During the renaissance, Europeans were fascinated with technological invention. The architects, navigators, engineers, and weapons experts of the Renaissance were important pioneers of a new reliance on measurement and observation that affected many things, including how problems in physics were addressed. Interest in experimentation was also growing among anatomists. Thus, during the sixteenth and seventeenth century, many new instruments were invented which helped make scientific discovery possible; the telescope, the thermometer, the vacuum pump, the barometer, and the microscope. These made new scientific discoveries possible. The printing press had an indirect but crucial role in spreading innovative ideas quickly and easily.

Mathematics developed as a response to the demands of the sciences, which grew up in the late sixteenth century. It was fundamental to the scientific achievements of the sixteenth and seventeenth centuries, was promoted in the Renaissance by the rediscovery of the works of ancient mathematicians and the influence of Plato, who had emphasized by the importance of mathematics in explaining the universe. While mathematics was applauded as the key to navigation, military science and geography the Renaissance also held the widespread belief that mathematics was the key to understanding the nature of things. However, few mathematical advances had effects as immediate as the study of optics. As the importance of observation of the natural had grown, Scientists had constantly sought the magnification of observed subjects. It was not long before the principles of geometry were applied to the field of optics. The culmination of these efforts was the introduction of the telescope and microscope by Galileo in 1609, both of which revolutionized natural science.

The Renaissance encompassed another revival of learning based on...

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