Egypt has very hot summers, so a garden was always a place for the privileged to sit in the shade and gaze upon water. Even if the water didn't actually cool the garden much, looking at it made the people in the garden feel a bit cooler, also the formal ponds and canals irrigated the trees which grew alongside them. The Islamic garden is a direct descendant of these ancient Egyptian gardens, both in the use of formal water features, and in a garden being about cool green shade, rather than a riot of flowers.
The ancient Greeks were not known for their ornamental gardens, and they didn't have abundant water sources, so ornamental ponds were never fashionable. For the ancient Greeks, a garden was always what the 8th century BC poet Homer described in the Odyssey: "Pears and pomegranates and apples full of fruit, also figs and bounteous olives......here too a fertile vineyard". Trees have always been valued in Greece, a number of ancient Greek shrines were known for their sacred groves, and shade trees were often planted in towns, not along the streets, but in markets and gymnasia. The Lyceum was the gymnasium and exercise ground of ancient Athens, it was known for it's fine groves of plane trees. Aristotle and his students habitually discussed philosophy while walking along the shaded pathway (peripatos) of the Lyceum, this is why they were known as the Peripatetics.
It was only after Alexander the Great conquered Persia in 334 BC that Greeks began to create ornamental gardens, and even then it was mainly in the Hellenistic kingdoms of Egypt and Syria, rather than in Athens. The ancient Persians loved gardens, in 408 BC, the Spartan general Lysander was visiting Cyrus the Younger (the son of Darius II, king of Persia), he was shocked to discover that Cyrus worked in the garden, in Greece no gentleman would think of gardening with his own hands.
