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Gregoire de Saint-Vincent (1584-1667)

Born in Belgium.
He discovered the expansion of log(1+x) in ascending powers of x.
Joseph Saurin (1659-1737)

Born in France.
he showed how the tangents at the multiple points of curves can be determined by analysis.
Henry Smith (1826-1882)

Born in England.
He did research on linear indeterminate equations and congruences.
He also researched on the orders and genera of ternary quadratic forms.
He established the principles on which the extension to the general case of n indeterminates depends, and obtained the general formulae.
Willebrod Snell (1581-1626)

Born in Netherlands.
In geodesy, he stated the principles for determining the length of an arc of a meridian from the measurement of any base line.
In spherical geometry, he discovered the properties of the polar or supplemental triangle.
Karl Georg Christian von Staudt (1798-1867)

Born in Germany.
He constructed a system of geometry built up without any reference to number or magnitude.
He established the non-metrical projective properties of figures, using his system.
He obtained a geometrical definition of a number.
Jacob Steiner (1796-1863)

Born in Switzerland.
He discovered the Steiner (Roman) surface, which has a double infinity of conic sections on it.
His Steiner theorem states that two pencils (collections of geometric objects) by which a conic is projected from two of its points are projectively related.
He proved that any Euclidean figure can be generated, using only a straight rule if the plane of construction has a circle with its centre marked on it.
Simon Stevinius (1548-1620)

Born in Netherlands.
He suggested the use of fractional, but not negative, exponents.
He introduced the triangle of force in statics.
James Joseph Sylvester (1814-1897)

Born in England.
He wrote on canonical forms, on the theory of contavariants, on reciprocants, and on the theory of equations in higher algebra.