Letters of Euler on Different Subjects in Physics and Philosophy: Addressed to a German PrincessMurray and Highley, 1802 - Science |
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Common terms and phrases
agitation angle attraction becauſe cafe caufe cauſe cife colours conclufion confequently confiderable confifts diminiſhed diſcovered diſtance diſtinguiſh eafily earth elaſticity eſtabliſhed EULER exift exiſtence expreffed faid fame thing fcience fecond fenfation fenfes fenfible fhall fhould fimilar fimple firft firſt folar fome force foul fpirits ftate ftill ftraight fubftance fubject fubtile fuch fufficient furface fyftem fyllogifm glaſs gravity greater greateſt heavenly bodies himſelf idea impoffible impreffion increaſe itſelf juſt lefs leſs LETTER light likewife luminous meaſure moft moon moſt motion mufic muft muſt neceffary obferve object octave opaque bodies pafs particles perfons philofophers planets poffible prefent preferve produce propofition queſtion rays rays of light reafon reflected refpect refracted ray refraction reft refult repreſent retina ſee ſmall ſmaller ſpace ſtate ſtill ſtraight line thefe themſelves theſe thofe thoſe tion tranſparent unifon univerfal unleſs uſe velocity vibrations whofe
Popular passages
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 340 - 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 60 - ... to us, and even far beyond the height of the loftieft mountains, is a mere nothing, compared to the diftance of the fun, which is about thirty millions of miles.* This is, therefore, a very important difficulty, which we muft endeavour to folve. For this purpofe I begin with remarking, that the rays of the fun do not communicate heat to any bodies, but fuch as do not grant them a free paffage.
Page 174 - What hands are here ? ha ! they pluck out mine eyes. Will all great Neptune's ocean wash this blood Clean from my hand ? No, this my hand will rather The multitudinous seas incarnadine, Making the green one red.
Page 339 - 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 94 - 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 xvi - ... 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 31 - Thus two notes which differ an octave, excite a perception of the relation of i to 2 ; a fifth, of that of 2 to 3 ; and a greater third, of that of 4 to 5. We comprehend then the order which is found in harmony, when we know all the relations which pervade the notes of which it is compofed, and it is the perception of the ear which leads to this knowledge.
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 337 - ... were all good : for time is requisite to the formation of evil inclinations: there is, therefore, no difficulty in affirming that God created spirits. But it being the essence of spirits to be free, and liberty not being capable of subsisting without a power to sin, to create a spirit possessed of the power of sinning has nothing inconsistent with divine perfection, because a spirit could not be created destitute of that power. God has...