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Business Acquisitions and Assets and Liabilities Held for Sale - Narrative (Details) $ / shares in Units, $ in Millions |  |  |  | 12 Months Ended |  |  |  |  |  |  |  |  |
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Jun. 04, 2018 USD ($) | May 15, 2017 USD ($) | Dec. 27, 2016 USD ($) | Dec. 31, 2018 USD ($) acquisition | Dec. 31, 2017 USD ($) acquisition | Dec. 31, 2016 USD ($) business | Jul. 10, 2018 | Jun. 30, 2018 USD ($) | Jun. 07, 2018 | Nov. 17, 2017 $ / shares | Sep. 15, 2017 | Aug. 04, 2017 | Oct. 31, 2016 | Apr. 01, 2016 | Jan. 07, 2016
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Goodwill |  |  |  | $ 9,346.8 | $ 8,820.3 | $ 8,647.1 |  |  |  |  |  |  |  |  |
Deferred tax liability, excess of book basis over tax basis |  |  |  | 10.0 | 0.0 |  |  |  |  |  |  |  |  |  |
Deferred tax asset, excess of tax basis over book basis |  |  |  | 2.7 | $ 0.0 |  |  |  |  |  |  |  |  |  |
Gatan | Disposal group, held-for-sale, not discontinued operations |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Deferred tax liability, excess of book basis over tax basis |  |  |  |  |  |  |  | $ 10.0 |  |  |  |  |  |  |
Gatan | Thermo Fisher | Disposal group, held-for-sale, not discontinued operations |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Percentage of interests to be sold |  |  |  |  |  |  |  | 100.00% |  |  |  |  |  |  |
Consideration receivable or received on disposal |  |  |  |  |  |  |  | $ 925.0 |  |  |  |  |  |  |
Vision businesses | Disposal group, held-for-sale, not discontinued operations |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Deferred tax asset, excess of tax basis over book basis |  |  |  | 1.8 |  |  |  |  |  |  |  |  |  |  |
Vision businesses | Teledyne | Disposal group, held-for-sale, not discontinued operations |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Consideration receivable or received on disposal |  |  |  | $ 225.0 |  |  |  |  |  |  |  |  |  |  |
Energy Systems & Controls | Disposal group, disposed of by sale, not discontinued operations |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Consideration receivable or received on disposal |  | $ 10.4 |  |  |  |  |  |  |  |  |  |  |  |  |
Gain on sale |  | $ 9.4 |  |  |  |  |  |  |  |  |  |  |  |  |
2018 Acquisitions |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Number of businesses acquired | acquisition |  |  |  | 7 |  |  |  |  |  |  |  |  |  |  |
Consideration transferred |  |  |  | $ 1,279.0 |  |  |  |  |  |  |  |  |  |  |
Goodwill |  |  |  | 717.5 |  |  |  |  |  |  |  |  |  |  |
Identifiable intangibles |  |  |  | 711.3 |  |  |  |  |  |  |  |  |  |  |
2018 Acquisitions | Customer related intangibles |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Finite-lived intangibles |  |  |  | $ 635.1 |  |  |  |  |  |  |  |  |  |  |
Weighted average useful life of finite-lived intangible assets |  |  |  | 19 years |  |  |  |  |  |  |  |  |  |  |
2018 Acquisitions | Unpatented technology |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Finite-lived intangibles |  |  |  | $ 48.6 |  |  |  |  |  |  |  |  |  |  |
Weighted average useful life of finite-lived intangible assets |  |  |  | 7 years |  |  |  |  |  |  |  |  |  |  |
Quote Software, PlainSwift Software, and Smartbid |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Number of businesses acquired | acquisition |  |  |  | 3 |  |  |  |  |  |  |  |  |  |  |
PowerPlan, Inc. |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Consideration transferred | $ 1,111.4 |  |  |  |  |  |  |  |  |  |  |  |  |  |
Percentage of voting interests acquired | 100.00% |  |  |  |  |  |  |  |  |  |  |  |  |  |
ConceptShare, Inc. |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Percentage of voting interests acquired |  |  |  |  |  |  |  |  | 100.00% |  |  |  |  |  |
BillBlast |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Percentage of voting interests acquired |  |  |  |  |  |  | 100.00% |  |  |  |  |  |  |  |
Avitru |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Percentage of voting interests acquired |  |  |  | 100.00% |  |  |  |  |  |  |  |  |  |  |
2017 Acquisitions |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Number of businesses acquired | acquisition |  |  |  |  | 4 |  |  |  |  |  |  |  |  |  |
Consideration transferred |  |  |  |  | $ 152.0 |  |  |  |  |  |  |  |  |  |
Goodwill |  |  |  |  | 82.7 |  |  |  |  |  |  |  |  |  |
Identifiable intangibles |  |  |  |  | 85.0 |  |  |  |  |  |  |  |  |  |
2017 Acquisitions | Customer related intangibles |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Finite-lived intangibles |  |  |  |  | $ 68.0 |  |  |  |  |  |  |  |  |  |
Weighted average useful life of finite-lived intangible assets |  |  |  |  | 15 years |  |  |  |  |  |  |  |  |  |
2017 Acquisitions | Unpatented technology |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Finite-lived intangibles |  |  |  |  | $ 13.0 |  |  |  |  |  |  |  |  |  |
Weighted average useful life of finite-lived intangible assets |  |  |  |  | 6 years |  |  |  |  |  |  |  |  |  |
Handshake Software, Inc. |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Percentage of voting interests acquired |  |  |  |  |  |  |  |  |  |  |  | 100.00% |  |  |
Workbook Software A/S |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Percentage of voting interests acquired |  |  |  |  |  |  |  |  |  |  | 100.00% |  |  |  |
Onvia |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Percentage of voting interests acquired |  |  |  |  |  |  |  |  |  | 100.00% |  |  |  |  |
Share price (in dollars per share) | $ / shares |  |  |  |  |  |  |  |  |  | $ 9.00 |  |  |  |  |
2016 Acquisitions |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Number of businesses acquired | business |  |  |  |  |  | 6 |  |  |  |  |  |  |  |  |
Transaction costs |  |  |  |  |  | $ 4.2 |  |  |  |  |  |  |  |  |
Deltek |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Consideration transferred |  |  | $ 2,800.0 |  |  |  |  |  |  |  |  |  |  |  |
Percentage of voting interests acquired |  |  | 100.00% |  |  |  |  |  |  |  |  |  |  |  |
Transaction costs |  |  | $ 4.3 |  |  |  |  |  |  |  |  |  |  |  |
Revenue of acquiree since acquisition date |  |  |  |  |  | 7.9 |  |  |  |  |  |  |  |  |
Earnings of acquiree since acquisition date |  |  |  |  |  | 0.8 |  |  |  |  |  |  |  |  |
Deltek | Acquisition-related costs |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Pro forma earnings adjustment |  |  |  |  |  | $ 47.4 |  |  |  |  |  |  |  |  |
Other acquisitions |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Number of businesses acquired | business |  |  |  |  |  | 5 |  |  |  |  |  |  |  |  |
Consideration transferred |  |  |  |  |  | $ 920.0 |  |  |  |  |  |  |  |  |
Goodwill |  |  |  |  |  | 642.0 |  |  |  |  |  |  |  |  |
Identifiable intangibles |  |  |  |  |  | $ 372.0 |  |  |  |  |  |  |  |  |
CliniSys |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Percentage of voting interests acquired |  |  |  |  |  |  |  |  |  |  |  |  |  |  | 100.00%
GeneInsight Inc. |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Percentage of voting interests acquired |  |  |  |  |  |  |  |  |  |  |  |  |  | 100.00% |
ConstructConnect |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Percentage of voting interests acquired |  |  |  |  |  |  |  |  |  |  |  |  | 100.00% |  |

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