It is from these three equalities we deduce as consequence the equality of F and the weight of P.
To-day only whole numbers are left in analysis, or systems finite or infinite of whole numbers, bound by a plexus of equalities and inequalities.
The equality and the inequality deduced from experience would be incompatible with the two equalities deduced from the postulate.
By this transformation of all questions of quality into questions only of quantity, geometry is reduced to the single problem of the measurement of magnitudes, that is, the ascertainment of the equalities which exist between them.
But here observe that material equalities fall short of the conception of absolute equality with which they are compared, and which is the measure of them.
Did we not see equalities of material things, such as pieces of wood and stones, and gather from them the idea of an equality which is different from them?
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "equalities" in a variety of sentences. We hope that you will now be able to make sentences using this word.
