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Hanno,

       My post http://fer3.com/arc/m2.aspx/Flat-Bygrave-alternative-configuration-Stuart-mar-2014-g27166 shows two versions of flat Bygrave scales. There is no slanting in either. The first is Gary LaPook's classic design in which there are 2 cycles of the the cotan scale. The second is the alternative in which both the cosine and cotan scales have one cycle (plus a small overhang on the ends) allowing longer and more accurate scales to be produced for a given area of paper. In the alternative configuration running off the end is prevented by providing two pointers to the zero position of the cosine scale. One pointer will always be on the cotan scale. This is analogous to using a standard linear slide rule where if the number you need is off the scale you reverse direction to the other end of the slide. Another version of the flat Bygrave alternative configuration can be found at http://fer3.com/arc/m2.aspx/Postscript-code-for-making-Bygrave-Scales-Stuart-mar-2014-g27398 which also gives Postscript code that would allow you to construct Bygrave scales of any size shape or form that you like,

Regards,

Robin Stuart