Letters of Euler on Different Subjects in Natural Philosophy: Addressed to a German Princess. With Notes, and a Life of Euler, Volume 1

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Harper & Brothers, 1833 - Physics - 819 pages
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Page 339 - Thou shalt love the Lord thy God with all thy heart, with all thy soul, with all thy strength, and with all thy mind ; and the other, which is like unto it: Thou shalt love thy neighbour as thyself.
Page 260 - ... intelligent being ; and that the arrangement of all events was disposed in perfect harmony with all these circumstances. When, therefore, a man addresses to God a prayer worthy of being heard, it must not be imagined that such a prayer came not to the knowledge of God till the moment it was formed. That prayer was already heard from all eternity ; and if the Father of Mercies deemed it worthy of being answered, he arranged the world expressly in favour of that prayer, so that the accomplishment...
Page 193 - we are reduced to explain what is to be understood by the term matter, without which extension cannot be body. Now, the signification of these two terms is so much the same, that all body is matter, and all matter is body ; so that even now we have made no great progress. We easily discover, however, a general character, inseparable from all matter, and consequently pertaining to all bodies ; it is impenetrability, the impossibility of being penetrated by other bodies, or the impossibility that...
Page 72 - And rays which make such a number of vibrations in a second may, with equal propriety, be denominated red rays ; and finally, when the optic nerve is affected by these same rays, and receives from them a number of impulsions, sensibly equal, in a second, we receive the sensation of the red colour. Here every thing is clear ; and I see no necessity for in' traducing dark and mysterious phrases, which really mean nothing.
Page 35 - A string which vibrates 100 times in a second will give precisely the note C ; and if it vibrated only 50 times, the note would be lower or more flat. But with regard to our ear, there are certain limits beyond which sound is no longer perceptible. It would appear that we are incapable of determining either the sound of a string which makes less than 30 vibrations in a second, because it is too low ; or that of a string which would make more than 7552 in a second, because such a note would be too...
Page 189 - ... so that the effect is, nevertheless, the same in both cases. This last opinion is most satisfactory to those who are fond of clear principles in philosophy, as they do not see how two bodies at a distance can act •upon each other, if there be nothing between them.
Page 35 - This air is likewife too remote from terreftrial bodies to receive a communication of heat from them ; they act only upon fuch as are adjacent. Hence you will eafily perceive that the rays of the fun cannot produce any effect in regions of the air very much elevated above the furface of the earth ; and that the fame degree of cold...
Page 102 - ... the angle of reflection is always equal to the angle of incidence, the image for any point can be seen only in the reflected ray prolonged.
Page 257 - There remains only one objection more to be considered — namely, that it would have been better not to create such spirits, as God foresaw they must sink into criminality. But this far surpasses human understanding; for we know not whether the plan of the world could subsist without them. We know, on the contrary, by experience, that the wickedness of some men frequently contributes to the correction and amendment of others, and thereby conducts them to happiness. This consideration alone is sufficient...
Page 151 - But in attempting to dive into the mysteries of nature, it is of importance to know if the heavenly bodies act upon each other by impulsion, or by attraction; if a certain subtile invisible matter impels them towards each other ; or if they are endowed with a secret or occult quality, by which they are mutually attracted.