Etymology
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conjecture (n.)

late 14c., "interpretation of signs, dreams, and omens," also "a supposing, a surmising," from Old French conjecture "surmise, guess," or directly from Latin coniectura "conclusion, interpretation, guess, inference," literally "a casting together (of facts, etc.)," from coniectus, past participle of conicere "to throw together," from assimilated form of com "together" (see con-) + iacere "to throw" (from PIE root *ye- "to throw, impel").

Sense of "an unverified supposition" is from 1520s; that of "act of forming of opinion without proof" is from 1530s.

conjecture (v.)

early 15c., "infer, predict, form (an opinion or notion) upon probabilities or slight evidence," from conjecture (n.) or from verbs in Medieval Latin and Old French. Middle English had also the parallel forms conjecte (n.), conjecten (v.). Related: Conjectured; conjecturing.

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Definitions of conjecture
1
conjecture (n.)
a hypothesis that has been formed by speculating or conjecturing (usually with little hard evidence);
he dismissed it as mere conjecture
Synonyms: speculation
conjecture (n.)
a message expressing an opinion based on incomplete evidence;
Synonyms: guess / supposition / surmise / surmisal / speculation / hypothesis
conjecture (n.)
reasoning that involves the formation of conclusions from incomplete evidence;
2
conjecture (v.)
to believe especially on uncertain or tentative grounds;
From wordnet.princeton.edu