opes cannot be brought to a
greater perfection, because of that refraction, and of that very
refrangibility, which at the same time that they bring objects nearer to
us, scatter too much the elementary rays. He has calculated in these
glasses the proportion of the scattering of the red and of the blue rays;
and proceeding so far as to demonstrate things which were not supposed
even to exist, he examines the inequalities which arise from the shape or
figure of the glass, and that which arises from the refrangibility. He
finds that the object glass of the telescope being convex on one side and
flat on the other, in case the flat side be turned towards the object,
the error which arises from the construction and position of the glass is
above five thousand times less than the error which arises from the
refrangibility; and, therefore, that the shape or figure of the glasses
is not the cause why telescopes cannot be carried to a greater
perfection, but arises wholly from the nature of light.

For this reason he invented a telescope, which discovers objects by
reflection, and not by refraction. Telescopes of this new kind are very
hard to make, and their use is not easy; but, according to the English, a
reflective telescope of but five feet has the same effect as another of a
hundred feet in length.

LETTER XVII.--ON INFINITES IN GEOMETRY, AND SIR ISAAC NEWTON'S CHRONOLOGY

The labyrinth and abyss of infinity is also a new course Sir Isaac Newton
has gone through, and we are obliged to him for the clue, by whose
assistance we are enabled to trace its various windings.

Descartes got the start of him also in this astonishing invention. He
advanced with mighty steps in his geometry, and was arrived at the very
borders of infinity, but went no farther. Dr. Wallis, about the middle
of the last century, was the first who reduced a fraction by a perpetual
division to an infinite series.

The Lord Brouncker employed this series to square the hyperbola.

Mercator published a demonstration of this quadrature; much about which
time Sir Isaac Newton, being then twenty-three years of age, had invented
a general method, to perform on all geometrical curves what had just
before been tried on the hyperbola.

It is to this method of subjecting everywhere infinity to algebraical
calculations, that the name is given of differential calculations or of
fluxions and integral calculation. It is the art of numbering and
measurin