 ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.  Plane and Solid Geometry - Page 105by James Howard Gore - 1898 - 210 pagesFull view - About this book
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...have (II. 21, 24) \ h F V \ \ \ B \ \ \ ! ft \ ! \ V \ THEOREM IX. 34. Rectangular parallelopipeds are to each other as the products of their bases by their altitudes. Let AB, CD, be rectangular parallelopipeds, then Produce the edge EA to G making EG equal to FC; if... | |
 | George Albert Wentworth - 1881 - 266 pages
...other as their altitudes ; parallelograms having equal altitudes are to each other as their bases ; and any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 324. The area of a triangle is equal to one-half of the product of its bnse... | |
 | Charles Scott Venable - 1881 - 380 pages
...part of the prism having the same base and the same altitude. COR. 2. First. — Any two pyramids are to each other as the products of their bases by their altitudes. Secondly. — Two pyramids having the same altitude are to each other as their bases. Thirdly. —... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...one-half of any parallelogram having an equal base and an equal altitude. Cor. II.—Any two triangles are to each other as the products of their bases by their altitudes. For, let T and T' denote two triangles whose bases are b and b', and whose altitudes are a and a'.... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...other as their bases ; two parallelograms having equal bases are to each other as their altitudes ; and any two parallelograms are to each other as the products of the'ir bases by their altitudes. PROPOSITION V. THEOREM. 327. The area of a triangle is equal to one-half the product of its base and... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...to be understood " surface of the rectangle." PROPOSITION III.—THEOREM. 7. Any two rectangles are to each other as the products of their bases by their altitudes, Let E and R' be two rectangles, k and k their bases, h and h ' their altitudes; then E _ k XA R ' Jfx... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...other as their altitudes; parallelograms having equal altitudes are to each other as their bases ; any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. / 368. The area of a triangle is equal to one-half of product of its base by... | |
 | George Albert Wentworth - 1889 - 264 pages
...square = square of one side. 180. Theorem. Area of a parallelogram = base X altitude. 181. Theorem. Two parallelograms having equal bases are to each other as their altitudes ; and two parallelograms having equal altitudes are to each other as their bases. 182. Theorem. Area of a... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...is the same as that of the first ? Proposition 2. Theorem. 358. The areas of any two rectangles are to each other as the products of their bases by their altitudes. Hyp. Let R and R' be two rectangles, b and b' their bases, a and a' their altitudes, R a X b To prove... | |
 | Edward Albert Bowser - Geometry - 1891 - 424 pages
...bases and equal altitudes are equivalent, because they are all equivalent to the same rectangle. 365. COR. 2. Any two parallelograms are to each other as...equal bases are to each other as their altitudes, arid parallelograms of equal altitudes are to each other as their bases. Proposition 5. Theorem. 366.... | |
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