This author dates to C1 BC-AD, and was a Greek historian, whose account of Babylon appears in Book II of his Bibliotheca historica (Historical Library). According to the Livius site, most of Book II is based on Ctesias.
Unfortunately, there is some controversy about whether his description of Babylon and the Hanging Gardens (Book II, chapter 10, not included in Livius' summary) is founded on Ctesias or Clitarchus, both of whose works are known only through later quotations, although both are credited with transmitting eye witness descriptions.
Still, we can see from Livius' summary that the description of the Hanging Gardens (§ 10) would have completed the description of Semiramis' improvements to Babylon in § 9). And the description would certainly fit very smoothly there. So it may be that issues about the garden builder are causing difficulties here.
From Rusty Seitsemar
The Garden was 100 feet long by 100 wide and built up in tiers so that it resembled a theater. Vaults had been constructed under the ascending terraces which carried the entire weight of the planted garden; the uppermost vault, which was seventy-five feet high, was the highest part of the garden, which, at this point, was on the same level as the city walls. The roofs of the vaults which supported the garden were constructed of stone beams some sixteen feet long, and over these were laid first a layer of reeds set in thick tar, then two courses of baked brick bonded by cement, and finally a covering of lead to prevent the moisture in the soil penetrating the roof. On top of this roof enough topsoil was heaped to allow the biggest trees to take root. The earth was leveled off and thickly panted with every kind of tree. And since the galleries projected one beyond the other, where they were sunlit, they contained conduits for the water which was raised by pumps in great abundance from the river, though no one outside could see it being done. (Wellard, 1972, pp. 156) [Wellard, James. 1972. Babylon. New York, NY. Saturday Review Press.]
Originally from Garden Visit (the text here seems somewhat garbled, although much quoted on the web)
And then there were the Hanging Gardens. Paracleisos [Paradeisos?] going up to the top is like climbing a mountain. Each terrace rises up from the last like the syrinx, the pipes of pan, which are made of several tubes of unequal length. This gives the appearance of a theater. It was flanked by perfectly constructed walls twenty-five feet thick. The galleries were roofed with stone balconies. Above these there was the first of a bed of reeds with a great quantity of bitumen, then a double layer of baked bricks set in gypsum, then over that a covering of lead so that moisture from the soil heaped above it would not seep through. The earth was deep enough to contain the roots of the many varieties of trees which fascinated the beholder with their great size and their beauty. There was also a passage which had pipes leading up to the highest level and machinery for raising water through which great quantities of water were drawn from the river, with none of the process being visible from the outside
—C. W. Müller, Scriptores Rerum Alexandrii Magni, in the Didot edition of Arrian, 1846, 137
From Finkel, an unattributed translation which has a problematic extra component (picked out in red):
Diod/Finkel: There was also, beside the acropolis, the Hanging Garden, as it is called, which was built, not by Semiramis, but by a later Syrian king to please one of his concubines; for she, they say, being a Persian by race and longing for the meadows of her mountains, asked the king to imitate, through the artifice of a planted garden, the distinctive landscape of Persia.
QCR: Tradition affirms that a king of Assyria, reigning in Babylon, executed this work to gratify his queen, who, delighting in forest scenery, persuaded her husband to imitate the beauties of nature by a garden on this imperial scale.
Berossus: This he did to gratify his queen, because she had been brought up in Media, and was fond of a mountainous situation.
The park extended four plethra on each side, and since the approach to the garden sloped like a hillside and the several parts of the the structure rose from one another tier on tier, the appearance of the whole resembled that of a theatre. When the ascending terraces had been built, there had been constructed beneath them galleries which carried the entire weight of the planted garden and rose little by little one above the other along the approach; and the uppermost gallery, which was fifty cubits high, bore the highest surface of the park, which was made level with the circuit wall of the battlements of the city. Furthermore, the walls, which had been constructed at great expense, were twenty-two feet thick, while the passageway between each two walls was ten feet wide. The roofs of the galleries were covered over with beams of stone sixteen foot long, inclusive of the overlap, and four feet wide. The roof above these beams had first a layer of reeds laid in great quantities of bitumen, over these two courses of baked brick bonded by cement, and as a third layer a covering of lead, to the end that the moisture from the soil might not penetrate beneath. On all this again the earth had been piled to a depth sufficient for the roots of the largest trees; and the ground, when levelled off, was thickly planted with trees of every kind that, by their great size or any other charm, could give pleasure to the beholder. And since the galleries, each projecting beyond another, all received the light, they contained many royal lodges of every description; and there was one gallery which contained openings leading from the topmost surface and machines for supplying the gardens with water, the machines raising the water in great abundance from the river, although no one outside could see it being done.
—Diodorus Siculus II, 10