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" After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles... "
Yale University Entrance Examinations in Mathematics: 1884 to 1898 - Page 125
1898 - 208 pages
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Psychology by Experiment

Linus Ward Kline, Frances Littleton Kline - Psychology - 1927 - 360 pages
...employed or methods used. Material. B. Common problems in algebra and geometry : 1. Prove that the sum of the three angles of a triangle is equal to two right angles. 2. Find two numbers such that twice the first plus three times the second is equal to 105 ; and three...
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The Evolution of Scientific Thought from Newton to Einstein

A. D'Abro - Relativity (Physics). - 1927 - 556 pages
...that no parallel geodesies can exist in Riemann's geometry. Likewise, whereas in Euclid's geometry the sum of the three angles of a triangle is equal to two right angles, in Riemann's geometry this sum is always greater than two right angles. This we could easily...
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Philosophical Writings of Peirce

Charles S. Peirce - Philosophy - 1955 - 424 pages
...inferences. Locke explains it as follows: After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles because he apprehends the geometrical proof, he thus continues: "But another man who never took...
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Non-Euclidean Geometry: A Critical and Historical Study of Its Development

Roberto Bonola - Mathematics - 1955 - 452 pages
...not differ materially from that of SACCHEEt. We shall rather show how LEGENDEE proves that the sam of the three angles of a triangle is equal to two right angles. Suppose that in the triangle ABC [cf. Fig. 29] ^A + <-# + -C C< 2 right angles. A point D heing...
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Great Moments in Mathematics (before 1650)

Howard Whitley Eves - History - 1983 - 292 pages
...would you choose? 1. The three altitudes of a triangle, produced if necessary, meet in a point. 2. The sum of the three angles of a triangle is equal to two right angles. 3. An angle inscribed in a circle is measured by half its intercepted arc. 4. The tangents...
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Writings of Charles S. Peirce: A Chronological Edition, Volume 1: 1857-1866

Charles S. Peirce - Literary Criticism - 1982 - 680 pages
...inferences. Locke explains it as follows: After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles because he apprehends the geometrical proof, he thus continues: But another man who never took...
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Foundations and Fundamental Concepts of Mathematics

Howard Whitley Eves - Mathematics - 1997 - 370 pages
...geometry, and why? (1) The three altitudes of a triangle, produced if necessary, meet in a point. (2) The sum of the three angles of a triangle is equal to two right angles. 2.1.2 A mathematics instructor is going to present the subject of geometric progressions to...
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The Cambridge History of Seventeenth-century Philosophy, Volume 1

Daniel Garber, Michael Ayers - Philosophy - 1998 - 992 pages
...act of affirming or denying are one and the same thing. When, for example, the mind affirms that the sum of the three angles of a triangle is equal to two right angles, that affirmation cannot exist or be thought without the idea of a triangle. Conversely, the...
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Algebra in Ancient and Modern Times

V. S. Varadarajan - Mathematics - 1998 - 164 pages
...than Euclid's Elements. Among the most famous of the theorems in the Elements are the following. The sum of the three angles of a triangle is equal to two right angles. The area of the square on the hypotenuse of a right angled triangle is equal to the sum of...
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Chance, Love, and Logic: Philosophical Essays

Charles Sanders Peirce - Philosophy - 1998 - 368 pages
...inferences. Locke explains it as follows: After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles because he apprehends the geometrical proof, he thus continues: " But another man who never...
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