Revenue (Disaggregation of Revenue by Geographical Region) (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 29, 2019	Mar. 30, 2018
Disaggregation of Revenue [Line Items]
Sales	$ 4,879.9	$ 4,695.4
North America
Disaggregation of Revenue [Line Items]
Sales	1,967.4	1,797.4
Western Europe
Disaggregation of Revenue [Line Items]
Sales	1,169.0	1,200.7
Other developed markets
Disaggregation of Revenue [Line Items]
Sales	310.6	312.6
High-growth markets
Disaggregation of Revenue [Line Items]
Sales	1,432.9	1,384.7
Operating segments | Life Sciences
Disaggregation of Revenue [Line Items]
Sales	1,626.9	1,476.0
Operating segments | Life Sciences | North America
Disaggregation of Revenue [Line Items]
Sales	587.3	480.4
Operating segments | Life Sciences | Western Europe
Disaggregation of Revenue [Line Items]
Sales	460.3	449.9
Operating segments | Life Sciences | Other developed markets
Disaggregation of Revenue [Line Items]
Sales	149.3	144.9
Operating segments | Life Sciences | High-growth markets
Disaggregation of Revenue [Line Items]
Sales	430.0	400.8
Operating segments | Diagnostics
Disaggregation of Revenue [Line Items]
Sales	1,536.8	1,519.7
Operating segments | Diagnostics | North America
Disaggregation of Revenue [Line Items]
Sales	632.4	607.4
Operating segments | Diagnostics | Western Europe
Disaggregation of Revenue [Line Items]
Sales	288.9	310.4
Operating segments | Diagnostics | Other developed markets
Disaggregation of Revenue [Line Items]
Sales	92.0	92.2
Operating segments | Diagnostics | High-growth markets
Disaggregation of Revenue [Line Items]
Sales	523.5	509.7
Operating segments | Dental
Disaggregation of Revenue [Line Items]
Sales	659.7	672.6
Operating segments | Dental | North America
Disaggregation of Revenue [Line Items]
Sales	298.5	291.3
Operating segments | Dental | Western Europe
Disaggregation of Revenue [Line Items]
Sales	160.1	175.6
Operating segments | Dental | Other developed markets
Disaggregation of Revenue [Line Items]
Sales	40.4	43.9
Operating segments | Dental | High-growth markets
Disaggregation of Revenue [Line Items]
Sales	160.7	161.8
Operating segments | Environmental & Applied Solutions
Disaggregation of Revenue [Line Items]
Sales	1,056.5	1,027.1
Operating segments | Environmental & Applied Solutions | North America
Disaggregation of Revenue [Line Items]
Sales	449.2	418.3
Operating segments | Environmental & Applied Solutions | Western Europe
Disaggregation of Revenue [Line Items]
Sales	259.7	264.8
Operating segments | Environmental & Applied Solutions | Other developed markets
Disaggregation of Revenue [Line Items]
Sales	28.9	31.6
Operating segments | Environmental & Applied Solutions | High-growth markets
Disaggregation of Revenue [Line Items]
Sales	$ 318.7	$ 312.4