Reading Questions for Hodgson's Doctrine of Fluxions

1. Read the introductory paragraph discussing the difference between fluxions and differentials. Write a short paragraph describing the Newton-Leibniz controversy, and discuss how it relates to this introduction.

2. Read Example III, the calculation of the volume of a sphere.

1. In the early 1700's, when this text was written, there was no uniformly agreed upon symbol for pi. Explain how the author gets around this difficulty.
2. Define the terms ordinate and abcissa (sometimes spelled abscissa). You may use a standard dictionary and/or the context of the problem.
3. Is the answer given for the volume of a sphere correct? Explain why it is the same as our modern formula.
4. The symbol for an integral does not appear in this problem. Does the author use an antiderivative? What is his language or notation for this?
5. Rewrite this section using modern notation, while keeping as close to the original text as possible.

3. Read Examples IV - VI. Each of these examples uses a different method for computing volumes. For each example, answer parts a through d.

1. Discuss the method used (disks, washers, shells, etc.).
2. Draw a three dimensional picture of the solid of revolution. Include a representative slice in your drawing.
3. Set up an integral to calculate the desired volume, and compute this integral.
4. Show that your answer agrees with Hodgson's.

4. Compare Hodgson's explanations in this reading with those in your textbook. Which are clearer? Which would you rather read? Explain your reasoning and support your answer with examples.

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