
672 N.W.2d 829 (2003)
CITY OF MARQUETTE, Iowa, Appellee,
v.
Steven A. GAEDE and Ruth Gaede, Appellants.
No. 02-1008.
Supreme Court of Iowa.
December 17, 2003.
*831 Dale L. Putnam of Putnam Law Office, Decorah, for appellants.
James A. Garrett of Jacobson, Bristol, Garrett & Swartz, Waukon, for appellee.
CARTER, Justice.
Steven A. Gaede and Ruth Gaede, who claim ownership of a thirty-three-foot strip of land that the City of Marquette claims is a city street, appeal from a decree quieting title to the disputed strip in the city. The Gaedes urge that (1) the platted street that forms the basis for the city's claim never extended far enough east to coincide with the area in dispute, (2) the city's claim is barred by a forty-year chain of title in the Gaedes and their predecessors in interest, and (3) the city is estopped from claiming title to the disputed strip. We reject each of these contentions and affirm the district court's decree quieting title in the city.
We make the following findings of fact on our de novo review of the evidence at trial. The plat that forms the basis for the city's claim to the disputed strip was filed of record on August 12, 1858. The city (town) was incorporated on June 15, 1874, and the articles of incorporation filed with the secretary of state referenced the August 12, 1858 plat. As originally incorporated, the city was known as North McGregor. The name was changed to Marquette on March 29, 1920.
The city streets shown to be running east and west on the 1858 plat include North Street, Main Street, Milwaukee Street, and Madison Street. All of these streets are shown on that plat as extending to the west bank of the Mississippi River. These streets are shown on the plat to be sixty-six feet wide. The property the Gaedes are now claiming coincides with the south thirty-three feet of North Street (as shown on the 1858 plat) lying between the river and a railway right-of-way. The tract at issue extends west of the river approximately eighty feet on its north boundary and 131 feet on its south boundary.
On January 4, 1870, John and Catharine Lawler executed a deed conveying certain real estate to The Milwaukee and St. Paul Railway Company. The land described in that deed included the strip now in dispute in the present litigation. That deed was not recorded. Another deed from the Lawlers to the same railway company was executed on the same date and recorded on March 14, 1870. That deed conveyed "a narrow strip of land situated directly *832 east of Blocks numbers one (1), seven (7), and eight (8) and lots number one (1), two (2), three (3), and four (4) in Block number nineteen in the Town of North McGregor." The property thus described would intersect North Street directly east of the eastern most platted lots in the city. The distance between that point and the river would allow for a 100-foot railway right-of-way lying entirely west of the disputed property.
The property conveyed in the 1870 Lawler deed appears to have been disposed of in a subsequent federal court reorganization of an entity called the Chicago, Milwaukee, and St. Paul Railway Company. There is nothing in the chain of title to indicate whether this was the same entity as The Milwaukee and St. Paul Railway Company. The Chicago, Milwaukee, and St. Paul Railway Company conveyed property described only as "railway extending: From Green Island, State of Iowa, in a northwesterly direction along the west bank of the Mississippi River to River Junction, State of Minnesota and other real estate" to the Chicago, Milwaukee, St. Paul, and Pacific Railroad Company in 1927. In 1977 the Chicago, Milwaukee, St. Paul, and Pacific Railroad Company went through federal bankruptcy proceedings. All of its property was conveyed to a corporation known as SLRC, Inc. on February 19, 1985. Through a series of transactions, a portion of this property was conveyed to a corporation known as CMC Real Estate Company, a Wisconsin corporation. Nothing in the 1977 or 1985 conveyances indicates that the property at issue here was included among that being conveyed.
CMC conveyed the north thirty-three feet of a strip coinciding with the platted North Street and other property to Darwin and Violet Johnson on June 11, 1987. The Johnsons later sold their thirty-three-foot strip to Roger and Connie Halverson. The Halversons were originally included as parties in this quiet-title litigation but reached a settlement with the city, allowing them to acquire ownership of the north thirty-three feet of North Street east of the railway right-of-way subject to certain easements in favor of the city.
CMC conveyed the south thirty-three feet of North Street east of the railway plus additional land to Henry S. Wildermuth on December 20, 1988. This thirty-three-foot strip was approximately eighty feet long on the north and 131 feet long on the south. Wildermuth conveyed this same property to Leslie and Margery Stansberry on September 28, 1992. The Stansberrys conveyed that property to the Gaedes on August 5, 1998. The property that the Gaedes received is described, commencing at a point approximately fifty-two feet east of the railway centerline (the extent of the right-of-way) and then south from the centerline of North Street 137 feet parallel to the railway right-of-way, east 115 feet to the river, north 131 feet along the river, and then west eighty feet to the point of beginning. As so described, the property lies outside of the railway right-of-way.
North Street has always been a main downtown street in Marquette. No portion of it has ever been vacated. The portion of this public way between the railway and the river has never been surfaced. For many years, there was a boat ramp where North Street intersected the river. This ramp was at all times maintained by the City of Marquette. City personnel performed a considerable amount of maintenance in relation thereto. It was annually coated with asphalt, driftwood was removed, and snow was plowed by the city to permit access for boaters in the wintertime.
*833 Mary Jo Pirc, who at the time of the trial had lived on North Street for fifty-seven years, testified that she used the portion of the street east of the railroad as a route to the river for boating and fishing. She testified that she had used the boat ramp regularly between 1955 and 1993. Gerald Ploog, who was eighty-six years of age at the time of trial, testified that he had used the boat ramp as early as 1921 and that the strip of land, designated as North Street on the 1858 plat, was the route to the ramp. We credit the testimony of both Pirc and Ploog. In 1981 the existing bridge between Marquette and the State of Wisconsin was closed awaiting the building of a new bridge. As a result, a ferry service was maintained that used the North Street ramp for access to the river.
After receiving their deed from the Stansberrys, the Gaedes placed a considerable amount of fill dirt on the disputed parcel and constructed a retaining wall along the riverbank. This work was done pursuant to a permit issued to them by the Iowa Department of Natural Resources. The application for this permit required approval by the city, which was granted. After Leslie Stansberry, the Gaedes' predecessor in interest, obtained a deed to the disputed property in 1992, he interfered with the public use of the ramp. The Halversons and the Gaedes continued that practice. There was much public agitation concerning the Halversons' and Gaedes' use of what had been regarded as a public area. In the fall of 2000, the city formally declared its claim to ownership of the sixty-six-foot strip east of the railway right-of-way adverse to the Gaedes and the Halversons.
After hearing the evidence, the district court concluded that the city acquired title to the disputed tract as a city street by virtue of the 1858 plat. The court further concluded that an unbroken chain of title in the Gaedes and their predecessors in interest was not shown to have existed for forty years. In addition, the court concluded that because North Street as originally platted provided access to a navigable waterway it was public trust property. The court rejected the Gaedes' claim of estoppel on the basis that their unchallenged possession had not existed for more than ten years. Other facts that are important to our decision on appeal will be discussed in our consideration of the legal issues presented.

I. Scope of Review.

This quiet-title action was tried by equitable proceedings and, as a consequence, our review of the facts is de novo. Fencl v. City of Harpers Ferry, 620 N.W.2d 808, 811 (Iowa 2000); Rouse v. Union Township, 530 N.W.2d 714, 716 (Iowa 1995). We have the responsibility to examine the facts as well as the law and to decide anew the issues properly presented. Fencl, 620 N.W.2d at 811. We give weight to the fact-findings of the trial court, but are not bound by them. Id. We are also not bound by the trial court's conclusions of law. Id.; Rouse, 530 N.W.2d at 716.
II. Whether the Property at Issue is a City Street Established by the 1858 Plat.
A. Location of the platted street. The Gaedes argue that the city has not established that it owns the property at issue. They urge that North Street as platted did not extend to the west bank of the Mississippi River. That claim is dispelled by the plat itself, which clearly shows the location of North Street as extending to the riverbank.
We have recognized that the recording of a plat, followed by the subsequent incorporation of the platted area as a city, is the equivalent of a deed in fee simple to the *834 city of the land set apart in the plat for streets or other public uses. Fencl, 620 N.W.2d at 812; Kelroy v. City of Clear Lake, 232 Iowa 161, 164, 5 N.W.2d 12, 16 (1942); Inc. Town of Ackley v. Cent. States Elec. Co., 206 Iowa 533, 536, 220 N.W. 315, 316 (1928).
Because plats are prepared by private landowners, the dedication of streets is subject to the city's formal acceptance in order that the city may not be forced to accept a burden it does not wish to assume. Burlington, C.R. & N.R. Co. v. City of Columbus Junction, 104 Iowa 110, 112-13, 73 N.W. 501, 502 (1897). Because this requirement is for the city's protection, lack of a formal acceptance will not defeat a city's claim to a platted street that has been used as a public way. Id. Such use need only be that which the public wants and necessities demand. Henry Walker Park Ass'n v. Mathews, 249 Iowa 1246, 1253, 91 N.W.2d 703, 708 (1958). Moreover, the legislature has provided that a showing of formal acceptance of city streets is not necessary in the case of plats filed before 1897. Iowa Code § 592.2 (2001). In the present case, a dedication of all of the streets shown on the 1858 plat was acknowledged by Alexander MacGregor and Ann G. MacGregor, the owners of the land. At the time of the incorporation of the city, thirty-five electors attested to the acceptance of the designations shown on the 1858 plat as the city (town) of North McGregor.
The Gaedes contend the language in the 1858 plat describing the location of the northeast corner of the city demonstrates that North Street did not extend all the way to the river. The language to which they refer provides:
The North East corner of the plat commences one hundred eighty feet due West of the North East corner of the Bazil Giard Claim No. 1 Clayton County, Iowa.
The point so described lies west of the river more than 100 feet. The Gaedes would establish the east boundary of the city by extending this point due south. As a surveyor who testified for the city declared, the location of the northeast corner only establishes one point on the boundary of the city. No further description of the city's boundaries is contained in the plat. To establish the eastern boundary in the manner that the Gaedes suggest would eliminate not only a portion of North Street as shown on the plat but other portions of the city as well. We find that North Street did extend to the west bank of the river as shown on the plat and has, in its entirety, been a duly constituted city street ever since the incorporation of the town in 1874.
B. Abandonment. Although the Gaedes urge that there have been long periods of nonuser of North Street as a public way and that a tree has obstructed the unimpeded use of a portion thereof, these circumstances do not sustain their claim that the platted street has been abandoned by the city. There is a presumption that, once a highway or street is shown to exist, it continues to exist. Allamakee County v. Collins Trust, 599 N.W.2d 448, 451 (Iowa 1999). To establish abandonment, an intent to abandon must be proven by clear and satisfactory evidence. Id.; Sterlane v. Fleming, 236 Iowa 480, 483, 18 N.W.2d 159, 161 (1945). Actual acts of relinquishment accompanied by an intention to abandon must be shown. Collins Trust, 599 N.W.2d at 451; Town of Marne v. Goeken, 259 Iowa 1375, 1382, 147 N.W.2d 218, 224 (1966). Obstructions, encroachments, or the failure to keep a road in repair do not necessarily result in abandonment. Sterlane, 236 Iowa at 484, 18 N.W.2d at 162.
C. Absence of a deed for the railway line. At the time of the 1858 plat, *835 there was no railway line in existence. The railway line we have earlier described was built at a later time. That line crossed over the location of North Street as shown on the plat. The Gaedes argue that because there is no deed of record conveying a portion of North Street to a railway company it must be assumed that the railway already owned the disputed property as a result of the unrecorded Lawler deed. In response to this argument, we believe that we may only fairly assume from these facts that the entity that constructed the railway line acquired some type of ownership interest in a strip of land crossing over North Street. But, there is no reason to assume that this strip of land was any wider than 100 feet, which is the dimension of the railway right-of-way. The property in dispute lies east of the eastern boundary of the railway right-of-way. The Gaedes' argument concerning the lack of a deed to a railway company provides no basis for negating the city's ownership of North Street from the railway line east to the west bank of the river.
D. The effect of the Halverson settlement. The Gaedes argue that, because the plat provides that streets be sixty-six feet in width and the city's settlement with the Halversons has precluded its use of the north thirty-three feet of North Street as a street, it may not maintain the remaining thirty-three feet as a public way. They have cited no authority for this proposition and, consequently, have waived any argument concerning the city's right to use the remaining portion of the street. See Iowa R.App. P. 6.14(1)(c) (providing that failure to cite authority in support of proposition may be deemed to be waiver of the issue).
III. The Forty-Year Chain of Title Act (Iowa Code § 614.31).
The Gaedes argue that the facts reveal that they enjoy an unbroken chain of title of record for more than forty years. That circumstance, they urge, vests them with marketable title to the property in dispute by reason of the provisions of Iowa Code section 614.31. This provision is known as a marketable title act and is designed to shorten the period of search required to establish title to real estate and give stability to record titles. Fencl, 620 N.W.2d at 812.
It is the Gaedes' contention that they enjoy an uninterrupted chain of title for more than forty years extending from the unrecorded 1870 Lawler deed. The district court rejected that contention. So do we. An unrecorded deed does not provide a basis for establishing an uninterrupted record title. See Iowa Code § 614.29(5) (defining root of title as the interest that was the most recent transaction "to be recorded ... as of a date forty years prior to the time marketability is being determined") (emphasis added). Nor may the Gaedes rely on the recorded 1870 Lawler deed because, as we have previously stated, the description in that deed only refers to "a narrow strip of land situated directly east of [certain described lots]." As we have noted, the distance between the east edge of those lots and the river was sufficient to allow a 100-foot railway right-of-way entirely west of the disputed property.
The Gaedes also argue that the necessary forty-year record title may be found in later transactions. Unfortunately for their claim, the only possible transaction that might be a root of title more than forty years prior to the time when marketability was being determined is the 1927 deed from the Chicago, Milwaukee, and St. Paul Railway Company to the Chicago, Milwaukee, St. Paul, and Pacific Railroad Company. There is no basis to determine from the description in that deed that it included the property now in dispute. The district court properly rejected the Gaedes' claim of marketable title based on a *836 claimed forty-year chain of title. Consequently, it is unnecessary to discuss the district court's alternative conclusion that the property now in dispute is public trust property.

IV. Estoppel.

Finally, we consider the Gaedes' contention that the city is estopped from claiming title to the disputed strip. They point out that the city approved their filling in of the riverbank and the building of a retaining wall. They also point out that they and the Stansberrys before them paid property taxes on a tract of land that embraced the disputed strip.
A city may be estopped from asserting its rights in an unused public street under the doctrine of equitable estoppel. Fencl, 620 N.W.2d at 816. The elements that we have established to establish such an estoppel include (1) conduct of a city indicating an abandonment of interest (including actual nonuse for more than ten years), (2) facts constituting title by adverse possession (including a requirement of possession for more than ten years with the knowledge of the city), and (3) unfair damage to the claimant. Id. None of the matters upon which the Gaedes rely to establish their estoppel claim occurred over a period of ten years prior to the city's formal declaration of ownership in the fall of 2000. Accordingly, they have failed to meet the test for establishing an estoppel against a municipal corporation.
We have considered all issues presented and conclude that the district court's decree should be affirmed.
AFFIRMED.
All justices concur except WIGGINS, J., who takes no part.
