Principia - Softcover
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1863 Excerpt: ...E. From these observed facts, we see that when the force, under the action of which E moves, is applied to the Moon in the contrary direction, the remaining force tends in the directions of the arrows. By the supposition that the Earth and Moon are acted on by forces tending to the Sun, whose distance compared with EM is very great, and that the differences of the forces on these bodies are not very great, the circumstances of the description of areas in the motion of the Moon are accounted for. Prop. IV. Theorem IV. The centripetal forces of equal bodies, which describe different circles with uniform velocity, tend to the centers of the circles, and are to each other as the squares of arcs described in the same time, divided by the radii of the circles. The bodies move uniformly, therefore the arcs described are proportional to the times of describing them; and the sectors of circles are proportional to the arcs on which they stand, therefore the areas described by radii drawn to the centers are proportional to the times of describing them; hence, by Prop. II, the forces tend to the centers of the circles. Again, let AB, ab be small arcs described in equal times, AD, ad tangents at A, a, ACSG, acsg diameters through A, a. Join AB, ab, and draw BC, be perpendicular to AG, ag. By similar triangles, AC: AB:: AB: AG,:. AC. AG = (chord AB?;. A„... (chord ABf (chord abf Air ag But, ultimately, when the arcs AB,'ab are indefinitely diminished, since AC, ac are sagittse of the double of arcs AB, ab, and are therefore, by Prop. i. Cor. 4, ultimately as the forces at A and a, therefore ultimately, „,.,. (chord AB) (chord ab) force at A:force at a:: j-77---: ' AG ag (wrcAB) (arcaft)2. T:: Ag:' byLemraam Take AE, ae two arcs described in any equal finite t...
"synopsis" may belong to another edition of this title.
About the Author:
ISAAC NEWTON was born in Woolsthorpe, Lincolnshire, England, on December 25, 1642. His father having died before his birth and his mother having remarried, Newton was sent to live with his maternal grandmother in the neighboring town of Grantham, where he attended school. An inattentive student, Newton nonetheless showed a great aptitude for making mechanical contrivances such as windmills and water clocks. While at school, Newton boarded with an apothecary, who may have imparted to the youngster a lifelong love of chemical experiments.
In 1656, following the death of her second husband, Newton's mother removed him from school and brought him back to Woolsthorpe with the idea of making her son a farmer. Newton's teacher at Grantham, recognizing the boy's talents, prevailed upon her to allow Newton to prepare for entrance to Cambridge University. He entered Trinity College, Cambridge, in 1661, under the tutelage of Isaac Barrow, Lucasian Professor of Mathematics, and took his degree four years later.
Between 1665 and 1667, Newton made great strides in his method of "fluxions" (an early form of differential calculus) and began work on gravitation. It was also at this time that Newton inaugurated his studies on the nature of light: he demonstrated that differences in color resulted from differences in refrangibility, i.e., the ability of a ray of light to bend when passed through a refracting medium. In 1667, Newton returned to Cambridge from Woolsthorpe (where he had gone to escape the plague); two years later he succeeded Barrow as Lucasian Professor. In 1672 Newton was elected to the Royal Society.
Newton's great work, Philosophiae naturalis principia mathematica, or The Mathematical Principles of Natural Philosophy (1687), grew out of his ongoing investigations into gravitation and planetary motion. Written over a period of only eighteen months, this book was immediately hailed as a masterpiece: it demonstrated how the law of gravitation could explain diverse phenomena, ranging from the tides to the irregularities of the moon's motion, and made possible a mathematical principle, unrealized up to that time, of the workings of a dynamic universe. Although Newton's system needed to be revised in the twentieth century in view of the theory of relativity and quantum mechanics, it remains valid for systems of ordinary dimensions, involving velocities that do not approach the speed of light.
Newton's contributions to science brought him fame and financial security: in addition to his professorship at Cambridge, Newton served for two years as a member of the Convention Parliament following the overthrow of King James II during the "Glorious Revolution" of 1688. In 1696 Newton was appointed warden, and later master, of the mint, a lucrative position he held until his death. In 1704 he was made president of the Royal Society, and in 1705 he received a knighthood from Queen Anne. While a member of Parliament, Newton came into contact with such luminaries as the philosopher John Locke and the diarist Samuel Pepys.
Newton's life was not without bitterness, however: a protracted controversy raged over whether Newton or Gottfried Wilhelm von Leibniz had been first in the invention of calculus, which strained scientific relations between England and the Continent. And, despite the Principia's enthusiastic reception, Newton's system would not be fully accepted among scientists and in university teaching until after his death.
Following his retirement from Cambridge in 1701, Newton prepared revised editions of the Principia (1713, 1726) and published his second great treatise, the Opticks, in 1704. He died in Kensington, England, on March 20, 1727.
Language Notes:
In 1656, following the death of her second husband, Newton's mother removed him from school and brought him back to Woolsthorpe with the idea of making her son a farmer. Newton's teacher at Grantham, recognizing the boy's talents, prevailed upon her to allow Newton to prepare for entrance to Cambridge University. He entered Trinity College, Cambridge, in 1661, under the tutelage of Isaac Barrow, Lucasian Professor of Mathematics, and took his degree four years later.
Between 1665 and 1667, Newton made great strides in his method of "fluxions" (an early form of differential calculus) and began work on gravitation. It was also at this time that Newton inaugurated his studies on the nature of light: he demonstrated that differences in color resulted from differences in refrangibility, i.e., the ability of a ray of light to bend when passed through a refracting medium. In 1667, Newton returned to Cambridge from Woolsthorpe (where he had gone to escape the plague); two years later he succeeded Barrow as Lucasian Professor. In 1672 Newton was elected to the Royal Society.
Newton's great work, Philosophiae naturalis principia mathematica, or The Mathematical Principles of Natural Philosophy (1687), grew out of his ongoing investigations into gravitation and planetary motion. Written over a period of only eighteen months, this book was immediately hailed as a masterpiece: it demonstrated how the law of gravitation could explain diverse phenomena, ranging from the tides to the irregularities of the moon's motion, and made possible a mathematical principle, unrealized up to that time, of the workings of a dynamic universe. Although Newton's system needed to be revised in the twentieth century in view of the theory of relativity and quantum mechanics, it remains valid for systems of ordinary dimensions, involving velocities that do not approach the speed of light.
Newton's contributions to science brought him fame and financial security: in addition to his professorship at Cambridge, Newton served for two years as a member of the Convention Parliament following the overthrow of King James II during the "Glorious Revolution" of 1688. In 1696 Newton was appointed warden, and later master, of the mint, a lucrative position he held until his death. In 1704 he was made president of the Royal Society, and in 1705 he received a knighthood from Queen Anne. While a member of Parliament, Newton came into contact with such luminaries as the philosopher John Locke and the diarist Samuel Pepys.
Newton's life was not without bitterness, however: a protracted controversy raged over whether Newton or Gottfried Wilhelm von Leibniz had been first in the invention of calculus, which strained scientific relations between England and the Continent. And, despite the Principia's enthusiastic reception, Newton's system would not be fully accepted among scientists and in university teaching until after his death.
Following his retirement from Cambridge in 1701, Newton prepared revised editions of the Principia (1713, 1726) and published his second great treatise, the Opticks, in 1704. He died in Kensington, England, on March 20, 1727.
Text: English (translation)
Original Language: Latin
Original Language: Latin
"About this title" may belong to another edition of this title.
- PublisherRarebooksclub.com
- Publication date2012
- ISBN 10 1236081528
- ISBN 13 9781236081520
- BindingPaperback
- Number of pages70
- Rating
(No Available Copies)
Search Books: Create a WantIf you know the book but cannot find it on AbeBooks, we can automatically search for it on your behalf as new inventory is added. If it is added to AbeBooks by one of our member booksellers, we will notify you!
Create a Want