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Letters of Euler to a German Princess, on Different Subjects in Physics and ...
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according agitation angle appear attraction become called cause centre certain colours common concluded consequently consider considerable contains continue determined direction distance earth effect elasticity employed equal ether Euler example exist experience expressed extremely fall fame feet figure fluid force foul give glass gravity greater heat Hence idea illuminated it's knowledge less LETTER light likewise luminous manner mass matter means miles minute mirror moon motion move nature necessary object observe octave once opaque bodies particles pass perfect perfectly philosophers planets plate possible present principles produce proportion proposition rays reason receive reflected refraction remain remarked render represent respect rest similar simple smaller soul sound space spirit substance surface take place term thing tion transparent truth universe vibrations weight whole
Page 336 - 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 should be a consequence of the natural course of events.
Page 123 - Sthly, the angle RCF, or SCF, formed by the refracted CR or CS, with the perpendicular CF, is called the angle of refraction. Therefore, because of the bending which the ray of light undergoes, the angle of refraction is not equal to the angle of incidence PCE ; for producing the line PC to Q, the angles PCE and FCQ, being vertical, are equal to each other (Euclid's Elements, Book I., Prob. 15), as you will easily recollect. The angle QCF, then, is equal to the angle of incidence PCE ; therefore...
Page 335 - He hath given us. Philosophy, on the other hand, instructs us that all events take place in strict conformity to the course of Nature, established from the beginning, and that our prayers can effect no change whatever, unless we pretend to expect that God should be continually working miracles in compliance...
Page 96 - According to this opinion, we see the moon and the planets only by the rays of the sun which they reflect; and you must frequently have heard it affirmed, that the light of the moon is a reflection of the light of the sun. In the same manner. say they, the rays of the sun are reflected by the first opaque bodies which are exposed to them, on other bodies of the same nature, and undergo a series of similar reflections, till they are entirely weakened. But however plausible this opinion may at first...
Page 63 - If the water be very deep, fo that the .rays cannot penetrate to the bottom, it has no perceptible heat, though the fun bears upon it. As air is a very tranfparent body to a much higher degree than...
Page 207 - 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.
Page xviii - ... of the ftudy of the elegant and amufing poetical fictions of Antiquity. Without meaning to decry this, may I not be permitted to hint, that it might be of importance frequently to recall young minds from an ideal world, and its ideal inhabitants, to the real world, of which they are a part, and of which it is a fhame to be ignorant. Let your pupil, by all means, read the poets ; let him read Ovid, and, after he has amufed himfelf with the golden age of old Saturn, lead him out into the open firmament...
Page 334 - 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 to justify the existence of evil spirits. And as God has all power over the consequences of human wickedness, every one may rest assured, that in conforming to the...
Page 303 - ... qualities in the highest degree is GOD. There is, then, an infinite difference between body and spirit. Extension, inertia, and impenetrability — qualities which exclude all thought — are the properties of body ; but spirit is endowed with the faculty of thinking;, of judging, of reasoning, of feeling, of reflecting, of willing, or of determining in favour of one object preferably to another. There is here neither extension, nor inertia, nor impenetrability ; these material qualities are...
Page 64 - 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...