Useful proportional variations
Given four quantities a, b, c, and d in continued proportion, i.e.we can use the following variations of the ratios.

In each case, convince yourself that the statement is true, by

• testing it with specific numbers, and
• giving a general algebraic explanation.

Can you think what each name means?
Note: The names are not important — it is not necessary that learners learn the names, but they should understand the concepts!

1. Invertendo:
   If then
   
   
2. Alternando:
   If then
   
   
3. Componendo:
   If then
   
   
4. Dividendo:
   If then
   
   
5. Compenendo et dividendo:
   If then