in Geometry and Arithmetic, is a ratio between two lines, two numbers, or the like, where one of them contains the other once, with the addition of a half.

Thus 6 and 9 are in a sesqui-alternate ratio, since 9 contains 6 once, and 3, which is half of 6, over; and 20 and 30 are in the same, as 30 contains 20 and half 20, or 10.

SESQUI-DUPLICATE Ratio is when of two terms the greater contains the less twice, and half the less remains; as 15 and 6, 50 and 20.

SESQUI-TERTIAL Proportion is when any number or quantity contains another once and one third.