Plane and solid geometry . to the two triangular prismsABC-F and CDA-H. To prove prism ^i?C-i^=o= prism CDA-H. Argument Only 1. Let MNOP be a rt. section of parallelopiped BH^ cuttingthe plane AG in line MO, 2. Face AF II face DG and face ^5 II face BG, 3. .-. MN II PO and MP II NO. 4. .-. MNOP is a /Z7. 5. •. A MNO = A 0PM, 6. Now triangular prism ABC~F=o=d rt. prism whose base isA MNO, a rt. section of prism ABC-F, and whose altitude is AE,a lateral edge of prism ABC-F, 7. Likewise triangular prism CDA-H<^2i rt. prism whose baseis A 0PM and whose altitude is AE. 8. But two such prisms are
Plane and solid geometry . to the two triangular prismsABC-F and CDA-H. To prove prism ^i?C-i^=o= prism CDA-H. Argument Only 1. Let MNOP be a rt. section of parallelopiped BH^ cuttingthe plane AG in line MO, 2. Face AF II face DG and face ^5 II face BG, 3. .-. MN II PO and MP II NO. 4. .-. MNOP is a /Z7. 5. •. A MNO = A 0PM, 6. Now triangular prism ABC~F=o=d rt. prism whose base isA MNO, a rt. section of prism ABC-F, and whose altitude is AE,a lateral edge of prism ABC-F, 7. Likewise triangular prism CDA-H<^2i rt. prism whose baseis A 0PM and whose altitude is AE. 8. But two such prisms are equivalent. 9. ., ^vism ABC-F o^Y^vism CDA-H. 796. Questions. Is there a theorem in Book I that corresponds toProp. VIII ? If so. state it. Could an oblique prism exist such that aright section, as MNOP, might intersect either base ? If so, draw afigure to illustrate. 370 SOLID GEOMETRY pROPOsiTiox IX. Theorem 797. Tlie volume of a triangular prism is equal tothe product of its base and its altitude. ^..Mi ~^^Q. Given triangular prism ^C7)-Xwitli its volume denoted byF, its base by B^ and its altitude by mTo prove V = B - H,The proof is left as an exercise for the student. 798e Questions. What proposition in Book IV corresponds to above ? Can you apply the proof there given ? What is the name ofthe figure CZ in § 797 ? What is its volume ? What part of CZ isACD-X (§ 795) ? Ex. 1319. The volume of a triangular prism is equal to one half theproduct of any lateral face and the perpendicular from any point in theopposite edge to that face. HixT. The triangular prism is one half of a certain parallelopiped (§ 95). Ex. 1320. The base of a coal bin which is 8 feet deep is a trianglewith sides 10 feet, 15 feet, and 20 feet, respectively. How many tons ofcoal will the bin hold considering 35 cubic feet of coal to a ton ? Ex. 1321. One face of a triangular prism contains 45 square inches ;the perpendicular to this face from a point in the opposite edge is 6
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
