بُدَاهَةٌ

(S, K) and ↓ بَدَاهَةٌ (Sgh, K) and ↓ بَدِيهَةٌ (JK, S, K) and ↓ بَدْهٌ and ↓ بُدْهٌ (K) substs. from بَدَهَهُ بِأَمْرٍ, (JK, S,) meaning The first of anything; and an occurrence thereof by which one is taken unawares: (K:) or the first occurrence of a thing, that happens to one unexpectedly. (M, in explanation of the first word, in article بدأ.)

Also the first (S, TA) and ↓ second (JK) and ↓ third (TA) The first part of the running of a horse; (JK, S, TA;) opposed to عُلَالَةٌ, signifying [the “remaining part of the running,” or “an afterrunning,” or] “a running after a running.” (TA.) You say, وَعُلَالَةٍ ↓ هُوَ ذُو بَدِيهَةٍ, and بُدَاهَةٍ, [He has a first running and an after-running, differing, the one from the other]. (Az, TA.) And لَحِقَهُ فِى بُدَاهَةِ جَرْيِهِ [He overtook him in the first part of his running]. (Z, TA.) ISd thinks that in all these cases the ه is a substitute for ء. (TA.) [Hence,] ↓ غَمْرُ البَدِيْهَةِ [properly Fleet in the first part of his running; meaning] (tropical:) a man who takes by surprise with large bounty. (TA, in article غمر.)

See also the next paragraph. in three places.