This must be added to the Moon's mean Motion, while the Nodes are passing from their Syzygys with the Sun, to their Quadratures with him; but subtracted while they pass from the Quadratures to the Syzygys.
And the least Attraction will be about the Quadratures of these Lunar Months, because the Declination of the Moon from the Equator is then greatest.
Aboue ouer the coronice, by an inuers gradation there were fowre Quadratures or square Tables, two right ouer the chamfered columnes, and channelled pyllars, and two within them.
Hence, in the conjunction and opposition, their gravity towards each other is diminished by the action of the sun, while in the quadratures it is increased.
Twice a month, also, namely, at the quadratures of the moon, the tides neither rise so high nor fall so low as at other times, because then the sun and moon act against each other.
This restrictive condition being understood, we may say that Fermat's formulation of the problem of quadratures is the same as our definition of a definite integral.
The germs of this method of formulating the problem of quadratures are found in the writings of Archimedes.
The introduction of the process of differentiation, together with the theorem here proved, placed the solution of the problem of quadratures on a new basis.
In his answer of June 1677 Leibnitz gave Newton a candid account of his differential calculus, nearly in the form in which he afterwards published it, and explained how he used it for quadratures and inverse problems of tangents.
When Barrow wrote, quadratures were familiar and differentiation unfamiliar, just as hyperbolas were trusted while logarithms were strange.
This artifice is now merely an incident in the conduct of a limiting process, but in the 17th century, when limiting processes other than the Greek methods for quadratures were new, the introduction of the artifice was a great advance.
Fermat did not use fractional or negative indices, but he regarded his problems as the quadratures of parabolas and hyperbolas of various orders.
Barrow's inversion-theorem and its application to quadratures are not mentioned.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "quadratures" in a variety of sentences. We hope that you will now be able to make sentences using this word.
