Deduction and induction are not about observation, but certainty in inference.
It may be tempting to define deduction as moving from general to specific claims, and induction vice versa, but this is not entirely accurate. Let's take an example to show the difference between deduction and induction.
DEDUCTION: If a man is in a kitchen, then he is in the house in which the kitchen is located. Bob is in the kitchen, therefore we can conclude Bob is in the house the kitchen is located. Note, that since the kitchen is in the house, it is an inescapable conclusion that Bob, if entirely in the kitchen, is also entirely in the house. This is a deduction that is called a conditional in logic, and has the form p -> q.
INDUCTION: Bob frequently is at home on Monday mornings. Bob was at home on Monday mornings for the last 11 weeks, and given that Bob's car is always present when he is home, observing that today, on the 12th Monday Bob's car is present, it is likely Bob is home though we have not directly observed him.
Simply put, in the first example the conclusion MUST follow from the premises, and that reflects a basic reality about space-time, in this case a volume in space-time follows transitivity. In the second example, while it is likely that the conclusion is true, it is not known with certainty. For instance, Bob may have gone on vacation this week leaving his car home, and the conclusion can only be verified by empirical means (ringing the doorbell might verify he's home if he answers). That is the essential difference between the types of inference. Note there is a third form of inference called abduction which is aligned with heuristics.
As far as the Greek reference to deduction, of course the Greek named Euclid of Alexandria is recognized as the Father of Geometry and a the proponent of the axiomatic method, which is a chain of deductions that allows certainty of conclusion. Euclid's Elements has served as a model of reasoning for mathematicians and philosophers since it was put to paper, and many thinkers have sought to bring the certainty of logic even to disciplines other than mathematics. Scientists, for instance, have long sought the deductive certainty that math provides in their knowledge of the universe (see Netwonian mechanics) and have often been shocked or refused to believe that certainty in physics is not absolute (see Einstein and Bohr).
Another place where the questions of determinism and probability clash is in the philosophy of mathematics itself, where
David Hilbert and Kurt Gödel raised and settled questions regarding the nature of truth and certainty in mathematics itself (see Hilbert's Program).
In review, induction and deduction are not about observation, per se, but rather the certainty of conclusions drawn from premises, regardless of the nature of the observations, premises, and conclusions involved.