Enlargement without Maths

 Setting out an enlargement grid can be done without the mathematics of ratios.  It uses an old method of estimated interval size and angles relating to the ends of the estimation and the width of the design.  This gives the method in simple images.

     Start with your original design

Draw line at a shallow angle from one corner

Determine number of grid lines (say 10) along the bottom edge.  Choose a length approximately the size needed for the grid.  Mark out the number of divisions with dividers or compass on that slope.

Connect the final mark with the corner at the end of the line started on.  Place a right angle on that line.

   Fix a long straight edge under that right angle and fix it so it does not move

·        Transfer the marks on the sloped line to the edge of the image.

This gives ten equal divisions. Adjust the divider opening to the width of the division.

Use dividers with this opening to transfer the division size to the other edge.

Do this on all four edges if a rectangle.

Do the same process for the enlarged size.

Draw a slope

Estimate the size of the division.  Mark that estimate on the slope as for the original design.  Fix a right angle between the end of the slope marks and the corner of the design.  Fix the straight edge and mark off the divisions on the enlarged size.  Transfer these divisions with the new division opening of the dividers

Draw the grid.

Note where the design crosses the grid lines. Transfer marks onto the enlarged grid proportionally.  To avoid confusion, mark one line in at a time.

An intersection of the design line two thirds up the design grid vertical gets a mark two thirds up the corresponding enlarged vertical.  The same with horizontal grid lines.  Connect the dots one line at a time in pencil.  They can be altered later and erased once the final lines are inked in.