Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory, and N. Bosworth assisted by other gentlemen of eminence, Volume 5

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Page 16 - 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 13 - 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 19 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Page 14 - ... 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 10 - 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 14 - 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 16 - 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 6 - 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.

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