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Books Books 1 - 10 of 31 on AT into equal parts .Ax, xy, yz, &c., each less than Aa, and let k be one of those....  
" AT into equal parts .Ax, xy, yz, &c., each less than Aa, and let k be one of those parts : through the points of division pass planes parallel to the plane of the bases : the corresponding sections formed by these planes in the two pyramids will be respectively... "
Elements of Geometry and Trigonometry: With Notes - Page 140
by Adrien Marie Legendre - 1822 - 367 pages
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...TA being the same ia both. If they are not equivalent, let sa bc, be the smaller ; and suppose A a to be the altitude of a prism, which having ABC for...AT into equal parts Ax, xy, yz, &c., each less than A a, and let fc be one of these parts ; through the points of division suppose planes parallel to the...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 224 pages
...TA being the same in both. If they are not equivalent, let sa bc, be the smaller ; and suppose A a to be the altitude of a prism, which having ABC for...AT into equal parts Ax, xy, yz, &c., each less than A a, and let k be one of these parts ; through the points of division suppose planes parallel to the...
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Elements of Geometry

Adrien Marie Legendre - 1825 - 224 pages
...TA being the same in both. If they are not equivalent, let sa 6 c, be the smaller ; and suppose A a to be the altitude of a prism, which having ABC for...Divide the altitude AT into equal parts Ax, xy, yz, &x., each less than A a, and let A; be one of these parts ; through the points of division suppose...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...situated in the same plane, and let AT be their common altitude. If they are not equivalent, let S-o6c be the smaller : and suppose Aa to be the altitude...one of those parts ; through the points of division pass planes parallel to the plane of the bases ; the corresponding sections formed by these planes...
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Elements of geometry and trigonometry

Adrien Marie Legendre - Geometry - 1837 - 359 pages
...equivalent bases ABC, abc, be situated in the same plane, and let AT . their common altitude. If they are not equivalent, let S-abc be the smaller...equal parts Ax, xy, yz, &c. each less than Aa, and let h be one of those parts ; through the points of division pass planes parallel to the plane of the bases...
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Elements of geometry and trigonometry

Adrien Marie Legendre - Geometry - 1838 - 359 pages
...plane, and let AT be their common altitude. If they are not equivalent, let S-abc BOOK VII. .t 159 be the smaller : and suppose Aa to be the altitude...altitude AT into equal parts Ax, xy, yz, &c. each Jess than Aa, and let k be one of those parts ; through the points of division pass planes parallel...
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Elements of geometry

Adrien Marie Legendre - Mathematics - 1841 - 235 pages
...TA being the same in both. If they are not equivalent, let sa bc, be the smaller ; and suppose A a to be the altitude of a prism, which having ABC for...difference. Divide the altitude AT into equal parts A x, xy, yz, &c., each less than A a, and let k be one of these parts ; through the points of division'...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson, Sir David Brewster - Geometry - 1844 - 237 pages
...having equivalent bases and equal altitudes, are equivalent, or equal in solidity. Let SABC, sabe, be those two pyramids, of which the two bases ABC,...division extend planes parallel to the plane of the bases ; the corresponding sections formed by these planes in the two pyramids will be respectively...
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Elements of Geometry: With Proctical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 pages
...situated in the same plane, and let AT be their common altitude. If they are not equivalent, let Sabe be the smaller ; and suppose Aa to be the altitude...one of those parts ; through the points of division, pass planes parallel to the plane of the hases : the corresponding sections forihed by these planes...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies, Sir David Brewster, Adrien Marie Legendre - Trigonometry - 1849 - 359 pages
...pyramids will be respectively equivalent, namely DEF to def, GHI to ghi, &c. (Prop. III. Cor. 2.). be the smaller: and suppose Aa to be the altitude...having ABC for its base, is equal to their difference. This being granted, upon the triangles ABC, DEF, GHI, &c. taken as bases, construct exterior prisms...
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