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The engineering design process is a series of steps that engineers follow to come up with a solution to a problem. Many times the solution involves designing a product (like a machine or computer code) that meets certain criteria and/or accomplishes a certain task.
Above text from Science Buddies.org - http://www.sciencebuddies.org/engineering-design-process/engineering-design-process-steps.shtml
The engineering method (also known as engineering design process) is a systematic approach used to reach the desired solution to a problem. There are six steps (or phases): idea, concept, planning, design, development, and launch from problem definition to desired result.
The scientific method is a procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses.
It was not until the 17th century that the experimental method was agreed to be the main way to find the truth. This was done in western Europe by men like Galileo, Kepler, Hooke, Boyle, Halley and Newton. At the same time, the microscope and the telescope were invented (both inHolland), and the Royal Society was formed. Both instruments and societies helped science greatly.
source - https://simple.wikipedia.org/wiki/Scientific_method