[dih-doos, -dyoos]
verb (used with object), deduced, deducing.
to derive as a conclusion from something known or assumed; infer: From the evidence the detective deduced that the gardener had done it.
to trace the derivation of; trace the course of: to deduce one's lineage.

1520–30; < Latin dēdūcere to lead down, derive, equivalent to dē- de- + dūcere to lead, bring

deducible, adjective
deducibility, deducibleness, noun
deducibly, adverb
nondeducible, adjective
subdeducible, adjective
undeduced, adjective
undeducible, adjective

1. adduce, deduce, induce ; 2. deduce, deduct ; 3. deducible, deductible.

1. conclude, reason, gather, determine. Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
deduce (dɪˈdjuːs)
1.  (may take a clause as object) to reach (a conclusion about something) by reasoning; conclude (that); infer
2.  archaic to trace the origin, course, or derivation of
[C15: from Latin dēdūcere to lead away, derive, from de- + dūcere to lead]

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Word Origin & History

early 15c., from L. deducere "lead down, derive" (in M.L. "infer logically"), from de- "down" + ducere "to lead" (see duke). Originally literal, sense of "draw a conclusion from something already known" is first recorded 1520s, from M.L.
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
But listening to it is like trying to deduce all of Bach from a single sonata.
His voice adds a level of immanency that a reader might not deduce from reading
  it alone.
But they were not able to deduce what exactly they had produced.
While short in geologic terms, that's enough to deduce climate trends.
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