The Collaborative International Dictionary of English v.0.48:

Assumpsit \As*sump"sit\ (?; 215), n. [L., he undertook, pret. of
   L. assumere. See Assume.] (Law)
   (a) A promise or undertaking, founded on a consideration.
       This promise may be oral or in writing not under seal. It
       may be express or implied.
   (b) An action to recover damages for a breach or
       nonperformance of a contract or promise, express or
       implied, oral or in writing not under seal. Common or
       indebitatus assumpsit is brought for the most part on an
       implied promise. Special assumpsit is founded on an
       express promise or undertaking. --Wharton.
       [1913 Webster]

Bouvier's Law Dictionary, Revised 6th Ed (1856):

ASSUMPSIT, contracts. An undertaking either express or implied, to perform a
parol agreement. 1 Lilly's Reg. 132.
     2. An express assumpsit is where one undertakes verbally or in writing,
not under seal, or by matter of record, to perform an act, or to pa a sum of
money to another.
     3. An implied assumpsit is where one has not made any formal promise to
do an act or to pay a sum of money to another, but who is presumed from his
conduct to have assumed to do what is in point of law just and right; for,
1st, it is to be presumed that no one desires to enrich himself at the
expense of another; 2d, it is a rule that he who desires the antecedent,
must abide by the consequent; as, if I receive a loaf of bread or a
newspaper daily sent to my house without orders, and I use it without
objection, I am presumed to have accepted the terms upon which the person
sending it had in contemplation, that I should pay a fair price for it; 3d,
it is also a rule that every one is presumed to assent to what is useful to
him. See Assent



Bouvier's Law Dictionary, Revised 6th Ed (1856):

ASSUMPSIT, remedies, practice., A form of action which may be defined to be
an action for the recovery of damages for the non-performance of, a parol or
simple contract; or, in other words, a contract not under seal, nor of
record; circumstances which distinguish this remedy from others. 7 T. R.
351; 3 Johns. Cas. 60. This action differs from the action of debt; for, in
legal consideration, that is for the recovery of a debt eo nomine, and in
numero, and may be upon a deed as well as upon any other contract. 1 h. Bl.
554; B. N. P. 167. If differs from covenant, which, though brought for the
recovery of damages, can only be supported upon a contract under seal. See
Covenant.
     2. It will be proper to consider this subject with reference, 1, to the
contract upon which this action may be sustained; 2, the declaration 3, the
plea; 4, the judgment.
     3.-1. Assumpsit lies to recover damages for the breach of all parol
or simple contracts, whether written or not written express or implied; for
the payment of money, or for the performance or omission of any other act.
For example, to recover, money lent, paid, or had and received, to the use
of the plaintiff; and in some cases, where money has been received by the
defendant, in consequence of some tortious act to the plaintiff's property,
the plaintiff may waive the tort, and sue the defendant in assumpsit. 5
Pick. 285; 1 J. J. Marsh. 543 3 Watts, R. 277; 4 Binn. 374; 3 Dana, R. 552;
1 N. H. Rep. 151; 12 Pick. 120 4 Call. R. 461; 4 Pick. 452. It is the proper
remedy for work and. labor done, and services rendered 1 Gill, 95; 8 S. & M.
397 2 Gilman, 1 3 Yeates, 250 9 Ala. 788 but such work, labor, or services,
must be rendered at the request, express or implied, of the defendant; 2
Rep. Cons. Ct. 848; 1 M'Cord, 22; 20 John. 28 11 Mass. 37; 14 Mass. 176; 5
Monr. 513 1 Murph. 181; for goods sold and delivered; 6 J. J. Marsh. 441; 12
Pick. 120; 3 N. H. Rep. 384; 1 Mis. 430; for a breach of promise of
marriage. 3 Mass. 73 2 Overton, 233 2 P. S. R. 80. Assumpsit lies to recover
the purchase money for land sold; 14 Johns. R. 210; 14 Johns. R. 162; 20
Johns. R. 838 3 M'Cord, R. 421; and it lies, specially, upon wagers; 2 Chit.
Pl. 114; feigned issues; 2 Chit. Pl. 116; upon foreign judgments; 8 Mass.
273; Dougl. 1; 3 East, 221; 11 East, 124; 3 T. R. 493; 5 Johns. R. 132. But
it will not lie on a judgment obtained in a sister state. 1 Bibb, 361 19
Johns. 162; 3 Fairf. 94; 2 Rawle, 431. Assumpsit is the proper remedy upon
an account stated. Bac. Ab. Assumpsit, A. It will lie for a corporation, 2
Lev. 252; 1 Camp. 466. In England it does not lie against a corporation,
unless by express authority of some legislative act; 1 Chit. Pl. 98; but in
this country it lies against a corporation aggregate, on an express or
implied promise, in the same manner as against an individual. 7 Cranch, 297
9 Pet. 541; 3 S. & R. 117 4 S. & R. 16 12 Johns. 231; 14 Johns. 118; 2 Bay,
109 1 Chipm. 371, 456; 1 Aik. 180 10 Mass, 397. But see 3 Marsh. 1; 3 Dall.
496.
     4.-2. The declaration must invariably disclose the consideration of
the contract, the contract itself, and the breach of it; Bac. Ab. h.t. F 5
Mass. 98; but in a declaration on a negotiable instrument under the statute
of Anne, it is not requisite to, allege any consideration; 2 Leigh, R. 198;
and on a note expressed to have been given for value received, it is not
necessary to aver a special consideration. 7 Johns. 321. See Mass. 97. The
gist of this action is the promise, and it must be averred. 2 Wash. 187 2 N.
H. Rep. 289 Hardin, 225. Damages should be laid in a sufficient amount to
cover the real amount of the claim. See 4 Pick. 497; 2 Rep. Const. Ct. 339;
4 Munf. 95; 5 Munf. 23; 2 N. H. Rep. 289; 1 Breese, 286; 1 Hall, 201; 4
Johns. 280; 11 S. & R. 27; 5 S. & R. 519 6 Conn. 176; 9 Conn. 508; 1 N. & M.
342; 6 Cowen, 151; 2 Bibb, 429; 3 Caines, 286.
     5.-3. The usual plea is non-assumpsit, (q.v.) under which the
defendant may give in evidence most matters of defence. Com. Dig. Pleader, 2
G 1. When there are several defendants they cannot plead the general issue
severally; 6 Mass. 444; nor the same plea in bar, severally. 13 Mass. 152.
The plea of not guilty, in an action of assumpsit, is cured by verdict. 8 S.
& R. 541; 4 Call. 451. See 1 Marsh, 602; 17 Mass. 623. 2 Greenl. 362; Minor,
254 Bouv. Inst. Index, h.t.
     6.-4. Judgment. Vide Judgment in Assumpsit. Vide Bac. Ab. h.t.; Com.
Dig. Action upon the Case upon Assumpsit; Dane's Ab. Index, h.t.; Viner's
Ab. h.t.; 1 Chit. Pi. h.t.; Petersd. h.t.; Lawes Pl. in Assumpsit the
various Digests, h.t. Actions; Covenant; Debt; Indebitatus assumpsit; Padum
Constitutiae pecuniae.