A Mathematical Solution Book Containing Systematic Solutions to Many of the Most Difficult Problems: Taken from the Leading Authors on Arithmetic and Algebra, Many Problems and Solutions from Geometry, Trigonometry and Calculus, Many Problems and Solutions from the Leading Mathematical Journals of the United States, and Many Original Problems and Solutions
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Page 378 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Page 410 - Two triangles which have an angle of the one equal to an angle of the other may be placed with their equal angles in coincidence. Let ABC, ADE, be the two triangles having the common angle A ; then, ABC AB X AC...
Page 474 - And you, ye undevelopable scrolls ! Above the host wave your emblazoned rolls, Ruled for the record of his bright inventions. Ye Cubic surfaces ! by threes and nines Draw round his camp your seven-and-twenty lines — The seal of Solomon in three dimensions.
Page 196 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 453 - Dimensions," in which he shows, for instance, that if a fourth dimension were added to space, a closed material surface (or shell) could be turned inside out by simple flexure without either stretching or tearing.
Page 371 - Now the mathematics are peculiarly well adapted for this purpose, on the following grounds : 1. Every term is distinctly explained, and has but one meaning, and it is rarely that two words are employed to mean the same thing. 2. The first principles are self-evident, and, though derived from observation, do not require more of it than has been made by children in general. 3. The demonstration is strictly logical, taking nothing for granted except the self-evident first principles, resting nothing...
Page 453 - He was awarded the Gold Medal of the Royal Astronomical Society in 1954.
Page 359 - The hour and minute hands of a watch are together at 12 o'clock ; when are they next together ? Ans.