Sir Isaac Newton: Mathematical Principles of Natural Philosophy
From: Biographical note on Sir Isaac Newton
· Born on Christmas 1645
· Widowed mother remarries and sends him to be raised by grandmother, sent away to school at age 12.
· Calls himself an indifferent scholar.
· Well red in mathematics, mechanics
· Read Kepler – didn’t want to read it, a teacher later convinced him of its value.
· Bothered by his inability to comprehend the diagrams in an astrology book he bought at a fair, so he studied Euclid.
· Inspired by the Descartes Geometry, wanted to do original mathematical works
· Teacher came to him with a problem he had been working on for years, Newton had already solved it. Showed him his work and then considered publishing his work.
Humble, even when famous for his work – “I do not know what I may appear to the world, but to myself I seem only like a boy playing on the seashore, and diverting myself in now and then, finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.”
From: Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Preface pg. 1
· Mechanical arts
· Artificers
· Practical arts (accurate & practical)
· Manual arts
· Geometry: the art of measuring
Newton wrote:
To describe right lines and circles are problems, but not geometrical problems. The solution of these problems is required from mechanics, and by geometry the use of them, when so solved, is shown; and it is the glory of geometry that from those few principle, brought from without, it is able to produce so many things. Therefore geometry is founded in mechanical practice, and is nothing but that part of universal mechanics which accurately proposes and demonstrates the art of measuring.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Preface pg. 1
Newton wrote:
What is perfectly accurate is called geometrical; what is less so is called mechanical.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Preface pg. 1
Newton wrote:
Geometry – the art of measuring
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Preface pg. 1
Newton wrote:
Geometry does not teach us to draw these line, but requires them to be drawn, for it requires that the learner should first be taught to describe these accurately before he enters upon geometry, then it shows how by these operations problems may be solved.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Preface pg. 1
BORN 1642
1686 – published (44 years old)
1713 – 2nd edition (81 years old)
1725 – 3rd edition (93 years old
DIED 1727
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Prefaces, pg. 1 – 3
Newton wrote:
A body, from the inert nature of matter is not without difficulty put out of its stae of rest or motion. Upon which account, this vis insita may, by a most significant name, be called inertia (vis iertia) or force of inactivity. But a body only exerts this force when another force, impressed upon it, endevours to change its condition.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Definition 3, pg. 3
3 kinds of centripetal force:
absolute – definition 6
acclerative – definition 7
motive – definition 8
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Definition 5, pg. 7
Newton wrote:
… equally accelerates all falling bodies whether heavy, light, great, or small.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Definition 7, pg. 7
Newton wrote:Wherefore, if the earth is really at rest, the body, which relatively rests in the ship, will really and absolutely move with the same velocity which the ship has on earth. But if the earth also moves, the true and absolute motion of the body will arise, partly from the true motion of the earth in immovable space, partly from the relative motion of the ship in the earth…Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Definitions. Scholium IV, pg. 9
Newton wrote:
Absolute time in astronomy is distinguished from relative by the equation or correction of the apparent time. For the natural days are truly unequal, though they are commonly considered as equal, and used for a measure of time; astronomers correct this inequality that they may measure the celestial motions by a more accurate time.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Definitions. Scholium IV, pg. 9
Newton wrote:
It is indeed a matter of great difficulty to discover and effectually to distinguish the true motions of particular bodies from the apparent; because the parts of that immovable space in which these motions are performed do by no means come under the observation of our senses. Yet the thing is not all together desperate; for we have some arguments to guide us, partly from the apparent motions, which are the difference of the true motion; partly form the forces which are the causes and effects of the true motions.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Definitions, Scholium IV, pg. 12
Newton wrote:
Law 1 – every body continues in its state of rest or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.
Law 2 – The change of motion is proportional to the motive force impressed; and it is made in the direction of the right line in which that force is impressed.
Law 3 – To every action there is always opposed an equal reaction; or, the mutual actions of the two bodies upon each other are always equal, and directed to contrary parts.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Axioms; pg. 14 – 24
Newton wrote:
Corollary 1 – A body, acted on by two forces simultaneously, will describe the diagonal of a parallelogram in the same time as it would describe the sides by those forces separately.
Corollary 2 – And hence is explained the composition of any one direct force AD, out of any two oblique forces AC and CD; and on the contrary, the resolution of any one direct force AD into two oblique forces AC and CD; which composition and resolution are abundantly confirmed from mechanics.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Axioms; pg. 15
Newton wrote:
Corollary 3 – The quantity of motion, which is obtained by taking the sum of the motions directed towards the same parts, and the differences of those that are directed to contrary parts, suffers no change from the action of bodies among themselves.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Axioms; pg. 16
Newton wrote:
Corollary 4 – The common centre of gravity of two or more bodies does not alter its state of motion or rest by the actions of the bodies among themselves; and therefore the common centre of gravity of all bodies action upon each other excluding external actions and impediments is either at rest or moves uniformly in a right line.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Axioms; pg. 18
Newton wrote:
Corollary 5 – The motions of bodies included in a given space are the same among themselves whether that space is at rest, or more uniformly forwards in a right line without any circular motion.
Corollary 6 – If bodies moved in any manner 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 not been urged by those forces.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Axioms; pg. 19
Newton wrote:
Scholium: By the first two Laws and the first two Corollaries, Galileo discovered that the descent of bodies varied as the square of the time and the motion of the projectiles was in the curve of a parabola; experience agreeing with both…
When a body is falling, the uniform force of its gravity acting equally, impresses, in equal intervals of time, equal forces upon that body, and therefore generates equal velocities; and in the whole time impresses a whole force.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Axioms; pg. 19
Newton wrote:
The most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being. And if the fixed stars are the centers of other like systems, these, being formed by the like wise counsel, must be all subject to the dominion of One; especially since the light of the fixed stars is of the same nature with the light of the sun, and from every system light passes into all the other systems; and lest the systems of the fixed stars should, by their gravity, fall on each other, he hath placed these systems at immense distances from one another.
This Being governs all things, not as the soul of the world, but as Lord over all and on account of his dominion He is wont to be called Lord God … or Universal Ruler, for God is a relative word
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Book 3: General Scholium, pg. 369 -370
Newton wrote:
But hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called an hypotheses; and hypotheses, whether metaphysical or physical , whether of occult qualities or mechanical, have no place in experimental philosophy. …to us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Book 3: General Scholium, pg. 371
VOCABULARY - Sir Isaac Newton: Mathematical Principles of Natural Philosophy
Apothecary (medicine, pharmacist?) pg. ix
Emulation, pg. ix
Repudiate, pg. x
Emendations, Preface 2, pg. 2
Equinox, Preface 2, pg. 2
Interstices, Preface 2, pg. 2
Vis insta, Definitions, pg. 5
Innate force, Definitions, pg. 5
Inert, Definitions, pg. 5
Centripetal force, Definitions, pg. 6
Defined in definition 5: that by which bodies are drawn or impelled
3 kinds of centripetal force:
absolute – definition 6
acclerative – definition 7
motive – definition 8
Definition 5, pg. 7
Scholium, Definitions, pg. 8
Impinge, Axioms, or Laws of motion, pg. 14
Quiescence, General Scholium, pg. 371
Aphelion, General Scholium, pg. 371
From: Biographical note on Sir Isaac Newton
· Born on Christmas 1645
· Widowed mother remarries and sends him to be raised by grandmother, sent away to school at age 12.
· Calls himself an indifferent scholar.
· Well red in mathematics, mechanics
· Read Kepler – didn’t want to read it, a teacher later convinced him of its value.
· Bothered by his inability to comprehend the diagrams in an astrology book he bought at a fair, so he studied Euclid.
· Inspired by the Descartes Geometry, wanted to do original mathematical works
· Teacher came to him with a problem he had been working on for years, Newton had already solved it. Showed him his work and then considered publishing his work.
Humble, even when famous for his work – “I do not know what I may appear to the world, but to myself I seem only like a boy playing on the seashore, and diverting myself in now and then, finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.”
From: Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Preface pg. 1
· Mechanical arts
· Artificers
· Practical arts (accurate & practical)
· Manual arts
· Geometry: the art of measuring
Newton wrote:
To describe right lines and circles are problems, but not geometrical problems. The solution of these problems is required from mechanics, and by geometry the use of them, when so solved, is shown; and it is the glory of geometry that from those few principle, brought from without, it is able to produce so many things. Therefore geometry is founded in mechanical practice, and is nothing but that part of universal mechanics which accurately proposes and demonstrates the art of measuring.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Preface pg. 1
Newton wrote:
What is perfectly accurate is called geometrical; what is less so is called mechanical.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Preface pg. 1
Newton wrote:
Geometry – the art of measuring
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Preface pg. 1
Newton wrote:
Geometry does not teach us to draw these line, but requires them to be drawn, for it requires that the learner should first be taught to describe these accurately before he enters upon geometry, then it shows how by these operations problems may be solved.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Preface pg. 1
BORN 1642
1686 – published (44 years old)
1713 – 2nd edition (81 years old)
1725 – 3rd edition (93 years old
DIED 1727
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Prefaces, pg. 1 – 3
Newton wrote:
A body, from the inert nature of matter is not without difficulty put out of its stae of rest or motion. Upon which account, this vis insita may, by a most significant name, be called inertia (vis iertia) or force of inactivity. But a body only exerts this force when another force, impressed upon it, endevours to change its condition.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Definition 3, pg. 3
3 kinds of centripetal force:
absolute – definition 6
acclerative – definition 7
motive – definition 8
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Definition 5, pg. 7
Newton wrote:
… equally accelerates all falling bodies whether heavy, light, great, or small.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Definition 7, pg. 7
Newton wrote:Wherefore, if the earth is really at rest, the body, which relatively rests in the ship, will really and absolutely move with the same velocity which the ship has on earth. But if the earth also moves, the true and absolute motion of the body will arise, partly from the true motion of the earth in immovable space, partly from the relative motion of the ship in the earth…Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Definitions. Scholium IV, pg. 9
Newton wrote:
Absolute time in astronomy is distinguished from relative by the equation or correction of the apparent time. For the natural days are truly unequal, though they are commonly considered as equal, and used for a measure of time; astronomers correct this inequality that they may measure the celestial motions by a more accurate time.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Definitions. Scholium IV, pg. 9
Newton wrote:
It is indeed a matter of great difficulty to discover and effectually to distinguish the true motions of particular bodies from the apparent; because the parts of that immovable space in which these motions are performed do by no means come under the observation of our senses. Yet the thing is not all together desperate; for we have some arguments to guide us, partly from the apparent motions, which are the difference of the true motion; partly form the forces which are the causes and effects of the true motions.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Definitions, Scholium IV, pg. 12
Newton wrote:
Law 1 – every body continues in its state of rest or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.
Law 2 – The change of motion is proportional to the motive force impressed; and it is made in the direction of the right line in which that force is impressed.
Law 3 – To every action there is always opposed an equal reaction; or, the mutual actions of the two bodies upon each other are always equal, and directed to contrary parts.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Axioms; pg. 14 – 24
Newton wrote:
Corollary 1 – A body, acted on by two forces simultaneously, will describe the diagonal of a parallelogram in the same time as it would describe the sides by those forces separately.
Corollary 2 – And hence is explained the composition of any one direct force AD, out of any two oblique forces AC and CD; and on the contrary, the resolution of any one direct force AD into two oblique forces AC and CD; which composition and resolution are abundantly confirmed from mechanics.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Axioms; pg. 15
Newton wrote:
Corollary 3 – The quantity of motion, which is obtained by taking the sum of the motions directed towards the same parts, and the differences of those that are directed to contrary parts, suffers no change from the action of bodies among themselves.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Axioms; pg. 16
Newton wrote:
Corollary 4 – The common centre of gravity of two or more bodies does not alter its state of motion or rest by the actions of the bodies among themselves; and therefore the common centre of gravity of all bodies action upon each other excluding external actions and impediments is either at rest or moves uniformly in a right line.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Axioms; pg. 18
Newton wrote:
Corollary 5 – The motions of bodies included in a given space are the same among themselves whether that space is at rest, or more uniformly forwards in a right line without any circular motion.
Corollary 6 – If bodies moved in any manner 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 not been urged by those forces.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Axioms; pg. 19
Newton wrote:
Scholium: By the first two Laws and the first two Corollaries, Galileo discovered that the descent of bodies varied as the square of the time and the motion of the projectiles was in the curve of a parabola; experience agreeing with both…
When a body is falling, the uniform force of its gravity acting equally, impresses, in equal intervals of time, equal forces upon that body, and therefore generates equal velocities; and in the whole time impresses a whole force.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Axioms; pg. 19
Newton wrote:
The most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being. And if the fixed stars are the centers of other like systems, these, being formed by the like wise counsel, must be all subject to the dominion of One; especially since the light of the fixed stars is of the same nature with the light of the sun, and from every system light passes into all the other systems; and lest the systems of the fixed stars should, by their gravity, fall on each other, he hath placed these systems at immense distances from one another.
This Being governs all things, not as the soul of the world, but as Lord over all and on account of his dominion He is wont to be called Lord God … or Universal Ruler, for God is a relative word
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Book 3: General Scholium, pg. 369 -370
Newton wrote:
But hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called an hypotheses; and hypotheses, whether metaphysical or physical , whether of occult qualities or mechanical, have no place in experimental philosophy. …to us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea.
Sir Isaac Newton: Mathematical Principles of Natural Philosophy, Book 3: General Scholium, pg. 371
VOCABULARY - Sir Isaac Newton: Mathematical Principles of Natural Philosophy
Apothecary (medicine, pharmacist?) pg. ix
Emulation, pg. ix
Repudiate, pg. x
Emendations, Preface 2, pg. 2
Equinox, Preface 2, pg. 2
Interstices, Preface 2, pg. 2
Vis insta, Definitions, pg. 5
Innate force, Definitions, pg. 5
Inert, Definitions, pg. 5
Centripetal force, Definitions, pg. 6
Defined in definition 5: that by which bodies are drawn or impelled
3 kinds of centripetal force:
absolute – definition 6
acclerative – definition 7
motive – definition 8
Definition 5, pg. 7
Scholium, Definitions, pg. 8
Impinge, Axioms, or Laws of motion, pg. 14
Quiescence, General Scholium, pg. 371
Aphelion, General Scholium, pg. 371
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