I don't understand the part in boldface. The Oxford dictionary interprets "extend over" as "occupy a specified area or stretch to a specified point", but I'm not sure if that definition fits here.
However important it may be, in order to form a proper judgment of the natural state of man, to consider him from his origin, and to examine him, as it were, in the first embryo of the species; I shall not attempt to trace his organization through its successive approaches to perfection: I shall not stop to examine in the animal system what he might have been in the beginning, to become at last what he actually is; I shall not inquire whether, as Aristotle thinks, his neglected nails were no better at first than crooked talons; whether his whole body was not, bear-like, thick covered with rough hair; and whether, walking upon all-fours, his eyes, directed to the earth, and confined to a horizon of a few paces extent, did not at once point out the nature and limits of his ideas. I could only form vague, and almost imaginary, conjectures on this subject. Comparative anatomy has not as yet been sufficiently improved; neither have the observations of natural philosophy been sufficiently ascertained, to establish upon such foundations the basis of a solid system. For this reason, without having recourse to the supernatural informations with which we have been favoured on this head, or paying any attention to the changes, that must have happened in the conformation of the interior and exterior parts of man's body, in proportion as he applied his members to new purposes, and took to new aliments, I shall suppose his conformation to have always been, what we now behold it; that he always walked on two feet, made the same use of his hands that we do of ours, extended his looks over the whole face of nature, and measured with his eyes the vast extent of the heavens.
This sentence comes from A Discourse Upon the Origin and the Foundation of the Inequality among Mankind