...angles. When two of the diedral angles are equal, it is called isohedral, PROP. 1. If a polyhedral angle be contained by three plane angles, the sum of any two of these angles will be greater than the third. It is unnecessary to demonstrate this proposition, except...

...will be measured by AB, BC, CA, the sides of the spherical triangle. But when a solid angle is formed by three plane angles, the sum of any two of them is greater than the third (Prop. XVII., B. VII.); hence any two of the arcs AB, BC, CA must be greater than the third. Therefore,...

...will be measured by AB, BC, CA, the sides of the spherical triangle. But when a solid angle is formed by three plane angles, the sum of any two of them is greater than the third (Prop. XVII., B. VII.) ; hence any two of the arcs AB, BC, CA must b greater than the third. Therefore,...

...edges, the indefinite space bounded by them is called a polyhedral prismatic space. PROPOSITION I. If a solid angle be contained by three plane angles, the sum of any two of these angles will be greater than the third. It is unnecessary to demonstrate this D proposition except...

...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...

...will be measured by AB, BC, CA, he sides of the spherical triangle. But when a solid angle is formed by three plane angles, the sum of any two of them is greater than the third (Prop. XVII., B. VII.) ; hence any two of the arcs AB, BC, CA must b greater than the third. Therefore,...

...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...

...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...