Synthesized answer
The passages do not explicitly discuss Newton’s intent in choosing the title “Axioms, or Laws of Motion” over “hypotheses” or “observations.” However, they show that Newton presents these principles as foundational statements, immediately following the Definitions and preceding the mathematical demonstrations of Book I [1][2]. The term “Axioms” aligns with the Euclidean tradition of starting from self-evident truths, and the laws are stated without any suggestion of doubt or empirical testing—they are simply laid down as the basis for all that follows [1].
The Scholium in Passage 4 indicates that Newton considered these principles “received by mathematicians, and confirmed by abundance of experiments,” and he credits Galileo’s discoveries to the first two Laws [4]. This suggests Newton viewed them as more than mere hypotheses: they are principles that have been demonstrated to hold true and are used to derive further results. The passages do not, however, discuss Newton’s philosophical reasoning for rejecting the label “hypotheses” or “observations,” nor do they mention his famous “Hypotheses non fingo” stance. Thus, while the text shows the laws are treated as axiomatic and…
Synthesized from the book passages below. Chat with the book on Feynman for follow-up.
From the book
← Definitions The Mathematical Principles of Natural Philosophy (1846) by Isaac Newton , translated by Andrew Motte Axioms, or Laws of Motion Section I → 596269 The Mathematical Principles of Natural Philosophy (1846) — Axioms, or Laws of Motion Andrew Motte Isaac Newton AXIOMS, OR LAWS OF MOTION. LAW I. Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon. Projectiles persevere in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force…
← Axioms, or Laws of Motion The Mathematical Principles of Natural Philosophy (1846) by Isaac Newton , translated by Andrew Motte Book I, Section I. Section II → 596423 The Mathematical Principles of Natural Philosophy (1846) — Book I, Section I. Andrew Motte Isaac Newton BOOK I. OF THE MOTION OF BODIES. SECTION I. Of the method of first and last ratios of quantities, by the help whereof we demonstrate the propositions that follow. LEMMA I. Quantities, and the ratios of quantities, which in any finite time converge continually to equality, and before the end of that time approach nearer the…
ortional to the motive force impressed; and is made in the direction of the right line in which that force is impressed. If any force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force), if the body moved before, is added to or subducted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are…
ppen after the same manner, whether the ship is at rest, or is carried uniformly forwards in a right line. COROLLARY VI. If bodies, any how moved among themselves, are urged in the direction of parallel lines by equal accelerative forces, they will all continue to move among themselves, after the same, manner as if they had been urged by no such forces. For these forces acting equally (with respect to the quantities of the bodies to be moved), and in the direction of parallel lines, will (by Law II) move all the bodies equally (as to velocity), and therefore will never produce any change in…
ediate angles may be interposed, differing from one another by infinite intervals. Nor is nature confined to any bounds. Those things which have been demonstrated of curve lines, and the superfices which they comprehend, may be easily applied to the curve superfices and contents of solids. These Lemmas are premised to avoid the tediousness of deducing perplexed demonstrations ad absurdum , according to the method of the ancient geometers. For demonstrations are more contracted by the method of indivisibles: but because the hypothesis of indivisibles seems somewhat harsh, and therefore that…
More questions about this book
- Explain Newton's First Law of Motion, using only the provided examples, in a way that clarifies what "perseveres in its state" truly means for both rest and uniform motion.
- How does the second law's emphasis on "alteration of motion" and the direction of the "motive force" distinguish it from merely describing existing motion, and what does this imply about the nature of force itself?
- If a student only understood Law I, how might their understanding of the *cause* of changing motion be incomplete, and how does Law II specifically address this gap?
- Beyond a simple definition, what characteristics of "forces" can be inferred solely from their described effects in Laws I and II, and what implications does this have for observing physical phenomena?