"The area of a circle is equal to the area of a right-angled triangle whose sides containing the right angle are equal to the radius and circumference of the circle respectively."

"Any solid lighter than a fluid will, if placed in the fluid, be so far immersed that the weight of the fluid displaced by the immersed portion will be equal to the weight of the solid."

"By a method of mechanical reasoning, I first discovered that the area of a segment of a parabola is four-thirds of the triangle with the same base and equal height."

"The spiral, by a continuous motion, generates an infinite number of lines."

"It is not possible to find a number greater than the number of grains of sand which could be contained in a sphere of the size of the universe."