 | Edward Olney - Geometry - 1872 - 472 pages
...te, the pyramids are equivalent. OF PYRAMIDS AND CONES. Flo. 310. PROPOSITION TL 520. TJteorent. — The volume of a triangular pyramid is equal to one.third the product of its base and altitude. DEM.— Let S.ABC be a triangular pyramid, whose altitude is He; then is the volume equal ^ .5 to i... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...te, the pyramid! are equivalent. OP PYRAMIDS AND CONES. Fio. 310. PROPOSITION TI. 520. Theorem. — The volume of a triangular pyramid is equal to one-third the product of its base and altitude. DEM.— Let S-ABC be a triangular pyramid, whose altitude is H*; then is the volume equal ^ 5 to JH... | |
 | Edward Olney - 1872 - 270 pages
...the common altitude, it is evident that the volumes are equal. PROPOSITION VI. 520. Theorem.—Tlie volume of a triangular pyramid is equal to one-third the product of its base and altitude. DEM.—Let S-ABC be a triangular pyramid, whose altitude is H*; then is the volume equal ^ 2> to JHx... | |
 | United States Naval Academy - 1874 - 888 pages
...and the side AC=a: find the segments f the side А С by the bisector of the angle B. 5. Prove that the volume of a triangular pyramid is equal to one-third the product f its base and altitude. State and prore the proposition which gives the volume of he frustum of Ħi... | |
 | William Guy Peck - Conic sections - 1876 - 412 pages
...dividing it into triangular pyramids; these will have the same altitude as the given pyramid. Now, each triangular pyramid is equal to one•third the product of its base and altitude ; hence, their sum is equal to the sum of their bases multiplied by one•third their common altitude,... | |
 | George Albert Wentworth - Geometry - 1877 - 426 pages
...triangular pyramids is equal to £ the sum of their bases multiplied by their common altitude, § 573 (the volume of a triangular pyramid is equal to one-third the product of its base and altitude), that is, the volume of the pyramid S-ABСDE = \ QED 575. COROLLARY. Pyramids having equivalent bases... | |
 | Edward Olney - Geometry - 1877 - 272 pages
...the common altitude, it is evident that the volumes are equal. PROPOSITION VI. 520. Theorem.—The volume of a triangular pyramid is equal to one-third the product of its base and altitude. DEM.—Let S-ABC be a triangular pyramid, whose altitude is H*; then is the volume equal to i H x area... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...pyramids is equal to J the sum of their bases multiplied by their common altitude, § 573 (tlie voluiim of a triangular pyramid is equal to one-third the product of its base and altitude), that is, the volume of the pyramid SA B С DE = J ABCDEx SO. • QED 575. COROLLARY. Pyramids having... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...: hence the whole prism is divided into three equal triangular pyramids, and D-ABC = ^ABC-DEF. COR. The volume of a triangular pyramid is equal to onethird the product of its base by its altitude (7). XIII. Theorem. The volume of any pyramid is equal to onethird the product of its... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...number of equivalent laminae, and are consequently equivalent 14. ED PROPOSITION VI. 629. Theorem. — The volume of a triangular pyramid is equal to one-third the product of its base and altitude. DEMONSTRATION. Let S-ABC be a triangular pyramid, whose altitude is H. Then is the volume equal to... | |
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The volume of a triangular pyramid is equal to one-third the product of its base and altitude. 
