Motion: The distance traveled by an object, its velocity, its acceleration, and the relationships between these quantities.
Tangents: The tangents to curves and to solids. These were needed in geometry, and they were also useful in optics and in the study of motion.
Extremes: Maxima and minima for various functions. Notably, Galileo (1564–1642) found the correct angle (π/4) to fire a cannon for maximal range.
Lengths, areas, and volumes: The distance traveled by a planet around the sun, areas bounded by curves, volumes bounded by curved surfaces, centers of gravity, and total gravitational attraction of a body.
KeywordsCorrect Angle Outer Estimate Circular Cone Theoretical Volume Height Time
Unable to display preview. Download preview PDF.