 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 374 pages
...a linear unit. To PROVE—area of R = a X b, provided U is the unit of area. R_aX b_ [The areas of two rectangles are to each other as the products of their bases and altitudes.] But - = area of R. § 355 [The area of a surface is the ratio of that surface to the... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...unit. To PROVE — area of R = a X b, provided U is the unit of area. ^rlrr"**- §361 [The areas of two rectangles are to each other as the products of their bases and altitudes.] P But - = areaofAJ. §355 [The area of a surface is the ratio of that surface to the... | |
 | George Washington Hull - Geometry - 1897 - 408 pages
...second parallelogram, with a and b its altitude and base respectively. COR. 1.—Two parallelograms are to each other as the products of their bases by their altitudes. For P= A X B, and p — a X b (§ 229). COR. 2.— Two parallelograms having equal bases are to each... | |
 | Webster Wells - Geometry - 1898 - 264 pages
...EFGH EH' 300. Cor. Since either side of a rectangle may be taken as the base, it follows that PROP. II. THEOREM. 301. Any two rectangles are to each other...as the products of their bases by their altitudes. b b' b' Given M and N rectangles, with altitudes a and a', and bases b and b', respectively. To Prove... | |
 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...angle between a secant and a tangent is measured by one-half the difference of the intercepted arcs. 6. Any two rectangles are to each other as the products of their bases by their altitudes. 7. The area of a circle is equal to one-half the product of its circumference and radius. 8. A regular... | |
 | Webster Wells - Geometry - 1898 - 250 pages
...whose side is the linear unit. To Prove that, if N is the unit of surface, area M= a x b. Proof. Since any two rectangles are to each other as the products of their bases by their altitudes (§ 301), M axb N'' 1x1 - = a x b. But since N is the unit of surface, the ratio of M to N is the area... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...The area of a rectangle is equal to the product of its base and altitude. It is known (from 247) that two rectangles are to each other as the products of their bases by their altitudes ; therefore, but S is the unit of area ; hence R = h x b. 249. COB. If h = b, then R = bxb = b*. But... | |
 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...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. 260. 261. Cor. V. Can you show how to find the area of any triangle ? 262. Cor. VI. Can you show that... | |
 | James Howard Gore - Geometry - 1899 - 266 pages
...their numerical measures when referred to a common unit (§ 242). B a C i i § 248.] AREAS OF POLYGONS. Let A and B be any two rectangles having the altitudes a and a', and the bases b and b', respectively. B a' x b' To prove that - = -• A ax 6 Construct a rectangle C, with a base equal to the base of B... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...either side of a rectangle may be taken as the base, it follows that PLANE GEOMETRY. — BOOK IV. PROF. II. THEOREM. 301. Any two rectangles are to each other...as the products of their bases by their altitudes. b VV Given M and N rectangles, with altitudes a and a', and bases b and b', respectively. M _ axb To... | |
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Any two rectangles are to each other as the products of their bases by their altitudes. 
