... 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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