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Page 311 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 309 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Page 310 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
Page 310 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, is equal to the square of the line which touches it.
Page 310 - IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Page 151 - That he is properly certified as free from any physical defect or disease which would be likely to interfere with the proper discharge of his duties ; Third.
Page xxviii - Indeed, early superiority in literature and science generally indicates the existence of some qualities which are securities against vice, industry, self-denial, a taste for pleasures not sensual, a laudable desire of honourable distinction, a still more laudable desire to obtain the approbation of friends and relations. We, therefore, think that the intellectual test about to be established will be found in practice to be also the best moral test that can be devised.
Page 276 - But it must be remembered, that life consists not of a series of illustrious actions, or elegant enjoyments; the greater part of our time passes in compliance with necessities, in the performance of daily duties, in the removal of small inconveniences, in the procurement of petty pleasures ; and we are well or ill at ease, as the main stream of life glides on smoothly, or is ruffled by small obstacles and frequent interruption.
Page 278 - But my pride was soon humbled, and a sober melancholy was spread over my mind, by the idea that I had taken an everlasting leave of an old and agreeable companion, and that, whatsoever might be the future date of my history, the life of the historian must be short and precarious.