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If one considers further the other pieces H of the wave AC, it appears that they will not only have reached the surface AB by straight lines HK parallel to CB, but that in addition they will have generated in the transparent air, from the centres K, K, K, particular spherical waves, represented here by circumferences the semi-diameters of which are equal to KM, that is to say to the continuations of HK as far as the line BG parallel to AC. But all these circumferences have as a common tangent the straight line BN, namely the same which is drawn from B as a tangent to the first of the circles, of which A is the centre, and AN the semi-diameter equal to BC, as is easy to see.
For the athlete is the product of nature a step towards the more perfect type of animal, while the scholar is the outcome of artificiality. What, I ask, does the scholar gain, either morally or physically, or in any other way, by knowing who was tribune of the people in 284 BC or what is the precise difference between the various constructions of cum?
Some time between 12,000 and 8,000 BC, women must have discovered that by sowing the seeds of these grains they could reduce the amount of time required to gather fruits and vegetables. In so doing they allowed sedentary life in organized cities to emerge.
The two lines AB and BC are the French and British armies lying behind the Sambre, γβ, and the Middle Meuse, βδ, respectively; but the line of the Sambre ceases to protect eastward along the dotted line αγ beyond the point up to which the river forms a natural obstacle, while from K to B the line is protected by the river Sambre itself.
Apply the template to both faces of the side in turn, with its corner A at the line below the rung, and DE flush with the upper corner. When all the notches have been marked cut down the AC line of each with a tenon saw, and chisel along BC till the wedge-shaped chip is removed. Finish off every notch as neatly as possible, so that the rungs may make close contact and keep water out.
In the demonstration it is to be observed that, since the arc BC falls within the glass, there must be conceived an arc RX, concentric with it and on the other side of QD. Then after it shall have been shown that the piece G of the wave GT arrives at D at the same time that the piece T arrives at Q, which is easily deduced from the construction, it will be evident as a consequence that the partial wave generated at the point D will touch the arc RX at the moment when the piece Q shall have come to R, and that thus this arc will at the same moment be the termination of the movement that comes from the wave TG; whence all the rest may be concluded.
It is to be shown that the time of passage of light along AB and BC taken together, is the shortest that can be. Let us assume that it may have come by other lines, and, in the first place, along AF, FC, so that the point of refraction F may be further from B than the point A; and let AO be a line perpendicular to AB, and FO parallel to AB; BH perpendicular to FO, and FG to BC.
By far the larger portion of this last class and several instances in the second it seems most reasonable to refer to the habit of quoting from memory. A very remarkable case of combination is found in 36 BC, where a single quotation is made up of a cento of no less than six separate passages taken from all three Synoptic Gospels and in the most broken order.
That is to say that if the ray AB in entering the transparent body is refracted into BC, then likewise CB being taken as a ray in the interior of this body will be refracted, on passing out, into BA.
Taking, then, the parallelopiped AFB, of which the obtuse solid angle C is contained between the three equal plane angles, and imagining in it the three principal sections, one of which is perpendicular to the face DC and passes through the edge CF, another perpendicular to the face BF passing through the edge CA, and the third perpendicular to the face AF passing through the edge BC; I knew that the refractions of the incident rays belonging to these three planes were all similar.
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