What kind of reasoning does machiavelli use in this
excerpt?
o he uses inductive reasoning because he offers
statistics to prove his claim.
o he uses inductive reasoning because he observes
a pattern and proves a conclusion.
he uses deductive reasoning because he relies on
scientific experiments to prove a conclusion.
o he uses deductive reasoning because he
introduces a conclusion and proves it with
evidence.

Fourth Option: He uses deductive reasoning because he  introduces a conclusion and proves it with  evidence.

Explanation:

Although the excerpt for the question is not provided, it is safe to assume the excerpt to be from "The Prince", Nicolo Machiavelli's most famous book published in 1532.

Machiavelli uses the same method throughout the book for proving his arguments. So whatever the excerpt be, the answer would be the same.

Deductive reasoning first presents the conclusion or claim and then provides the evidence through various methods.

Inductive reasoning is type of reasoning in which provides evidence just for the purpose of proving a conclusion or argument. It means first details are provided and then a conclusion is made from these details.

First and third options are totally incorrect because, Machiavelli did not use any statistics (comparisons based on number), or scientific experiments (his area of discussion being history, so no possibility of experiments).

Machiavelli actually presented his arguments/claims in the start of each chapter, and then he proved them with examples from history and experiences gained from the society. So, fourth option is correct