An enthymeme is a syllogism in which one of the three propositions is omitted.
Suppressing the major premise gives an enthymeme of the first order; whereas if the minor premise be suppressed, the enthymeme becomes one of the second order; while omitting the conclusions gives an enthymeme of the third order.
Illustrations:
Complete syllogism.
All true teachers are just,
You are a true teacher,
(Hence) You are just.
Enthymeme of first order; major premise omitted.
..........................
You are a true teacher,