Pluvium: Torus, Plenum, Pax, Thorax, Dolus, Furor, Vinculum, Securis, Clavis, Gurges, Aestas, Capella, Corbis. Vesper: Uncus, Spicula, Mars, Ocrea, Cardo, Thyrsus, Cervix, Verbum, Orcus, Polus, Spes, Senex, Septum, Porrum, Cussis, Dolium. ANSWERS. The shapes are: 1. Urna, Moles, Plebs, Cura, Tessara, Lacerta, Clipeus, Ovis. 2. Urna, Frenum, Crates, Ocrea, Tessara, Glans, Colus, Tabula. 3. Comes, Tibicen, Mica, Sacerdos, Tigris, Lacerta. 4. Vestis, Oliva, Tyro, Pluma, Portio. 5. Mars, Merces, Vomer, Ovis, Portio, Tabula, Testudo, Lacerta, Penates. 6. Pallor, Tessara, Lacerta, Tigris, Segmen, Portio, Ovis, Arcus, Laurus, Axis, Troja, Aries. 7. Hospes, Tribus, Arista, Pellis, Colus, Pluma, Portio, Calathus, Turtur, Sepes. 8. Pallor, Tessara, Domitor, Testudo, Tabula, Clipeus, Portio, Calathus, Nux, Lectrum, Corymbus, Circaea, Cordax. 9. Fama, Conjux, Reus, Fera, Thorax, Pax, Furor, Dolus, Scala, Ira, Vulcan, Penates, Lapis, Palus, Sepes, Turtur, Diota, Drachma, Python. APPENDIX H. SECTIONS OF CUBE AND TESSARACT. There are three kinds of sections of a cube. 1. The sectional plane, which is in all cases supposed to be infinite, can be taken parallel to two of the opposite faces of the cube; that is, parallel to two of the lines meeting in Corvus, and cutting the third. 2. The sectional plane can be taken parallel to one of the lines meeting in Corvus and cutting the other two, or one or both of them produced. 3. The sectional plane can be taken cutting all three lines, or any or all of them produced. Take the first case, and suppose the plane cuts Dos half-way between Corvus and Cista. Since it does not cut Arctos or Cuspis, or either of them produced, it will cut Via, Iter, and Bolus at the middle point of each; and the figure, determined by the intersection of the Plane and Mala, is a square. If the length of the edge of the cube be taken as the unit, this figure may be expressed thus: Z X Y 0 . 0 . ¹⁄₂ showing that the Z and X lines from Corvus are not cut at all, and that the Y line is cut at half-a-unit from Corvus. Sections taken Z X Y 0 . 0 . ¹⁄₄ and Z X Y 0 . 0 . 1 would also be squares. Take the second case. Let the plane cut Cuspis and Dos, each at half-a-unit from Corvus, and not cut Arctos or Arctos produced; it will also cut through the middle points of Via and Callis. The figure produced, is a rectangle which has two sides of one unit, and the other two are each the diagonal of a half-unit squared. If the plane cuts Cuspis and Dos, each at one unit from Corvus, and is parallel to Arctos, the figure will be a rectangle which has two sides of one unit in length; and the other two the diagonal of one unit squared. If the plane passes through Mala, cutting Dos produced and Cuspis produced, each at one-and-a-half unit from Corvus, and is parallel to Arctos, the figure will be a parallelogram like the one obtained by the section