 That is, the number which represents its square units of area is the product of the two numbers which represent its base and altitude. For in prop. II, if R' = 1, the square unit of area, then a' and 6' must each equal 1, the unit of length.  New Plane Geometry - Page 202by Wooster Woodruff Beman, David Eugene Smith - 1899 - 252 pagesFull view - About this book
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...left the OAE FD. .-. rect. AB CD = n A EFD. Ax. 3 But the area of the rect. AB CD = ADX С D, § 319 (the area of a rectangle equals the product of its base and altitude). .-. the area of the О A EFD = ADX С D. Лх. 1 QED 322. COROLLARY 1. Parallelograms having equal... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...we have left the OAEF D. .-.rect. A BCD = nAEFD. Ax. 3 But the area of the rect. ABCD = ADXCD, §319 (the area of a rectangle equals the product of its base and allitiule). .-. the area of the OA EFD = ADXC D. Ax. 1 QED 322. COROLLARY 1. Parallelograms having... | |
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...have left the OAE FD. .-. rect. ABCD = nAEFD. Ax. 3 But the area of the rect. ABC D = AD X С D, §319 (the area of a rectangle equals the product of its base and altitude). .-. the area of the П AEFD = Л DX С D. Аx. 1 QED ' 322. COROLLARY 1. Parallelograms having equal... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...Equivalent Figures are such as have equal areas. ELEMENTS OF PLANE GEOMETRY. AREAS. THEOREM I. 240. The area of a rectangle equals the product of its base and altitude. Let AB CD be a rectangle, AB the base, and AC the altitude. To prove that the area of ABCD = AB X AC.... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...Parallelograms (or triangles) have the same ratio as the products of their bases and altitudes. (Why ?) 3. The area of a rectangle equals the product of its...numbers which represent its base and altitude. For in th. 2, if R' = 1, the square unit of area, then a' and b' must each equal 1, the unit of length. Hence,... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...Parallelograms (or triangles') have the same ratio as the products of their bases and altitudes. (Why ?) 172 That is, the number which represents its square units...numbers which represent its base and altitude. For in th. 2, if R'= 1, the square unit of area, then a' and b' must each equal 1, the unit of length. Hence,... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...§378 Multiplying, RX ba — x — = — x — , X R' b' a' R axb or QED PROPOSITION IV. THEOREM V 381. The area of a rectangle equals the product of its base and altitude, provided the unit of area is a square whose side is the linear unit. U — GIVEN — the rectangle... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...altitudes.] Multiplying, RX ba X R' b' a' — X — — — X — » ^i R axb PROPOSITION IV. THEOREM 381. The area of a rectangle equals the product of its base and altitude, provided the unit of area is a square whose side is the linear unit. GIVEN—the rectangle R and a... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...bases L . J [having = alt.] — — —=: multiply ar ... . ~\ N a'b' - II PROPOSITION IV 243. Theorem. The area of a rectangle equals the product of its base and altitude. [The area of the rectangle is to the square unit, taken as a standard, as the product of its base and... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 400 pages
...Then and b R a X a R' Prop. I Prop. I, cor. 1 2. .'.— = —fj'j, by multiplying corresponding .it ao members of the two equations. Ax. 6 281. Definition....prop. II, if R' = 1, the square unit of area, then a' and 6' must each equal 1, the unit of length. Hence 'R/l = ab/l, or B = ab. 3. The area of a parallelogram... | |
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