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Algebra AMERICAN MATHEMATICAL MONTHLY Arithmetic Astronomy axioms axis B. F. Finkel B. M. ZERR Bolyai Calculus Chemistry and Physics Chester High School circle curve Defiance College diameter distance ellipse equal equation Euclid Euclidean Euclidean geometry F. P. MATZ feet Finkel not later formula Franz Schmidt frustum Gauss given gives Hagerstown Hence inches integral intersection J. M. Colaw J. W. YOUNG Leland Stanford Jr mathematicians Mathematics and Astronomy Mathematics and Science method Non-Euclidean Geometry Ohio ol Mathematics Oolaw not later parallel particle perpendicular Philadelphia plane problems Professor of Chemistry Professor of Mathematics Professor ol Proposed by F. P. prove radius random rational result right angles right triangle roots SCHEFFER sent to B. F. sides Solution solved space sphere square straight line substitutions surface tangent Temple College theorem theory University vector velocity vertices Whence
Page 124 - propositions already proved by Euclid without it? Euclid, demonstrated things more axiomatic by far. He proves what every dog knows . that any two sides of a triangle are together greater than the third. Yet after he has finished his demonstration, that straight lines making with
Page 201 - I enjoy here," said Goethe, "both good days and good nights. Often before dawn I am already awake, and lie down by the open window to enjoy the splendor of the three planets, which are at present to be seen together, and to refresh myself with the increasing brilliancy of the morning red,
Page 204 - I enjoy here," said Goethe, "both good days and good nights. Often before dawn I am already awake, and lie down by the open window, to enjoy the splendor of the three planets, which are at present to be seen together, and to refresh myself with the increasing brilliancy of the morning-red.
Page 252 - I have hit upon promises me with certainty the attainment of the goal, if it in general is attainable. It is not yet attained, but I have discovered such magnificent things that I am myself astonished at them. It would be damage eternal if they were lost. When
Page 110 - Legendre proved that the sum of the angles of a triangle can never exceed two right angles, and that if there is a single triangle in which this sum is equal to two right angles, the same is true of all triangles. This was, of course, on the supposition that a line is of infinite length.
Page 130 - It is assumed, that a straight line may be drawn from any one point to any other point.
Page 126 - I have discovered such magnificent things that I am myself astonished at them. It would be damage eternal if they were lost. , When you see them, my father, you yourself will acknowledge it. Now I cannot say more, only so much
Page 56 - did not comprehend it or immediately forgot it, and went on with his work. After some little time, the servant came again to say that his mistress was much worse, and to beg that he would come to her at once; to which he replied : 'I will come presently.