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Isaac Newton presents his comprehensive theory on the properties of light, the laws of refraction, and the composition of colors. This volume also includes mathematical theorems regarding the squaring of curvilinear figures and their comparison with conic sections.

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though the Number of the refracting Substances be increased to Infinity, and the Distances from one another as much decreased, so that the Light may be refracted in every Point of its Passage, and by continual Refractions bent into a Curve-Line. And therefore the whole Refraction of Light in passing through the Atmosphere from the highest and rarest Part thereof down to the lowest and densest Part, must be equal to the Refraction which it would suffer in passing at like Obliquity out of a Vacuum immediately into Air of equal Density with that in the lowest Part of the Atmosphere.

Now, although a Pseudo-Topaz, a Selenitis, Rock Crystal, Island Crystal, Vulgar Glass (that is, Sand melted together) and Glass of Antimony, which are terrestrial stony alcalizate Concretes, and Air which probably arises from such Substances by Fermentation, be Substances very differing from one another in Density, yet by this Table, they have their refractive Powers almost in the same Proportion to one another as their Densities are, excepting that the Refraction of that strange Substance, Island Crystal is a little bigger than the rest. And particularly Air, which is 3500 Times rarer than the Pseudo-Topaz, and 4400 Times rarer than Glass of Antimony, and 2000 Times rarer than the Selenitis, Glass vulgar, or Crystal of the Rock, has notwithstanding its rarity the same refractive Power in respect of its Density which those very dense Substances have in respect of theirs, excepting so far as those differ from one another.

Again, the Refraction of Camphire, Oil Olive, Linseed Oil, Spirit of Turpentine and Amber, which are fat sulphureous unctuous Bodies, and a Diamond, which probably is an unctuous Substance coagulated, have their refractive Powers in Proportion to one another as their Densities without any considerable Variation. But the refractive Powers of these unctuous Substances are two or three Times greater in respect of their Densities than the refractive Powers of the former Substances in respect of theirs.

Water has a refractive Power in a middle degree between those two sorts of Substances, and probably is of a middle nature. For out of it grow all vegetable and animal Substances, which consist as well of sulphureous fat and inflamable

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