Commentaries on the Principia of sir Isaac Newton respecting his theory ... of the gravitation of the planets, by the author of 'A new theory of gravitation'.1846 |
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Página 25
... continually approach their parallels AD and A F , in which case this corollary would have been very well de- monstrated , for if F B be always equal to A D , in every part of their approach to each other , it is quite certain that when ...
... continually approach their parallels AD and A F , in which case this corollary would have been very well de- monstrated , for if F B be always equal to A D , in every part of their approach to each other , it is quite certain that when ...
Página 28
... continually approach to similitude and equality ad infinitum as в approaches A , they must become similar and equal when в coincides with A. But neither the construction nor the diagram illustrate the proposition ; for according to the ...
... continually approach to similitude and equality ad infinitum as в approaches A , they must become similar and equal when в coincides with A. But neither the construction nor the diagram illustrate the proposition ; for according to the ...
Página 35
... continually approach towards similarity , and therefore when they coin- cide in A , they become altogether similar , and are to each other in the duplicate ratio of their homologous sides . But the ques- tion recurs , what useful ...
... continually approach towards similarity , and therefore when they coin- cide in A , they become altogether similar , and are to each other in the duplicate ratio of their homologous sides . But the ques- tion recurs , what useful ...
Página 36
... continually diminished , are , in the very beginning of the motion , one to the other in the duplicate ratio of the times . " Let the times be represented by the lines a d , a E , ( see the last diagram , ) and the velocities generated ...
... continually diminished , are , in the very beginning of the motion , one to the other in the duplicate ratio of the times . " Let the times be represented by the lines a d , a E , ( see the last diagram , ) and the velocities generated ...
Página 42
... continually less and less than o ; which is absurd . The eleventh , which is the concluding lemma in this section , does not affect the question in controversy , and therefore does not demand any comment . On the whole , Newton does not ...
... continually less and less than o ; which is absurd . The eleventh , which is the concluding lemma in this section , does not affect the question in controversy , and therefore does not demand any comment . On the whole , Newton does not ...
Otras ediciones - Ver todas
Commentaries on the Principia of Sir Isaac Newton Respecting His Theory ... Joseph Denison Sin vista previa disponible - 2020 |
Commentaries On the Principia of Sir Isaac Newton Respecting His Theory ... Joseph Denison Sin vista previa disponible - 2023 |
Commentaries on the Principia of Sir Isaac Newton Respecting His Theory ... Joseph Denison Sin vista previa disponible - 2016 |
Términos y frases comunes
A B and A D aphelion approach arc A C B arcs described arcs directly areas A B D centre centri centrifugal force centripetal forces chord circle circular Commentaries Corol demon described in equal duplicate ratio earth elliptical orbit enunciated and demonstrated Euclid evanescent quantities existing quantities force of gravitation forces are inversely further planet gravitating forces homologous sides hypothesis impulse inference Kepler's Analogy length line A D mean distances monstrated nascent and evanescent nearer planet Newton Newton's theory obvious ordinates D B periodic petal forces pheno Principia Prop R A D radii inversely radius ratio compounded ratio of equality rectilinear areas remote points revolving body rollary scholium seventh lemma simple ratio Sir Isaac Newton sixth Corollary square-roots squares strate stration subduplicate ratio tances tangent tical triangles ultimate ratio vanish velocities versed sines wherefore
Pasajes populares
Página 36 - LEMMA X. THE SPACES WHICH A BODY DESCRIBES BY ANY FINITE FORCE URGING IT, WHETHER THAT FORCE IS DETERMINED AND IMMUTABLE, OR IS CONTINUALLY AUGMENTED OR CONTINUALLY DIMINISHED, ARE IN THE VERY BEGINNING OF THE MOTION ONE TO THE OTHER IN THE DUPLICATE RATIO OF THE TIMES. Let the times be represented by the lines AD, AE, and the velocities generated in those times by the ordinates DB, EC.
Página 46 - Join SC, and, because SB and Cc are parallel, the triangle SBC will be equal to the triangle SBc, and therefore also to the triangle SAB. By the like argument, if the centripetal force acts successively in C, D...
Página 26 - BF parallel to the tangent, always cutting any right line AF passing through A in F, this line BF will be ultimately in the ratio of equality with the evanescent arc ACB; because, completing the parallelogram AFBD, it is always in a ratio of equality with AD. COR. 2. And if through B and A more right lines are drawn, as BE, BD, AF, AG, cutting the tangent AD and its parallel BF; the ultimate ratio of all the abscissas AD, AE, BF, BG, and of the chord and arc AB, any one to any other, will be the...
Página 47 - SAFS, of those areas, are one to the other as the times in which they are described. Now let the number of those triangles be augmented, and their breadth diminished in infinitum; and (by Cor.
Página 45 - THE AREAS, WHICH REVOLVING BODIES DESCRIBE BY RADII DRAWN TO AN IMMOVABLE CENTRE OF FORCE DO LIE IN THE SAME IMMOVABLE PLANES, AND ARE PROPORTIONAL TO THE TIMES IN WHICH THEY ARE DESCRIBED.
Página 46 - E, &c., and makes the body, in each single particle of time, to describe the right lines CD, DE, EF, &c. , they will all lie in the same plane; and the triangle SCD will be equal to the triangle SBC, and SDE to SCD, and SEF to SDE. And therefore, in equal times, equal areas are described in one immovable plane: and, by composition, any sums SADS, SAFS, of those areas, are one to the other as the times in which they are described.
Página 27 - RAD, and the points A and B approach and meet, I say that the ultimate form of these evanescent triangles is that of similitude, and their ultimate ratio that of equality.
Página 91 - That the squares of the times of the revolutions of the planets are as the cubes of their mean distances from the sun.
Página 46 - THE TIMES IN WHICH THEY ARE DESCRIBED. For suppose the time to be divided into equal parts, and in the first part of that time let the body by its innate force describe the right line AB. In the second part of that time, the same would (by Law...
Página 82 - ... 72333, 38710. Their distances, according to Kepler and Bullialdus, scarcely differ by any sensible quantity, and where they differ most the distances drawn from the periodic times fall in between them. That the circum-terrestrial force likewise decreases in the duplicate proportion of the distances, I infer thus. The mean distance of the moon from the centre of the earth, is, in semi-diameters of the earth, according to...