626179 square
   cubits; circle chord at top corner of square = sqrt((-sqrt((2sin(10)/(cos
   (10)-sin(10))+2)^2-4)-2sin(10)/(cos(10)-sin(10))+2)^2+(-4sqrt(sin(10)/(cos
   (10)-sin(10)))+2)^2) = ~0.245524 cubits; central angle of top square corner
   circle sector = -arcTan(sqrt((2sin(10)/(cos(10)-sin(10))+2)^2-4)/2)-arcTan
   ((cos(10)-sin(10))sqrt(sin(10)/(cos(10)-sin(10)))/(cos(10)/2-sin(10)))+90
   = ~5.795988 degrees; top square corner circle sector area = (2sin(10)/(cos
   (10)-sin(10))+2)^2(-piarcTan(sqrt((2sin(10)/(cos(10)-sin(10))+2)^2-4)/2)/
   360-piarcTan((cos(10)-sin(10))sqrt(sin(10)/(cos(10)-sin(10)))/(cos(10)/2-
   sin(10)))/360+pi/4) = ~0.298212 square cubits; top square corner circle
   segment area = -sqrt(((-sqrt((2sin(10)/(cos(10)-sin(10))+2)^2-4)-2sin(10)
   /(cos(10)-sin(10))+2)^2+(-4sqrt(sin(10)/(cos(10)-sin(10)))+2)^2)(-(-sqrt
   ((2sin(10)/(cos(10)-sin(10))+2)^2-4)-2sin(10)/(cos(10)-sin(10))+2)^2/4-
   (-4sqrt(sin(10)/(cos(10)-sin(10)))+2)^2/4+(2sin(10)/(cos(10)-sin(10))+2)
   ^2))/2+(2sin(10)/(cos(10)-sin(10))+2)^2(-piarcTan(sqrt((2sin(10)/(cos(10)
   -sin(10))+2)^2-4)/2)/360-piarcTan((cos(10)-sin(10))sqrt(sin(10)/(cos(10)-
   sin(10)))/(cos(10)/2-sin(10)))/360+pi/4) = ~0.000508 square cubits; area
   of top square corner outside circle = sqrt(((-sqrt((2sin(10)/(cos(10)-sin
   (10))+2)^2-4)-2sin(10)/(cos(10)-sin(10))+2)^2+(-4sqrt(sin(10)/(cos(10)-sin
   (10)))+2)^2)(-(-sqrt((2sin(10)/(cos(10)-sin(10))+2)^2-4)-2sin(10)/(cos(10)
   -sin(10))+2)^2/4-(-4sqrt(sin(10)/(cos(10)-sin(10)))+2)^2/4+(2sin(10)/(cos
   (10)-sin(10))+2)^2))/2+(2sin(10)/(cos(10)-sin(10))+2)^2(piarcTan(sqrt((2sin
   (10)/(cos(10)-sin(10))+2)^2-4)/2)/360+piarcTan((cos(10)-sin(10))sqrt(sin(10)
   /(cos(10)-sin(10)))/(cos(10)/2-sin(10)))/360-pi/4)+(-2sqrt(sin(10)/(cos(10)
   -sin(10)))+1)(-sqrt((2sin(10)/(cos(10)-sin(10))+2)^2-4)-2sin(10)/(cos(10)-
   sin(10))+2) = ~0.014041 (= 0.0140410224358...) square cubits;

 * line segment "y" is also the shortest side of a scalene triangle, with
longest
   side the circle radius, and adjacent side "a" 100 degrees from vertical
center-
   line to the end of that same circle radius; thus solving for "a": a =
sqrt((-8
   sin(10)cos(10)cos(70)+4(sin(10))^2)/(-2sin(10)cos(10)+1)+(2si
(10)/(cos(10)-sin
   (10))+2)^2) = ~2.316912 cubits (2.31691186136...); area of triangle =
sin(10)cos
   (10)cos(20)/(-sin(10)cos(10)+1/2) = ~0.488455 (0.488455385956...) square
cubits;

 * segment "y" is shortest side of yet another, slightly smaller scalene
triangle
   with adjacent side "a" 110 degrees from vertical centerline, and longest
side
   60 degrees from the same vertical centerline; thus solving for "a": a =
sqrt(3)/
   (cos(10)-sin(10)) = ~2.135278 (2.13527752148...) cubits; longest side =
2sin(70)
   /(cos(10)-sin(10)) = ~2.316912 (2.31691186136...) cubits, which extends
2sin(70)
   /(cos(10)-sin(10))-4sqrt(3)/3 = ~0.00751078 cubits beyond intersection
w/square;
   area of triangle = sqrt(3)sin(10)sin(70)/(cos(10)-sin(10))^2 = ~0.429540
square
   cubits (0.429540457576...); the tiny fraction of this triangle outside
square is
   described by shortest side = sin(10)(2/(cos(10)-sin(10))-4sqr
(3)/(3sin(70))) =
   ~0.00138794 cubits (0.00138793689527...); longest side = 2sin
70)/(cos(10)-sin
   (10))-4sqrt(3)/3 = ~0.00751078 (0.00751078459977...) cubits; adjacent side
"a":
   a = sqrt(3)(1/(cos(10)-sin(10))-2sqrt(3)/(3sin(70))) = ~0.00692198 cubits
(0.00
   692197652921...); area of tiny triangle = (sqrt(3)sin(10)(csc
70))^2(sqrt(3)sin
   (10)/3-sqrt(3)cos(10)/3+sin(70)/2)(5sqrt(3)sin(10)sin(70)/6-4
qrt(3)sin(70)cos
   (10)/3+sin(10)cos(10)+2(sin(70))^2-(sin(10))^2)+(sin(10))^2(c
c(70))^2(-sqrt(3)
   (cos(10)-sin(10))+3sin(70)/2)(-sqrt(3)(cos(10)-sin(10))/3+sin
70)/2))/(cos(10)-
   sin(10))^2 = ~0.00000451394 square cubits (0.0000045139387711...);

 * segment "y" is the base of an isosceles triangle with vertex angle 160
degrees,

[continued in next message]

--- SoupGate-Win32 v1.05
 * Origin: you cannot sedate... all the things you hate (1:229/2)