 ... 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.  Elements of Plane and Solid Geometry - Page 179by George Albert Wentworth - 1877 - 398 pagesFull view - About this book
 | William James Milne - Geometry - 1899 - 396 pages
...Cor. I. The area of a parallelogram is equal to the product of its base by its altitude. 333. Cor. II. Parallelograms are to each other as the products of their bases by their altitudes; consequently, parallelograms which have equal altitudes are to each other as their bases, parallelograms... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...equivalent. COB. II. Parallelograms upon equal bases and between the same parallels are equivalent. COB. III. Any two parallelograms are to each other as the products of their bases and altitudes. COB. IV. Two parallelograms having equal altitudes are to each other as their bases.... | |
 | George Albert Wentworth - Geometry - 1899 - 500 pages
...the altitudes CO and C'O'. A ACB ABx CO AB CO Ihen ^^7^7 = A , B , x c , <) , = ^ * ^o, (two A are to each other as the products of their bases by their altitudes). But 7& = 7&' §361 (the homologous altitudes of two similar A have the same ratio as any two homologous... | |
 | Webster Wells - Geometry - 1899 - 196 pages
...2. Two prisms having equivalent bases are to each other as their altitudes. 3. -Any two prisms are to each other as the products of their bases by their altitudes. 289 PYRAMIDS. DEFINITIONS. 502. A pyramid is a polyedron bounded by a polygon, called the base, and... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...prism is equal to the product of its base by its altitude. That is, V=BXH. QED 629. COR. Two prisms are to each other as the products of their bases by their altitudes ; prisms having equivalent bases are to each other as their altitudes; prisms having equal altitudes... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...Proof. Draw the altitudes CO and C'O'. A ACB ABxCO AB CO B' A A'C'B' A'B ' X C'O' A'B' C'O' (two A are to each other as the products of their bases by their altitudes). But §405 AB CO A'B ' C'O' §361 (the homologous altitudes of two similar A have the same ratio as... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...ED 342. COR. 1. Parallelograms having equal bases and equal altitudes are equivalent. 343. COR. 2. Any two parallelograms are to each other as the products of their bases and altitudes. 344. COR. 3. Parallelograms having equal bases are to each other as their altitudes.... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...Prove ADEF a rectangle. ADEF = ADCB. (?) ADEF = AD x ED. (?) ABCD = AD x ED. (?) QED 589. COROLLARY II. Any two parallelograms are to each other as the products of their bases and altitudes; if their bases are equal the parallelograms are to each other as their altitudes; if... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...QED 342. COR. 1. Parallelograms having equal bases and equal altitudes are equivalent. 343. COR. 2. Any two parallelograms are to each other as the products of their bases and altitudes. 344. COR. 3. Parallelograms having equal bases are to each other as their altitudes.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...«.ED 342. COR. 1. Parallelograms having equal bases and equal altitudes are equivalent. 343. COR. 2. Any two parallelograms are to each other as the products of their bases and altitudes. 344. COR. 3. Parallelograms having equal bases are to each other as their altitudes.... | |
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