| 单词 | plane geometry |
| 例句 | But in the eleventh grade, I got good scores in plane geometry from the start. October Sky 1999-04-01T00:00:00Z All through the fall, I thumbed over to War every Sunday afternoon so Dorothy and I could work on plane geometry. October Sky 1999-04-01T00:00:00Z “Yes. I just have to work the same sort of plane geometry to find another point not labeled on our map.” The Smartest Kid in the Universe 2020-12-01T00:00:00Z One night, when I was having one of these visions, I had the startling revelation that plane geometry was, in fact, a message from God. October Sky 1999-04-01T00:00:00Z “What do you know about imaginary numbers, plane geometry, and vector algebra, Jake?” The Smartest Kid in the Universe 2020-12-01T00:00:00Z Unfazed, I presented my revelation that in the principles and theorems and axioms of plane geometry—these truths that stayed true across the universe—God had sent us a message. October Sky 1999-04-01T00:00:00Z “It’s just a very challenging plane geometry problem. How do we find ‘X’ without knowing ‘A’? I may need to ask an expert for help.” The Smartest Kid in the Universe 2020-12-01T00:00:00Z But their boxes, X-shapes and intersecting lines are as eternal as plane geometry. In the galleries: Anything but simplicity in these drawings 2015-07-02T04:00:00Z He learned in part by drawing biology and plane geometry projects and whatever else the teachers asked for. Benny Andrews: A Life in Portraits 2020-12-03T05:00:00Z The treatise contains 13 separate books, covering everything from plane geometry, the Pythagorean theorem, golden ratio, prime numbers, and quite a bit more. One of the world’s most influential math texts is getting a beautiful, minimalist edition 2017-09-02T04:00:00Z In 1952, my plane geometry book was a tattered volume first used by white students in 1935, the year I was born. The Power of Movies to Change Our Hearts 2017-02-18T05:00:00Z And these two theorems are perfectly fair types of upwards of one hundred sixty or seventy propositions comprising Euclid's books on plane geometry. The Teaching of Geometry 2011-10-12T02:00:52.133Z Of these the first four and the sixth are devoted to “plane geometry,” as the investigation of figures in a plane is generally called. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z The student who has studied plane geometry should be able to prove that one half of the angle between these lines is equal to the altitude of the star. A Text-Book of Astronomy 2011-01-05T03:00:57.347Z Are these beings able to regard the geometry of their universe as being plane geometry and their rods withal as the realisation of "distance" ? Relativity: The Special and General Theory She was a quiet girl who was designed like a tall problem in plane geometry. At Good Old Siwash Once a class has fairly got into Book I, if the interest in the subject can be maintained, there are only the incidental difficulties of logical advance throughout the plane geometry. The Teaching of Geometry 2011-10-12T02:00:52.133Z Euclidean interpretation of hyperbolic plane geometry, his results will be stated at some length14. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z Candidates for admission must be at least seventeen years of age, and must pass satisfactory examinations in algebra, plane geometry, either French or German, English, history, and either advanced algebra or solid geometry. The Brochure Series of Architectural Illustration, Volume 01, No. 06, June 1895 Renaissance Panels from Perugia The course of study not infrequently embraced such subjects as physiology, physics, and plane geometry. A Social History of the American Negro Being a History of the Negro Problem in the United States. Including A History and Study of the Republic of Liberia Far from the Higher Space Hypothesis complicating thought, it simplifies by synthesis and co-ordination in a manner analogous to that by which plane geometry is simplified when solid geometry becomes a subject of study. Four-Dimensional Vistas But the introduction to plane geometry is not so easily disposed of. The Teaching of Geometry 2011-10-12T02:00:52.133Z The Saggio shows that Lobatchewsky’s plane geometry holds in Euclidean geometry on surfaces of constant negative curvature, straight lines being replaced by geodesics. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z Instructional tests in plane geometry; revised edition and key and directions for scoring. U.S. Copyright Renewals, 1977 January - June Examination for admission to the United States Naval Academy: plane geometry and trigonometry. U.S. Copyright Renewals, 1974 July - December SEE Goff, Robert R. Work and test book in plane geometry. U.S. Copyright Renewals, 1958 January - June Indeed, it is desirable all through plane geometry to refer incidentally to solid geometry. The Teaching of Geometry 2011-10-12T02:00:52.133Z This last fact illustrates the necessity, which is also forced on plane geometry by three-dimensional considerations, of treating all points at infinity in a plane as lying on a single straight line. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z "English grammar, English composition, algebra through quadratic equations, plane geometry, descriptive geography, physical geography, United States history and the outlines of general history." Go Ahead Boys and the Racing Motorboat Why is it that Pascal, when twelve years old, succeeded in discovering for himself the greater part of plane geometry. Five Lectures on Reincarnation Are these beings able to regard the geometry of their universe as being plane geometry and their rods withal as the realisation of " distance " ? Relativity : the Special and General Theory This proposition may be omitted as far as its use in plane geometry is concerned, for we can prove the next proposition here given without using it. The Teaching of Geometry 2011-10-12T02:00:52.133Z In plane geometry, reckoning the line as a curve of the first order, we have only the point and the curve. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z All which makes it evident our pure intelligence could never attain to know so much as the first elements of plane geometry. A Essay Towards a New Theory of Vision These dwellers in "flatland" could construct a plane geometry which would be exactly like ours in being based on the axioms of Euclid. Side-Lights on Astronomy and Kindred Fields of Popular Science For the fourth class the studies are plane geometry, trigonometry, descriptive geometry, and fencing, including the use of the small-sword, broad- sword, and bayonet. The Colored Cadet at West Point Autobiography of Lieut. Henry Ossian Flipper, first graduate of color from the U. S. Military Academy It is advisable to cut through the figure along the given straight line, and see that we come back to the corresponding proposition in plane geometry. The Teaching of Geometry 2011-10-12T02:00:52.133Z The student should always have his attention called to the analogue in plane geometry, where there is one. The Teaching of Geometry 2011-10-12T02:00:52.133Z Euclid's one hundred seventy-three propositions of plane geometry were really upwards of one hundred eighty, because he several times combined two or more in one. The Teaching of Geometry 2011-10-12T02:00:52.133Z The theorem is one of the three most important propositions in plane geometry, the other two being the so-called Pythagorean Theorem, and a proposition relating to the proportionality of the sides of two triangles. The Teaching of Geometry 2011-10-12T02:00:52.133Z There have been numerous suggestions with respect to solid geometry, to the effect that it should be more closely connected with plane geometry. The Teaching of Geometry 2011-10-12T02:00:52.133Z In case the reason is not clear, let some student try to apply the proof used in plane geometry. The Teaching of Geometry 2011-10-12T02:00:52.133Z By changing "plane" to "line," and by making other obvious changes to correspond, this reduces to the analogous proposition of plane geometry. The Teaching of Geometry 2011-10-12T02:00:52.133Z In plane geometry it is easily proved that if two circles intersect, the tangents from any point on their common chord produced are equal. The Teaching of Geometry 2011-10-12T02:00:52.133Z As a result, it prepared a syllabus arranged by topics, the propositions of solid geometry being grouped immediately after the corresponding ones of plane geometry. The Teaching of Geometry 2011-10-12T02:00:52.133Z The other definitions of plane geometry need not be discussed, since all that have any historical interest have been considered. The Teaching of Geometry 2011-10-12T02:00:52.133Z Besides calling attention to the corresponding proposition of plane geometry, it is well now to speak of the fact that in propositions involving planes and lines we may often interchange these words. The Teaching of Geometry 2011-10-12T02:00:52.133Z Here again we may cut through the figure by the plane of the two parallels, and we get the figure of plane geometry relating to lines that are perpendicular to the same line. The Teaching of Geometry 2011-10-12T02:00:52.133Z This postulate is not so essential, however, as the one about the circle, because we are not so concerned with constructions here as we are in plane geometry. The Teaching of Geometry 2011-10-12T02:00:52.133Z Here again we may form a corresponding proposition of plane geometry by passing a plane through any three points of contact of the sphere and the tetrahedron. The Teaching of Geometry 2011-10-12T02:00:52.133Z Not until 1844 did Harvard require any plane geometry for entrance. The Teaching of Geometry 2011-10-12T02:00:52.133Z Questions like the following may be asked in connection with the proposition: What is the corresponding proposition in plane geometry? The Teaching of Geometry 2011-10-12T02:00:52.133Z Moreover, numerous attempts had been made at Athens to do exactly what Euclid succeeded in doing,—to construct a logical sequence of propositions; in other words, to write a textbook on plane geometry. The Teaching of Geometry 2011-10-12T02:00:52.133Z It seems to reduce the propositions to be proved in plane geometry to about one hundred fifteen, and it recommends the omission of the incommensurable case. The Teaching of Geometry 2011-10-12T02:00:52.133Z As to the fusion of trigonometry and plane geometry little need be said, because the subject is in the doctrinaire stage. The Teaching of Geometry 2011-10-12T02:00:52.133Z The East teaches plane geometry more thoroughly, but allows a pupil to enter college or to go into business with no solid geometry. The Teaching of Geometry 2011-10-12T02:00:52.133Z Here, again, it is desirable to ask for the corresponding proposition of plane geometry, and to ask why the proof of that proposition will not suffice for this one. The Teaching of Geometry 2011-10-12T02:00:52.133Z Given a year to the subject, it is possible to do little more than cover plane geometry; with a year and a half the solid geometry ought easily to be covered also. The Teaching of Geometry 2011-10-12T02:00:52.133Z According to De Morgan's plan, plane geometry consisted of three books, the number of propositions being as follows: Book I. Rectilinear figures 60 Book II. The Teaching of Geometry 2011-10-12T02:00:52.133Z The arrangement of the work and the number of propositions in plane geometry are as follows: Book I. The straight line 51 Book II. The Teaching of Geometry 2011-10-12T02:00:52.133Z In general, if we cut through any figure of solid geometry in some particular way, we are liable to get the figure of a proposition in plane geometry, as will frequently be seen. The Teaching of Geometry 2011-10-12T02:00:52.133Z It may interest some of the pupils to draw this general figure, analogous to the one in plane geometry. The Teaching of Geometry 2011-10-12T02:00:52.133Z The figure suggests the case of two circles in plane geometry. The Teaching of Geometry 2011-10-12T02:00:52.133Z |
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