Conjecture, n.
Etymology: [L. conjectura, fr. conjicere, conjectum, to throw together, infer, conjecture; con- + jacere to throw: cf. F. conjecturer. See Jet a shooting forth.]
An opinion, or judgment, formed on defective or presumptive evidence; probable inference; surmise; guess; suspicion. He [Herodotus] would thus have corrected his first loose conjecture by a real study of nature. Whewell. Conjectures, fancies, built on nothing firm. Milton.
2 other Webster entries under this spelling
Conjecture, v. t. [imp. & p.p. Conjectured; p.pr. & vb.n. Conjecturing.]
To arrive at by conjecture; to infer on slight evidence; to surmise; to guess; to form, at random, opinions concerning. Human reason can then, at the best, but conjecture what will be. South.
Conjecture, v. i.
To make conjectures; to surmise; to guess; to infer; to form an opinion; to imagine.
Shades of meaning
Fernald has no entry of its own for conjecture; he lists it under hypothesis, suppose.
Where he writes about it:
A conjecture is more methodical than a guess, while a supposition is still slower and more settled; a conjecture, like a guess, is preliminary and tentative; a supposition is more nearly final; a surmise is more floating and visionary, and often sinister; as, a surmise that a stranger may be a pickpocket. — from hypothesis
To conjecture is to put together the nearest available materials for a provisional opinion, always with some expectation of finding the facts to be as conjectured. — from suppose
To think, in this application, is to hold as the result of thought what is admitted not to be matter of exact or certain knowledge; as, I do not know, but I think this to be the fact: a more conclusive statement than would be made by the use of conjecture or suppose. — from suppose