This is based only on how you define basicity. If you use CaO/SiO2, lines from CaO-SiO2 side to Al2O3 could be plotted as isobasicity lines. Alternatively, you could use optical basicity, then you should calculate optical basicity values for all compositions and plot the lines. The calculation process for optical basicity (OP) is very simple

OP=(3*x(Al2O3)*0.605+2*x(SiO2)*0.48+1*x(CaO)*1)/(3*x(Al2O3)+2*x(SiO2)+1*x(CaO))

If you are interested in binary basicity (CaO/SiO2), the steps are as follows (for example, with CaO/SiO2 = 2):

1. Remember that the sum of all components of the ternary must be equal to 100 (CaO + SiO2 + Al2O3 =100);

2. From the CaO/SiO2 ratio, it is possible to obtain CaO = 2*SiO2;

3. Set Al2O3 to 0 (Al2O3 = 0%);

4. Now it is possible to rearrange equations from 'step 1' and 'step 2':

2*SiO2 + SiO2 + 0 = 100; Solving for SiO2 you will find: SiO2 = 33.3%;

5. Finally, if SiO2 = 33.3%, CaO must be equal to 66.7% (considering Al2O3 = 0%);

6. Draw a line from the vertex of Al2O3 to the point where SiO2 = 33.3% (CaO = 66.7%) and then you will have the isobasicity line, where any point exactly on top of that line will represent the same binary basicity of 2.

Nice ternary diagrams can be plotted viahttp://www.originlab.com/www/products/GraphGallery.aspx?GID=217

thank you all!!