No P is M.
All S are M.
[and there exists at least one S]*
Therefore, Some S are not P.
No circle is a rectangle.
All squares are rectangles.
[and there exists at least one square]*
Therefore, Some squares are not circles.
Modus Cesaro is the weaker form of the Modus Cesare, which only infers an existential conclusion. Since every universal quantification that does not refer to an empty extension set always implies an existential quantification, this variation is possible, but this is of course also a weaker statement than the universal conclusion of the Modus Cesaro.
The name “Cesaro” is a mnemonic term that helps to remember the most important characteristics of this mode: The “C” at the beginning indicates that it is related to the Modus Celarent, the “e” and “a” indicate the negative and affirmative universal statements in the premisses and the “o” indicates that the conclusion is a negative existential statement.