 ... 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 155by Claude Irwin Palmer, Daniel Pomeroy Taylor - 1918 - 436 pagesFull view - About this book
 | Olinthus Gregory - Euclid's Elements - 1840 - 208 pages
...generally, since they are respectively equivalent to the rectangles of the same bases and altitudes. Hence, parallelograms are to each other as the products of their bases and altitudes. (6.) Farther, to measure an area is to determine R R' H h R' T B b .-. R r BH bh R BH or... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...x BE\ hence, the area of the parallelogram is also equal to AB x BE ; which was to be proved. Cor. Parallelograms are to each other as the products of their bases and altitudes. If their altitudes are equal, they are to each other as their bases. If their bases are... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...other as their bases ; parallelograms having equal bases are to each other as their altitudes; and any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V.— THEOREM. 13. The area of a triangle is equal to half the product... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...each other as their bases; parallelograms having equal bases are to each other as their altitudes; and any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V.—THEOREM. 13. The area of a triangle is equal to half the product... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...T) FO hence, the area of the parallelogram is also equal to AB x BE ; which was to be proved. Cor. Parallelograms are to each other as the products of their bases and altitudes. If their altitudes are equal, they are to each other as their bases. If their bases are... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...algebraically, if a = AB and b = BC (a + b) (a — i) = a'' — b* _ Produce AB so that BD — B C. ACBD 42. Parallelograms are to each other as the products of their bases and altitudes. (10.) 43. . Parallelograms having equal bases are to each other as their altitudes; those... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...algebraically, if a = AB and 5 = BC (a -fb) (a — b) = a1 — b' Produce AB so that BD = BC. -**- CBD 42. Parallelograms are to each other as the products of their bases and altitudes. (10.) 43. Parallelograms having equal bases are to each other as their altitudes; those... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...x BE: hence, the area of the parallelogram is also equal to AB x BE ; which was to be proved. Cor. Parallelograms. are to each other as the products of their bases and altitudes. If their altitudes are equal, they are to each other as their bases. If their bases are... | |
 | William Guy Peck - Conic sections - 1876 - 412 pages
...the area of the parallelogram is also equal to the product of AC and CK, which was to be proved. Cor. Any two parallelograms are to each other as the products of their bases and altitudes. If their bases are equal, they are to each other as their altitudes ; if their altitudes... | |
 | George Albert Wentworth - Geometry - 1877 - 426 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 th... | |
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