...be either in the same plane or not, and if the three rectangles AB . CD. AC . DB, AD . BC be taken ; the sum of any two of them is greater than the third, except when the points lie on the circumference of a circle. Solution by PBOFESSOB CATLKT. Write for...

...It is manifest from the above that three forces acting on a point cannot be in equilibrium, unless the sum of any two of them is greater than the third. 40. Polygon of Forces.—If any number of forces acting at a point be represented in magnitude and...

...their intersection; prove that this straight line is perpendicular to the other plane. 3. Prove that if a solid angle is formed by three plane angles, the sum of either two of these angles is greater than the third. 4. Prove that sections of a pyramid made by parallel...

...preceding definitions. (1) The three moments of inertia A, B, C about three rectangular axes are such that the sum of any two of them is greater than the third. (2) The sum of the moments of inertia about any three rectangular axes meeting at a given point is...

...— — J î — 5.+ \ > ^ . A+c — я ' í+a — о я+о — г a+o+f 13. If a, A. i be such that the sum of any two of them is greater than the third ; shew that= 4.- =4. — —. > 3. A+c — а с-\-л — b' a+b — с XXVI. 11 1 Î. Ifa4- =landc+-...

...1 ,+-¡4 — > -pr — • b+c — a ' c+ a — 4 ' a+b — e a+b + c 13. If a, b, с be such that the sum of any two of them is greater than the third ; shew that; — - — _i_ - - 4. — ' — >з. b+c— <j^c+a— b^ a+b— e XXVI. 1. If e+ \ = 1...

...transmission of force. 3. Enunciate and prove the parallelogram of forces. Tf three forces are in equilibrium, the sum of any two of them is greater than the third. 4. If 0 be a point within a triangle ABC, and D, E, F, the middle points of the sides, the forces represented...

...EXAMPLE 72. In an acute-angled triangle similar figures are similarly described on the sides, show that the sum of any two of them is greater than the third. Fig. 125. Art. 161. PROPOSITION XLVII. (Eue. VI. 25.) ENUNCIATION. To describe a rectilineal figure...

...respectively; to the ends of the cords are attached the weights W, W], and JF 2 , so proportioned that the sum of any two of them is greater than the third. Each of the weights will produce a corresponding tension in its cord, and when, under the action of...

...triangles in general. Of course, any three rational numbers can be the sides of a triangle, provided the sum of any two of them is greater than the third. Thus a "rational triangle" should be one that is rational not only in its side lengths, but also in...