pic1) The red line has the length of 'y' and the blue line has the length of 'x'. |
pic2a) The red circle has the radii length of 'x' and the blue line
has the radii of 'y'. The left dot is the centre of the red circle and the
right dot is the centre of the blue circle. pic2b) Same as pic2a, only now we've erased the part of the blue circle that where in the red circle to make it clearer. |
pic3) Since the red circle had the radii of 'x', means that the part of the purple line that's on the right side of it's centre, and still inside the circles outline, has to have the length of 'x'. The same goes for the blue circle and since we only have the right side of it left, we conclude that everything on the right side of the red circles centre is 'y' + 'x'. |
pic4) The blue is 'x' and the red line is 'y'. We put them on top of each other. The green line shows their mutual length and the red line shows how much longer the red line is from the blue line. If you erase the green, you erase the length of 'x' from the length of 'y'. So the little red line that is left is 'y' - 'x' |
pic5) The white line is 1 l.u long and the blue line is 'x' long. |
pic6) The red line is 'y' long. The angle labelled with a green A is the arbitrary angle between 'y' and the 1 l.u. line. |
pic7) Yellow line connects the tips of the 'y' and the 1 l.u. line. |
pic8) Both the yellow lines are parallel to each other. The left one is 'l1' and the right one is 'l2'. |
pic9) The purple line is as long as 'y' * 'x' measured in your new l.u system. |
pic10) |
pic11) First the blue line is 'x' long. Then we segment it into two pieces: the white line which we say is 1 l.u. long and the other blue line which isn't as long as 'x' anymore but whom we'll still refer to as 'x'(just to confuse you more, dear reader). |
pic12) Same as pic6. |
pic13) The yellow line is 'l1'. |
pic14) The left, yellow line is 'l2'. The right one is 'l1'. |
pic15) The purple line equals 'y'/'x' using your own 1 l.u. based measuring system. |
pic)16 |
pic17) The white line is 1.l.u long and the blue line is 'x' long. The red circle around them have the diameter of both of the lines combined. |
pic18) The yellow line is perpendicular to the 'x' and 1 l.u. lines. The part of the yellow line that is inside the circle equals Ö ('x'), using our own measuring system of course. |
pic19) |
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