Benjamin Franklin (1705-1790) and Geometry

MATHEMATICS originally signified any kind of discipline or learning, but now it is taken for that science which teaches or contemplates whatever is capable of being numbered or measured. That part of the mathematics which relates to numbers only is called arithmetic; and that which is concerned about measure in general, whether length, breadth, motion, force, &c., is called geometry.

As to the usefulness of geometry, it is as certain that no curious art or mechanic work can either be invented, improved, or performed without its assisting principles.

It is owing to this that astronomers are put into a way of making their observations, coming at the knowledge of the extent of the heavens, the duration of time, the motions, magnitudes, and distances of the heavenly bodies, their situations, positions, risings, settings, aspects, and eclipses; also the measure of seasons, of years, and of ages.

It is by the assistance of this science that geographers present to our view at once the magnitude and form of the whole earth, the vast extent of the seas, the divisions of empires, kingdoms, and provinces.



It is by the help of geometry the ingenious mariner is instructed how to guide a ship through the vast ocean, from one part of the earth to another, the nearest and safest way and in the shortest time.



By geometry the surveyor is directed how to draw a map of any country, to divide his lands, and to lay down and plot any piece of ground, and thereby discover the area in acres, rods, and perches; the gauger is instructed how to find the capacities or solid contents of all kinds of vessels, in barrels, gallons, bushels &c.; and the measurer is furnished with rules for finding the areas and contents of superficies and solids, and casting up all manner of workmanship. All these and many more useful arts too many to be enumerated here, wholly depend upon the aforesaid sciences—viz., arithmetic and geometry.



Mathematical demonstrations are a logic of as much or more use than that commonly learned at schools, serving to a just formation of the mind, enlarging its capacity, and strengthening it so as to render the same capable of exact reasoning, and discerning truth from falsehood in all occurrences, even subjects not mathematical. For which reason, it is said, the Egyptians, Persians, and Lacedæmonians seldom elected any new kings but such as had some knowledge in the mathematics, imagining those who had not, men of imperfect judgments and unfit to rule and govern.

I shall conclude with what Plato says in the seventh book of his Republic with regard to the excellence and usefulness of geometry, being to this purpose;

“Dear friend; you see then that mathematics are necessary, because by the exactness of the method we get a habit of using our minds to the best advantage. And it is remarkable that all men being capable by nature to reason and understand the sciences, the less acute, by studying this, though useless to them in every other respect, will gain this advantage—that their minds will be improved in reasoning aright; for no study employs it more, nor makes it susceptible of attention so much; and those who we find have a mind worth cultivating ought to apply themselves to this study.”

Source: The Works of Benjamin Franklin, Vol. II Letters and Misc. Writings 1735-1753 [1904]
1735: XVI: On the Usefulness of the Mathematics 1

The Works of Benjamin Franklin, including the Private as well as the Official and Scientific Correspondence, together with the Unmutilated and Correct Version of the Autobiography, compiled and edited by John Bigelow (New York: G.P. Putnam’s Sons, 1904). The Federal Edition in 12 volumes. Vol. II (Letters and Misc. Writings 1735-1753).  Author: Benjamin Franklin  Editor: John Bigelow