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 Βιβλία Βιβλία Any side of a triangle is less than the sum of the other two sides. Elements of Plane and Solid Geometry - Σελίδα 38
των George Albert Wentworth - 1877 - 398 σελίδες
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο ## Introduction and books 1,2

Euclid - 1908
...OM. Consider the point Jlf, one of those which follow M, such that AfAf is equal to tr. Then, because any side of a triangle is less than the sum of the other two, OM' <OM + MM'. But OM+ MM1 = OM + a- < R, whence OM' < R, which is absurd. A similar absurdity would... ## Exercises in Geometry

Grace Lawrence Edgett - 1909 - 81 σελίδες
...adjacent angles which one straight line makes with another are together equal to two right angles. 7. Any side of a triangle is less than the sum of the other two sides. 8. The difference between two sides of a triangle is less than the third side. 9. If lines AB and MN... ## Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - 1910 - 280 σελίδες
...shortest distance between two points is measured along the straight line-segment connecting them. Thus one side of a triangle is less than the sum of the other two. IV. // each of two figures is congruent to the same figure, they are congruent to each other. See §§... ## Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - 1910 - 263 σελίδες
...angles are respectively equal. Equiangular. Mutually Equiangular Triangles. PROPOSITION IV. THEOREM. 86. Any side of a triangle is less than the sum of the other tivo, and greater than their difference. Given any A ABC. To prove I. any side, as AC < AB + BC. II.... ## Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - 1910 - 280 σελίδες
...shortest distance between two points is measured along the straight line-segment connecting them. Thus one side of a triangle is less than the sum of the other two. IV. // each of two figures is congruent to the same figure, they are congruent to each other. See §§... ## College Entrance Examination Papers in Plane Geometry

1911 - 178 σελίδες
...hexagon, compute the ratio of the areas of the inscribed and the circumscribed circles. 6. Prove that any side of a triangle is less than the sum of the other two, and greater than their difference. 8. The perimeter of a square is b meters, compute the perimeters... ## The Teaching of Geometry

David Eugene Smith - 1911 - 339 σελίδες
...moves figures without deformation, but states no postulate on the subject ; and be proves that one side of a triangle is less than the sum of the other two sides, when he might have postulated that a straight line is the shortest path between two points. Indeed,... ## LECTURES ON FUNDAMENTAL CONCEPTS OF ALGEBRA AND GEOMETRY

JOHN WESLEY YOUNG - 1911
...a triangle are unequal, the greater angle is opposite the greater side, and conversely; also, each side of a triangle is less than the sum of the other two. However, it is not possible to prove the following fundamental theorem : There exists a triangle whose... ## Advanced Calculus: A Text Upon Select Parts of Differential Calculus ...

Edwin Bidwell Wilson - 1911 - 280 σελίδες
...and ß are two complex numbers, the rule |«|-f|/3| = |« + /3| is a consequence of the fact that one side of a triangle is less than the sum of the other two. If the absolute value is given and the initial end of the vector is fixed, the terminal end is thereby... ## Elements of Solid Geometry

William Herschel Bruce, Claude Carr Cody - 1912 - 110 σελίδες
...intersect, the vertical angles are equal. 85. In congruent figures homologous parts are equal. 86. Any side of a triangle is less than the sum of the other two, and greater than their difference. 91. Two triangles are congruent if they have two sides and the included...