1757 in science

The year 1757 in science and technology involved some significant events.

Astronomy

April 16 – The works of astronomer Galileo Galilei espousing heliocentrism are removed from the Index Librorum Prohibitorum list of books banned by Roman Catholic Church, along with "all books teaching the earth's motion and the sun's immobility". Other works of heliocentrists Galileo, Nicolaus Copernicus, Johannes Kepler, Diego de Zúñiga and Paolo Foscarini remain on the list.
Nicolas Louis de Lacaille publishes his Astronomiae Fundamenta Novissimus, containing a standard catalogue of 398 bright stars with positions corrected for aberration and nutation.
Tobias Mayer presents accurate tables of the Moon's motion to the Board of Longitude in Great Britain.

Scottish physician Francis Home publishes The Principles of Agriculture and Vegetation, an early presentation of the chemical principles underlying plant nutrition, in Edinburgh.

March 30 – Founding of the Rigshospitalet, national hospital of Denmark, in Copenhagen.
December 8 – Opening of the "New Lying-In" or Rotunda Hospital in Dublin, designed by Richard Cassels.
Albrecht von Haller begins publication of Elementa physiologiae corporis humani in Switzerland.

London instrument maker John Bird makes the first navigational sextant.
Benjamin Franklin invents a three-wheel clock movement, which later leads to several variants in the design of pendulum clocks.
The Grubenmann brothers complete timber arch bridges in Switzerland which include the longest vehicular bridge spans extant at this date:
* Crossing the Rhine at Schaffhausen in two spans of 52 m and 59 m
* A single-span of 67 m at Reichenau