Jacob Brouwer, the son of Adam Brouwer and Magdalena Verdon, has been estimated to have been born in 1655, probably at Gowanus, Long Island. The estimated date is based upon the fact that he does not appear on the 1675 assessment roll at Brooklyn, but does appear on the 1676 list (with 1 poll). Totten in "Anneke Jans and Her Two Husbands," makes this observation, and makes the assumption that the age of 21 was the cutoff for being taxed. If this estimated birth year of 1655 is accurate, it would make Jacob the fourth son and fifth child of his parents. Jacob was certainly named for his maternal grandfather, Jacob Verdon. Traditionally, the second son was named for the maternal grandfather, and if Adam and Magdalena did follow this tradition then we would expect to find Jacob born sometime in the thirty month period between the baptism of eldest son, Pieter Brouwer (September 1646) and the next recorded son, Matthys Brouwer (May 1649). Perhaps Jacob was born in early 1648. Unfortunately, there is no surviving record that would answer this with certainty.

Jacob Brouwer's wife was Annetje Bogardus, baptized on October 3, 1663 at the New York Reformed Dutch Church, a daughter of Willem Bogardus and Wynnetje Sybrants. Her paternal grandparents were Domine Everardus Bogardus and Anneke Jans. Jacob and Annetje's marriage occurred at Brooklyn on January 29, 1682 and was recorded in both the New York and Flatbush Reformed Dutch Church records.

Citation
"New Jersey, Marriages, 1670-1980," database with images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/FZK4-N6X : 16 October 2017)

Name Jacob Brower
Event Type Marriage
Event Date 29 Jan 1682
Event Place , Salem, New Jersey, United States
Gender Male
Marital Status Married
Spouse's Name Anna Bogardus
Spouse's Gender Female∼Son of Adam Brouwer and Magdalena Jacobs Verdon.
T.G. Bergen, "Contributions to the History of the Early Settlers of Kings County, N.Y.", New York Genealogical & Biographical Record vols. 9-11 (1878-1880).
John Reynolds Totten, "Anneke Jans (1607-8?-1663) and Her Two Husbands", New York Genealogical & Biographical Record Vol. 56, pages 202-243 (1925): p.231-237..
William J. Hoffman, "Brouwer Beginnings; The First Three Generations of the Adam Brouwer Berchoven Family", The American Genealogist 23:193-206; 24:23-32, 96-102, 161-170 (1947, 1948): 24:23. #6 in the genealogy.

Jacob Brouwer was born circa 1655 at Gowanus, Long Island, the date being that what is generally accepted, however, he may have been born a bit earlier. As Jacob, he was named for his maternal grandfather, which would traditionally imply that he was second son born to his parents. If this were the case, Jacob may have been born in 1647 or 1648.

Married Annetje Bogardus, daughter of Willem Bogardus and Wynnetje Sybrants, at Brooklyn, Kings Co., Long Island, New York, on 29 January 1682 (banns 7 Jan 1682, Flatbush; 8 Jan 1682, New York).
Samuel S. Purple, Records of the Reformed Dutch Church in New Amsterdam and New York; Marriages from 11 December 1639 to 26 August 1801 (Bowie, MD: Heritage Books, reprint 2003, original 1890 NYG&BS), p.50. Jacobus Brouwer, j.m. Van de Gauwanes, en Annetje Bogardus, j.d. Van N. Yorck, beyde woonende aende Gauwanes. (The marriage is recorded at both the Flatbush and New York Dutch Churches).
David William Voorhees, editor, Records of The Reformed Protestant Dutch Church of Flatbush, Kings County, New York, Vol.1, 1677-1720 (New York: Holland Society of New York, 1998), page 233. Jacobus Brouwer, young man from Gowanus, and residing there, with Annetje Boogardus, young lady from N. York, also residing at Gowanus; and married the 29th Jan 1682 at Brooklyn

Gerrit Kroesen was taxed in Brooklyn in 1675 and 1676 for land between the home lots of Jacob Brouwer and Volkert Hendircksen Bries.
Lila James Roney, "The Kroesen-Croesen Family of Staten Island and Bucks County, Pennsylvania", New York Genealogical and Biographical Record Vol.75 (1944): 75:97.

He appeared on the assessment list of at Breukelen, Long Island, in September 1676 assessed at 18, with 1 poll.
Edmund Bailey O'Callaghan, Lists of Inhabitants of Colonial New York, Excerpted from The Documentary History of the State of New York (Baltimore, MD: Genealogical Pub. Co., 1979, 1989, 1999), p.100. Adam Brouwer, Willem Brouwer and Jabecq Brouwer all listed in succession.

He appeared on the assessment list of at Brooklyn, Kings Co., New York, on 26 September 1683 as Jacob Brouwer with 2 cows, 1 cow of 2 yrs., and 6 morgens of land and valley. Assessed at £42.10.
Ibid., p.119.

He took the Oath of Allegiance in September 1687 at Brooklyn, Kings Co., New York, as "Jacob brouwer, native."
Ibid., p.37.

Jacob is named in his father's will dated 22 Jan 1691/92, for his disobedience he is to receive "not a penny" and his share is devised to his children.
Will dated 22 January 1691/92 proved 21 March 1692 (on file at the office of the Clerk of the Court of Appeals in Albany). He calls himself "Adam Brouwer Berkhoven inhabitant of ye town of Bruckland, being at present sick a body but fully having his knowledge." His witnesses are named as Henry Sleght, Cornelius Sebring and John Fredricks. Adam leaves his "whole estate moveable and immoveable my wife Magdalena Brewer and my utmost will and desire is that none of my children shall trouble or move their mother during her life." Adam Brower "makes to his eldest sonn Peter Brewer three shillings for reasons that he was disobedient to his father, as also Jacob Brewer and Aeltie Brewer, who for reasons of their disobedience shall not receive a penny from their father Adam Brower, but ye testator bequeath ye land from ye three disobedient children Peter Brewer ye eldest, Jacob Brewer and Aeltie Brewer upon their children ye portion of Peter upon his children, ye portion of Jacob upon his children, ye portion of Aeltie upon her children." Adam names his children as Mathys, William, Adam, Abraham, Nicholas, daughter Mary, Fytie, Helena, Anna, Sara, Rachel, "these eleven children shall have equal portions amongst them, also ye children of ye disobedient children above named they shall also with ye other eleven children equally divided." Adam makes special bequests to Adolphus son of William Brewer "three pieces of eight"; to "Mathys his daughter Magdalena one piece of eight, and Mary her daughter Magdalena one piece of eight. Peter Brewer his daughter Magdalena one piece of eight and his daughter Vroutie one piece of eight, with Fytie daughter Magdalena one piece of eight."
Adam Brouwer will (22 Jan 1691/92), Albany Wills, 1629-1802 Vol. AB, page 3: FHL film #0824735, Albany Court of Appeals, Albany, New York.

Jacob Brouwer's lands at Gowanus are mentioned in a "Division of Common lands & woods into three parts, at a towne meeting held Febr. 25th, 1692/3 att Brooklyn, in manner following, I - All the lands and woods after Bedford & Cripplebush over the hills to the path of New Lotts shall be long to the inhabitants & free holders of Gowanus beginning from Jacob Brower and soe to the uttermost bounds of the limits of New Utrecht."
David McQueen, "Kings County, New York, Deeds", New York Genealogical and Biographical Record vol.48, pp. 110-118, 291-298, 355-361 (1917): 48:356.

He appeared on the census in 1698 at Brooklyn, Kings Co., New York, as Jacob Brouwer, with a family of 1 man, 1 woman, and 6 children. Recorded between Mighiel hanse Bergen and Adam Brouwer.
Edmund Bailey O'Callaghan, Lists of Inhabitants of Colonial New York, Excerpted from The Documentary History of the State of New York (Baltimore, MD: Genealogical Pub. Co., 1979, 1989, 1999), p.176.

On 17 Oct 1704, "William Brower Junr. son of Jacob Brower of Brookland, doth voluntarily and of his own free will and accord by and with the consent of his parents put himself apprentice to Stephen Bedent of Broockland, feltmaker, to serve him from the 17th day of October 1704 till the full term of four years." Jacob Brower, William Brower and Stephen Bedent all sign by their marks.
Kings County, New York, Deeds v.1-4; FHL #1413189 (New York, New York, Salt Lake City, Utah: Recordak Corp.; Genealogical Society of Utah, 1957), Microfilm of original records at the New York Registers Office in New York City., 3:64.

Children by Annetje Bogardus b. 3 Oct 1663:
Sybrandt Brouwer b. 29 Aug 1683, d. 3 Dec 1727
Jacob Brouwer b. 30 Nov 1684
Willem Brouwer b. 8 May 1687
Everardus Brouwer b. 8 Dec 1689, d. 26 Jan 1762
Anna Brouwer b. 15 Nov 1694
Adam Brewer b. 29 Mar 1696, d. beweent 22 Aug 1768 and 10 Mar 1769
Pieter Brouwer b. 29 Mar 1699, d. 10 Aug 1780
Wyntje Brouwer b. 1 Oct 1701, d. Nov 1773
Magdalena Brouwer b. 8 Mar 1704
A. P. G. Jos van der Linde, Old First Dutch Reformed Church of Brooklyn, New York: First Book of Records, 1660-1752, New York Historical Manuscripts: Dutch (Baltimore: Genealogical Publishing Co., Inc., 1983), page 124. Jakop; parents: Jakop Brouwer, Annitje Bogardus.
Ibid., page 126. Willem; parents: Jakop Brouwer, Annitje Bogardus.
Ibid., page 129. Everardes; parents: Jakop Brouwer, Annitje Bogardes.
Ibid., page 161. Anna Elisabet; parents: Jacob Brouwer, Annatje Bogardus.
Ibid., page 136. Adam; parents: Jakop Brouwer, Annitje Brouwer.
"Records of the Reformed Dutch Church in New York", New York Genealogical and Biographical Record Vols.5- (1874-): 14:178. Wyntje; parents: Jacob Brouwer, Anna Bogardus.
Ibid., 15:114. Magdalena; parents: Jacob Brouwer, Annetie Bogardus.

Jacob Brouwer died before 20 December 1706; when his wife, "Annitie Brower," appears on the Brooklyn town assessment list with 26 acres.
Kings County, New York, Deeds v.1-4; FHL #1413189 (New York, New York, Salt Lake City, Utah: Recordak Corp.; Genealogical Society of Utah, 1957), Microfilm of original records at the New York Registers Office in New York City., 3:91. A list of the assessment of Broocklands inmprovable lands and meadows within fence.

Bio includes data from The Brouwer Genealogy Database.
http://freepages.genealogy.rootsweb.ancestry.com/~brouwergenealogydata/surname_index.htm