# Assignments

For this course, there are two types of assignments: assigned study papers (two pages each) and six-page papers (six pages each). There are three papers of each type. The course has a total of six papers.

## Assigned Study Papers

Three two-page papers addressing assigned study questions, to be submitted electronically before the class in which they are discussed. These topics explained in the individual assignments.

### Assigned Study Paper 1 — Due Ses #4

Using Definition 3, explain Newton's concept of inherent force (inertia, vis insita). How does "inherent force" differ from the "impressed force" of Definition 4, which Newton calls an "action"? Is inertia truly a force?

### Assigned Study Paper 2 — Due Ses #15

Why do you suppose that Newton, co-inventor of the calculus, chose to prove his propositions in the ancient geometrical style, rather than by writing down and solving equations?

### Assigned Study Paper 3 — Due Ses #33

Considering Propositions II.24 and III.6, why should the gravitational attractions experienced by bodies—their weights—be exactly proportional to their inherent inertial forces—their masses? Is it merely a coincidence? What role does Newton's Third Rule of Philosophizing play in the demonstration of Proposition III.6?

## Six Pages Papers

Three six page papers are required for this course. The first two of these papers will be re-written in response to the instructor's comments and re-submitted. The grade will be assigned for the rewritten paper.

### First Paper — Due Ses #12

Using the Scholium to the Lemmas (Densmore, 117–121), explain what Newton means by "the ultimate sums and ratios of evanescent quantities" and "the first sums and ratios of nascent quantities." How does Newton meet the objection that "there is no ultimate ratio of evanescent quantities"? What use does Newton make of the concept of "limits"?

### Second Paper — Due Ses #25

Offer a critique or a defense of Newton's "Rules of Philosophizing." Where do they come from? In what domain of knowledge are they applicable? Are they imposed on knowledge from the outside, or do they merely describe the way we actually think if we are thinking philosophically? What does it mean (Rule 4) to "gather propositions from phenomena by induction"? How are arguments from induction "nullified by hypotheses"? This paper will be re-written in response to the instructor's comments and re-submitted. The grade will be assigned for the re-written paper.

### Third Paper — Due Ses #39

Analyze, defend, or critique this statement: "Newton transformed ancient and medieval natural philosophy into modern mathematical physics; but he was a transitional figure, with one leg firmly rooted in antiquity and one leg in modernity."