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Page 13 - How many things are there which a man cannot, with any face or comeliness, say or do himself! A man can scarce allege his own merits with modesty, much less extol them ; a man cannot sometimes brook to supplicate or beg; and a number of the like. But all these things are graceful in a friend's mouth, which are blushing in a man's own.
Page 13 - Men have their time, and die many times in desire of some things which they principally take to heart; the bestowing of a child, the finishing of a work, or the like. If a man have a true friend, he may rest almost secure that the care of those things will continue after him.
Page 13 - If the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Page 10 - IF two triangles have two sides of the one equal to two sides of the other, each to each, and have likewise their bases equal; the angle which is contained by the two sides...
Page 16 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Page 11 - ... subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle ACB, and from the point A let AD be drawn perpendicular to BC produced.
Page 9 - Next, it is evident, that what had its being and beginning from another, must also have all that which is in, and belongs to its being, from another too. All the powers it has must be owing to, and received from, the same source. This eternal source then of all being must also be the source and original of all power; and so this eternal being must be also the most powerful.
Page 11 - If a straight line be divided into any two parts, four times the rectangle contained ~by the whole line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made up of the whole and that part.
Page 13 - A greater magnitude is said to be a multiple of a less, when the greater is measured by the less ; that is, ' when the greater contains the less a certain number of times exactly.' 3. ' Ratio is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity.
Page 7 - The first time I was in company with Foote was at Fitzherbert's. Having no good opinion of the fellow, I was resolved not to be pleased ; and it is very difficult to please a man against his will. I went on eating my dinner pretty sullenly, affecting not to mind him. But the dog was so very comical, that I was obliged to lay down my knife and fork, throw myself back upon my chair, and fairly laugh it out. No, sir, he was irresistible.