'Did the Idea of Universal Gravitation predate Newton?'
(The question went on to mention the books of Ahmed Baba.)
I had a look to see whether Baba's work is available in any way online, but found nothing. Could the questioner point to any source, it would help discussion?
Commentators who discuss early origins of gravitational ideas, perhaps as a possible anticipation of Newton, often leave it very unclear just what sort of gravitational ideas they are discussing. Then, when details do emerge, it has always so far turned out that what is being discussed is quite different from Newtonian gravitation.
First, the word 'gravity' means just heaviness, and no-one has ever seriously suggested that Newton discovered that, or that it was unknown before him. Occasionally one reads unconsidered statements that Newton 'discovered gravity', but that is not what he is seriously reputed to have discovered. On the other hand, gravity before Newton was about terrestrial physics -- the properties of bodies at or near the earth's surface. There were older theories about what moved the celestial bodies, but they did not suggest that the same laws of physics applied to celestial bodies as to terrestrial objects. It seems that Newton was the first to suggest, and provide evidence in the form of his 'moon-test', that what moves the celestial bodies is of the same kind as what moves falling terrestrial bodies -- their heaviness, subject to the same laws of motion and inertia as heavy bodies on the earth.
What Newton produced was also very specific. Considered for example in its astronomical application, a Newtonian gravitational force, if I'm not mistaken, is
-- an accelerative force,
-- directed towards a massive body,
-- operating as an attraction on another body,
-- and its measure is inversely proportional to the square of the distance between them.
Besides not accounting for terrestrial and celestial motions in the same way, earlier ideas of celestial motion discussed as possible anticipations of Newton have so far turned out either not to involve accelerative force, or not to involve forces directed centrally, etc. R S Westfall's 1971 book 'Force in Newton's physics' offers detailed discussion of concepts of force before Newton, and shows how some of them were quite vague: the idea was slow to become clarified in the pre-Newtonian world.
For example, Kepler's work is sometimes suggested as an anticipation of Newton, but Kepler's idea of force was not accelerative, he supposed that force maintains velocity, he did not think of it as producing acceleration, and it was not central. Thus, Kepler supposed that the sun's force came from its rotation and somehow impelled the planets along and around their orbital paths, as if their natural state was rest. His ideas about the moon's irregularities of motion were that they are caused by the Sun's illumination of the moon. Kepler's ideas did not include Newton-like ideas either of force or of inertia, see Bruce Stephenson's 'Kepler's Physical Astronomy' for a good discussion.
The quotation from Bullialdus introduced by Conifold expressly states the idea of something that 'turns with the body of the Sun', which appears to show that whatever it is, it is not a central gravitational force: the central forces of Newtonian gravitation do not turn with rotation of the attracting body. (Bullialdus, if he thought that the turning of the Sun's body has anything to do with gravity, may have been expressing a similar idea as the one already mentioned as held by Kepler.)
It is also important to distinguish between the bare idea of an inverse square law and the specifics of Newtonian gravitation. Anything that becomes spread out uniformly through space from a point-source is likely to follow an inverse-square law -- for example, light-intensity, it follows from the geometrical law for the surface area of a sphere, proportional to the square of its radius. Inverse-square laws of something are not peculiar to Newton, but whether that something is anything like Newtonian accelerative gravitation clearly should not be taken for granted and merely assumed.
Newton's fame was, among other things, for producing a newly compiled set of laws of motion, which operate together with what was (then) a new law of accelerative gravitational force inversely proportional to the squares of the distances, and together these have enabled celestial motions to be accounted for with previously-unknown mathematical precision and accuracy.
There have been many excessive claims for the accuracy of this or that ancient historical account of planetary motions and orbits. What is accurate enough in one age or context might be very rough in another. It is very difficult to discuss such suggestions without concrete material such as a particular book or description to go on.