Exhibit 3.19

LIMITED LIABILITY COMPANY AGREEMENT

OF CYTYC SURGICAL PRODUCTS III, LLC

This Limited Liability Company Agreement, dated as of September 18th, 2012 (this “Agreement”), of Cytyc Surgical Products III, LLC, a Delaware limited liability company (“Company”), is entered into by Cytyc Corporation, a Delaware corporation, as the sole member of the Company (“Member”), and by the Manager (as defined herein).

RECITALS

WHEREAS, Cytyc Surgical Products III, Inc. (the “Corporation”), was formed as a Delaware corporation on July 17, 1997;

WHEREAS, by unanimous written consent, the board of directors of the Corporation adopted a resolution adopting and approving the conversion of the Corporation to a limited liability company and this Agreement, and recommending the approval of such conversion and this Agreement to the sole stockholder of the Company, pursuant to Section 266 of the General Corporation Law of the State of Delaware (8 Del. C. § 101, et seq.), as amended from time to time (the “DGCL”);

WHEREAS, by written consent, the sole stockholder of the Corporation approved the conversion of the Corporation to a limited liability company and this Agreement pursuant to Section 266 of the DGCL;

WHEREAS, on the date hereof, the Corporation was converted to a limited liability company (the “Conversion”) pursuant to Section 18-214 of the Delaware Limited Liability Company Act (6 Del. C. § 18-101, et seq.), as amended from time to time (the “Act”), and Section 266 of the DGCL, by the filing with the Secretary of State of the State of Delaware of the Certificate of Conversion to Limited Liability Company of the Corporation to the Company (the “Certificate of Conversion”) and the Certificate of Formation of the Company (the “Certificate of Formation”); and

WHEREAS, pursuant to this Agreement and the Conversion, (i) all of the shares of capital stock in the Corporation were converted to limited liability company interests in the Company, and (ii) Cytyc Corporation, as the sole stockholder of the Corporation, was admitted to the Company as the sole member of the Company and became the owner of all of the limited liability company interests in the Company.

NOW THEREFORE, by execution of this Agreement, the Member and the Manager hereby agrees as follows:

1. Name; Conversion.

(a) The name of the Company is Cytyc Surgical Products III, LLC. The business of the Company may be conducted under any other name deemed necessary or desirable by the Member.

(b) The execution, delivery and filing of the Certificate of Conversion and the Certificate of Formation with the Secretary of State of the State of Delaware, are hereby ratified, approved and confirmed. The Member and the Manager are each hereby designated as an “authorized person” of the Company within the meaning of the Act and shall continue as a designated “authorized person” of the Company within the meaning of the Act. The Member or the Manager, as an “authorized person” of the Company within the meaning of the Act, shall execute, deliver and file, or cause the execution, delivery and filing of, all certificates (and any amendments and/or restatements thereof) required or permitted by the Act to be filed with the Secretary of State of the State of Delaware. The Member or the Manager shall execute, deliver and file, or cause the execution, delivery and filing of any certificates (and any amendments and/or restatements thereof) necessary for the Company to qualify to do business in any jurisdiction in which the Company may wish to conduct business.

(c) Effective as of the time of the Conversion, (i) the Certificate of Incorporation of the Corporation and the Bylaws of the Corporation, each in effect on the date hereof, are replaced and superseded in their entirety by the Certificate of Formation and this Agreement in respect of all periods beginning on or after the Conversion, (ii) all of the shares of capital stock in the Corporation issued and outstanding immediately prior the Conversion are converted to all of the limited liability company interests in the Company, (iii) Cytyc Corporation, as the sole stockholder of the Corporation immediately prior to the Conversion, is hereby automatically admitted to the Company as the sole member of the Company (such admission effective simultaneously with the Conversion) and owns all of the limited liability company interests in the Company, (iv) all certificates, if any, evidencing shares of capital stock in the Corporation issued by the Corporation and outstanding immediately prior to the Conversion shall automatically be deemed cancelled and shall be surrendered to the Company, (v) the Corporation is being continued without dissolution in the form of a Delaware limited liability company governed by this Agreement, and (vi) in accordance with Section 18-214(g) of the Act, the Company shall constitute a continuation of the existence of the Corporation in the form of a Delaware limited liability company and, for all purposes of the laws of the State of Delaware, shall be deemed to be the same entity as the Corporation.

(d) The Member hereby agrees to conduct the operations of the Company in accordance with the Act, pursuant to this Agreement and the Certificate of Formation of the Company which was filed with the Secretary of State of the State of Delaware on September 27, 2012. Except as otherwise provided herein, the rights, duties and liabilities of the Member and the Manager (as defined below) shall be as provided in the Act for members and managers.

2. Purpose. The Company is formed for the object and purpose of, and the nature of the business to be conducted and promoted by the Company is, engaging in any lawful act or activity for which limited liability companies may be formed under the Act and engaging in any and all activities necessary or incidental to the foregoing.

3. Registered Offices Registered Agent. The address of the registered office of the Company in the State of Delaware is c/o Corporation Service Company, 2711 Centerville Road, Suite 400, Wilmington, New Castle County, Delaware 19808. The name and address of the registered agent of the Company for service of process on the Company in the State of Delaware is Corporation Service Company, 2711 Centerville Road, Suite 400, Wilmington, New Castle County, Delaware 19808.

4. Principal Office. The principal office address of the Company shall be such address as may be determined by the Manager from time to time.

5. Members. The name and the mailing address of the Member is as set forth in Annex A hereto. Effective simultaneous with the Conversion, the Member, upon execution of a counterpart to this Agreement, is admitted to the Company as a member of the Company and agrees to be bound by the terms of this Agreement.

6. Powers. The Company, and the Manager on behalf of the Company, (i) shall have and exercise all powers necessary, convenient or incidental to accomplish its purposes of the Company set forth in Section 2, and (ii) shall have and exercise all of the powers and rights conferred upon limited liability companies formed pursuant to the Act. Except as otherwise provided herein or as such power may be expressly delegated by the Manager, no Member who is not also a Manager, in that person’s capacity as Member, shall take any part in the control of the affairs of the Company, or undertake any transactions on behalf of the Company, or have any power to sign for or otherwise to bind the Company.

7. Management.

(a) The Member hereby appoints Cytyc Corporation as the initial manager of the Company (“Manager”), and the Manager hereby accepts such appointment and agrees to be bound by the provisions of this Agreement. The management, policies and control of the Company shall be vested exclusively in the Manager. All decisions to be made, or actions to be taken, by the Company may only be made by the Manager. Notwithstanding any provision of this Agreement, the Manager, without the consent of any other person or entity being required, is hereby authorized to execute any documents in the name of the Company required to effect any action that the Manager has authorized in accordance with this Section 7.

(b) The Member agrees that all determinations, decisions and, actions made or taken by the Manager in accordance with this Agreement shall be conclusive and absolutely binding upon the Company, the Member and their respective successors, assigns and personal representatives.

(c) Persons dealing with the Company are entitled to rely conclusively upon the power and authority of the Manager as herein set forth.

(d) The Manager shall hold office until a successor is selected and qualified or until such Manager’s earlier death, resignation or removal. Unless otherwise restricted by law, the Manager may be removed or expelled, with or without cause, at any time by the Member, and any vacancy caused by any such removal or expulsion may be filled by action of the Member. Each Manager shall execute a counterpart to this Agreement.

8. Capital Contributions. The Member has contributed to the Company such capital, if any, as is set forth in the books and records of the Company. The Member shall have no obligation to make any additional capital contributions to the Company.

9. Additional Contributions. The Member may make such additional capital contributions to the Company as the Manager in its discretion may deem necessary or advisable in connection with the business of the Company.

10. Distributions.

(a) The Member shall not be entitled to receive any amount of interest on its capital contributions to the Company nor have the right to any distribution or the return of any contribution to the capital of the Company except for distributions made in the discretion of the Manager in accordance with this Section 10 or upon dissolution of the Company. The entitlement to any such return at such time shall be limited to the value of the capital account of the Member. To the fullest extent permitted by the Act, a Member shall not be liable for the return of any such amounts. Notwithstanding any provision to the contrary contained in this Agreement, the Company shall not make a distribution to the Member if such distribution would violate the Act or other applicable law.

(b) Distributions shall be made to the Member at the times and in the aggregate amounts determined by the Manager.

11. Fiscal Year; Tax Matters.

(a) The Fiscal Year of the Company for accounting and tax purposes shall end on the last Saturday of September each year.

(b) Proper and complete records and books of account of the business of the Company shall be maintained at the Company’s principal place of business. The Member acknowledges and agrees that the Company is a domestic entity with a single owner and is to be disregarded as a separate entity for federal income tax purposes as provided in Treas. Reg. Section 1.7701-3. The Company’s books of account shall be maintained on a basis consistent with such treatment and on the same basis utilized in preparing the Member’s federal income tax return.

12. Admission of Additional Members. One (1) or more additional members may be admitted to the Company with the consent of the Manager and such additional member(s) execution of a counterpart to this Agreement. Upon the admission to the Company of any additional Members, the Manager shall cause this Agreement to be amended and restated to reflect the admission of such additional Member(s), the initial capital contribution, if any, of such additional member(s) and the intention of the Members to cause the Company to be classified as a partnership for federal income tax purposes.

13. Liability of Member. The Member shall not have any liability for the obligations or liabilities of the Company except to the extent provided in the Act.

14. Dissolution.

(a) Subject to the occurrence of an event of dissolution pursuant to section 14(b), the Company shall have perpetual existence.

(b) The Company shall dissolve, and its affairs shall be wound up upon the first to occur of the following; (i) a determination by the Manager to dissolve the Company, (ii) the entry of a decree of judicial dissolution of the Company under Section 18-802 of the Act, or (iii) at any time there are no members of the Company unless the Company is continued without dissolution in accordance with the Act

(c) The bankruptcy (as defined at Sections 18-101(1) and 18-304 of the Act) of the Member shall not cause the Member to cease to be a member of the Company and upon the occurrence of such an event, the Company shall continue without dissolution.

(d) In the event of dissolution, the Company shall conduct only such activities as are necessary to wind up its affairs (including the sale of the assets of the Company in an orderly manner), and the assets of the Company shall be applied in the manner, and in the order of priority, set forth in Section 18-804 of the Act.

(e) The Company shall terminate when (i) all of the assets of the Company, after payment of or due provision for all debts, liabilities and obligations of the Company shall have been distributed to the Member in the manner provided for in this Agreement and (ii) the Certificate of Formation of the Company shall have been canceled in the manner required by the Act.

15. Indemnification. To the fullest extent permitted by law, the Company shall (a) indemnify any person or such person’s heirs, distributees, next of kin, successors, appointees, executors, administrators, legal representatives or assigns who was or is a party or is threatened to be made a party to any threatened, pending or completed action, suit or proceeding, whether civil, criminal, administrative or investigative by reason of the fact that such person is or was a member, manager, director, officer, employee or agent of the Company or is or was serving at the request of the Company or its Members or Manager as a member, manager, director, officer, employee or agent of another corporation, limited liability company, partnership, joint venture, trust or other enterprise, domestic or foreign, against expenses, attorneys’ fees, court costs, judgments, fines, amounts paid in settlement and other losses actually and reasonably incurred by such person in connection with such action; suit or proceeding and (b) advance expenses incurred by a member, manager, officer, director employee or agent in defending such civil or criminal action, suit or proceeding to the full extent authorized or permitted by the laws of the State of Delaware. To the fullest extent permitted by law, the Manager shall have no personal liability to the Company or its members for monetary damages for breach of fiduciary duty as a manager; provided, however, that the foregoing provision shall not eliminate the liability of the Manager for acts or omissions not in good faith or which involve intentional misconduct or a knowing violation of law or for any transaction from which the manager derived an improper personal benefit.

16. Membership Interests and Securities. All Membership Interests and other limited liability company interests in the Company in the nature of an equity interest shall constitute securities governed under Article 8 of the Uniform Commercial Code as adopted in the State of Delaware.

17. Amendments. Any amendments to this Agreement may be made in the sole and absolute discretion of the Manager and shall be in writing signed by the Manager.

18. Governing Law. This Agreement shall be governed by, and construed under, the laws of the State of Delaware, all rights and remedies being governed by said laws. The parties hereto intend the provisions of the Act to be controlling as to any matters not set forth in this Agreement.

19. Counterparts. This Agreement may be executed in any number of counterparts with the same effect as if all parties hereto had signed the same document. All counterparts shall be construed together and shall constitute one instrument.

20. Severability of Provisions. Each provision of this Agreement shall be considered severable, and if for any reason any provision or provisions herein are determined to be invalid, unenforceable or illegal under any existing or future law, such invalidity, unenforceability or illegality shall not impair the operation of or affect those portions of this Agreement that are valid, enforceable and legal.

21. Entire Agreement. This Agreement constitutes the entire agreement of the parties hereto with respect to the subject matter hereof.

IN WITNESS WHEREOF, the undersigned intending to be legally bound hereby, have duly executed this Limited Liability Company Agreement as of the day first above written.

CYTYC CORPORATION MANAGER |  |  |  | CYTYC CORPORATION MEMBER
By: |  | /s/ Glenn P. Muir |  |  |  | By: |  | /s/ Glenn P. Muir
|  | Name: Glenn P. Muir Title: Executive Vice President, Treasurer and Assistant Secretary |  |  |  |  |  | Name: Glenn P. Muir Title: Executive Vice President, Treasurer and Assistant Secretary

Annex A

Name and Address of Member |  | Percentage Interest (%)
Cytyc Corporation 250 Campus Drive Marlborough, MA 01752 |  | 100%