... parallelepiped only those class q points are considered that do not fall within the boundaries of the maximum parallelepipeds already constructed . This ensures non rep- etition of the maximum parallelepipeds constructed relative to one ...

David Eugene Smith. Exercises . Parallelepipeds 1. Two rectangular parallelepipeds with congruent bases are to each other as their altitudes . In all such cases the words " the volumes of " are understood . 2. Two rectangular ...

... parallelepipeds BH , and BK . The parallelepiped CM , having its solid angle at B , equal to the solid angle b , of the parallelepiped cm , and the sides about these angles being equal in both the parallelepipeds , they are equal and ...

... parallelepipeds . Such pixels are of an unknown type . In the second extreme case the point lies inside just one of the parallelepipeds , and the corresponding pixel is therefore labelled as a member of the class represented by that ...

... parallelepipeds AE and CF are also equal to one an- other . Wherefore parallelepipeds which are upon equal bases , & c .: which was to be proved . Cor . Any parallelepiped is equal to a rectangular parallelepiped , ( that is , a ...

... parallelepipeds , and if to AB , to the perpendicular from A upon DC , and to the altitude of the parallele- piped ... parallelepipeds , by hypothesis ; therefore the ratio of LxMXN to lxmxn is compounded of the ratio of the areas ...

... parallelepipeds as desired . It remains only to show that they intersect each other in sets of dimension lower than k . Since these parallelepipeds are obtained by sweeping the ( k − 1 ) - parallelepipeds in half the boundary of S ...

... parallelepipeds , prisms , cones , cylinders , & c . are in the reciprocal ratio of their bases and altitudes . Rectangular parallelepipeds , contained under the cor- responding lines of three ranks of proportionals , are themselves ...

... parallelepipeds vi + B , Vi + 1 + parallelepipeds ( 9 ) , these ones corner , and by ( 13 ) , ( 14 ) , ( 15 ) 0 € 1 + B , ẞ a € vk + B. B ― ανκ - From ( 12 ) we even infer that 0 and ß a form corners of the last - mentioned parallelepipeds ...

... parallelepiped in which it will be enclosed. The set of possible parallelepipeds that can enclose the steady-state flux space is chosen by forming the faces of the parallelepiped along the directions defined by these v i,min con ...