
436 So.2d 233 (1983)
WILLIAMS, SALOMON, KANNER, DAMIAN, WEISSLER & BROOKS, Appellant,
v.
HARBOUR CLUB VILLAS CONDOMINIUM ASSOCIATION, INC., and Quayside Associates, Ltd., Appellees.
No. 82-1253.
District Court of Appeal of Florida, Third District.
July 5, 1983.
Rehearing Denied September 6, 1983.
Podhurst, Orseck, Parks, Josefsberg, Eaton, Meadow & Olin and Joel S. Perwin, Miami, for appellant.
Haddad, Josephs & Jack and Gilbert A. Haddad, Coral Gables, Lapidus & Stettin and Richard L. Lapidus, Miami, for appellees.
Before HENDRY, NESBITT and DANIEL S. PEARSON, JJ.
NESBITT, Judge.
The appellant is a law firm that agreed to represent the appellee, Harbour Club Villas *234 Condominium Association, Inc. (Harbour Club), in a zoning dispute with the developer of a neighboring condominium, Quayside Associates, Ltd. (Quayside)[1]. Quayside had sought and procured from the Dade County Commission a zoning variance to erect a high-rise condominium near Harbour Club. Harbour Club retained the law firm at a fixed fee of $3,500 to pursue appeals in the Dade County Circuit Court and the Third District Court of Appeal. The circuit court appeal resulted in an affirmance of the county commission. After oral argument in this court, but before any decision was handed down, the parties settled. Under the terms of the settlement, Quayside, obviously anticipating a reversal, agreed to pay Harbour Club the sum of $3,000,000. The law firm subsequently sued Harbour Club for rescission of the representation agreement, for quantum meruit damages and for imposition of an attorneys' charging lien. The trial court entered summary final judgment in favor of Harbour Club and the law firm brought this appeal.
The gravamen of the law firm's claims was that the fee agreement should be rescinded because the parties did not envision a monetary settlement when the agreement was struck. On appeal, this attack upon the agreement translates into four basic alternative arguments: (1) there was no valid contract between the parties because their minds did not meet upon definite, essential terms; (2) a coexistent implied contract was created providing for additional compensation in the event of a settlement; (3) the fee agreement should be rescinded due to frustration of purpose; and (4) the fee agreement should be rescinded due to either unilateral or mutual mistake.
We reject the law firm's contention that there was no valid contract between the parties. The terms of the fee agreement were memorialized in two letters from the law firm to Harbour Club. Harbour Club was to pay the law firm $3,500 for the performance of specified and defined legal services, the prosecution of two appeals. The services were performed and the $3,500 was in fact paid to and accepted by the law firm. Consequently, while it may have been that at the outset the parties did not intend a monetary settlement to be the end result of their contractual relationship, their minds clearly met upon the terms of that relationship. "The making of a contract depends not on the agreement of two minds in one intention, but on the agreement of two sets of external signs  not on the parties having meant the same thing but on their having said the same thing." Gendzier v. Bielecki, 97 So.2d 604, 608 (Fla. 1957) (quoting Holmes, The Path of the Law, 10 Harv.L.Rev. 457, 464 (1897). A valid fee contract was formed between the law firm and Harbour Club.
With respect to the implied contract theory, it being undisputed that the law firm took no part in actual negotiation of the $3,000,000 settlement, the law firm is confined to arguing that were it not for its legal efforts exerted in the two appeals, Quayside and Harbour Club would not have been placed in their respective positions as offeror and offeree of a large monetary settlement. The general rule in this regard has been stated as follows: "Recovery for the value of services which have inured to another's benefit is not generally allowed unless they were received with reason to know that compensation was expected for them." 13 S. Williston, A Treatise on the Law of Contracts § 1575 (3d ed. 1970). Since Harbour Club received only the services it knew it was already paying $3,500 for, it could not be expected to have known any additional compensation was due. Compare Freedman v. Horton, Schwartz & Perse, 383 So.2d 659 (Fla. 3d DCA 1980) (where contingency fee contract between client and trial counsel contained no provision for payment of appellate fees, but *235 where client knew or should have known that an appellate law firm was representing her in appellate courts of state with respect to complicated estate proceedings and yet did not inform the law firm that she did not intend to pay for its services, she was liable to that firm for reasonable attorneys' fees). As a result, none is owed the law firm just because a significant benefit inured to its client.
The remaining contentions of the law firm center on the theories of frustration of purpose and mistake. The law firm alleged that a settlement for money was never discussed before the representation agreement was entered into and that the sole purpose of its handling the case, as conveyed by representatives of Harbour Club, was to stop the Quayside development from being built as planned. Even accepting this as true, which we must in this appellate posture, we cannot agree that the purpose of the agreement was frustrated. The purpose of the parties' agreement was to establish an arrangement for the provision of legal services at a fixed fee. The results to be obtained or in fact obtained had no bearing whatsoever on the agreement. If the case had proceeded to a decision in this court and if a reversal had been won by the law firm, it certainly would not have been able to claim a higher fee than the $3,500 it had agreed to. Just as surely, if the law firm had lost the appeal in this court, Harbour Club could not be heard to complain that the $3,500 should not be paid. Thus, although it was obviously the law firm's duty to use its best efforts to obtain a favorable outcome for Harbour Club in the Quayside litigation, it cannot be said that the purpose of the parties' agreement was frustrated because the actual outcome was one not originally anticipated.
That the result achieved was not an essential element of the parties' agreement cuts into the heart of the law firm's argument concerning mistake. A mistake, whether unilateral or mutual, must go to a material, substantial element of a contract in order to justify rescission. Moore v. Wesley E. Garrison, Inc., 148 Fla. 653, 5 So.2d 259, 262 (1941); Langley v. Irons Land & Development Co., 94 Fla. 1010, 114 So. 769, 772 (1927); Ferguson v. Cotler, 382 So.2d 1315, 1316 (Fla. 5th DCA 1980); 13 S. Williston, A Treatise on the Law of Contracts § 1544 (3d Ed. 1970). A mistake as to a mere inducement or incident to a contract does not provide such justification. Grymes v. Sanders, 93 U.S. 55, 23 L.Ed. 798 (1876); Langley v. Irons Land & Development Co., supra; Williston, supra, § 1544. The mistake asserted by the law firm falls into the latter category.
Moreover, cases from other jurisdictions demonstrate that the type of mistake warranting rescission does not include one which the party seeking rescission had in mind as a possibility and as to the existence of which he took the risk. Beecher v. Able, 575 F.2d 1010 (2d Cir.1978); Glendale Federal Savings and Loan Assn. v. Marina View Heights Development, Inc., 66 Cal. App.3d 101, 135 Cal. Rptr. 802 (1977); Harvey v. Robey, 211 Va. 234, 176 S.E.2d 673 (1970). Certainly every attorney knows that settlement is a distinct possibility in a zoning case and while we recognize that there was no express assumption of the risk of settlement here, an attorney accepting employment by lay persons is clearly the party in the best position to foresee this risk and to provide for it. Cf. Jones v. Hearn, 230 So.2d 50, 52 (Fla. 1st DCA 1970) ("Lawyers are charged with a high degree of care in establishing with their clients the amount of their fees.") No matter what impressions he receives from his client, an attorney cannot simply ignore the possibility of a monetary settlement and when such a settlement is reached, complain that the failure to provide for one entitles him to rescission of his fixed fee agreement. The law firm's expertise bars it as a matter of law from raising the mistake of an allegedly uncontemplated monetary settlement.
For the foregoing reasons, the final summary judgment in favor of Harbour Club is affirmed.
Affirmed.
NOTES
[1]  Quayside intervened in the suit below and is an appellee here due to the as yet undetermined factual issue of whether Quayside is liable for indemnification of Harbour Club for the claims of the appellant law firm, see Quayside Associates, Ltd. v. Harbour Club Villas Condominium Association, Inc., 419 So.2d 678 (Fla. 3d DCA 1982), an issue rendered moot by our disposition of this appeal.
