 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...THEOREM. Two rectangles having equal bases are to each other as their altitudes. (Explain.) 370. THEOREM. Any two rectangles are to each other as the products of their bases by their altitudes. 188 A c X B BOOK IV To Prove : A : B = ab : c • d. Proof : Construct a third... | |
 | Webster Wells - Geometry, Plane - 1908 - 208 pages
...that Two rectangles having equal bases are to each other as their altitudes. PROP. II. THEOREM 277. Any two rectangles are to each other as the products of their bases by their altitudes. If a y a R L _j PLANE GEOMETRY — BOOK IV Draw any two rectangles M and N. We... | |
 | George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...value and AP AE ' LJAF approaches AB as a limit. Case 1 I i A r si& QED PROPOSITION II. THEOREM 318. Two rectangles are to each other as the products of their bases by their altitudes. b b' b Given the rectangles R and R', having for the numerical measure of their... | |
 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...half the radius of the circumscribed circle. BOOK IV. PLANE GEOMETRY. PROPOSITION II. THEOREM. 418. Two rectangles are to each other as the products of their bases and altitudes. Given two rectangles whose areas are P and Q with altitudes a and a' and bases b and... | |
 | Geometry, Plane - 1911 - 192 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... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 332 pages
...limits. (See § 593.) 478. Cor. I. The area of a square is equal to the square of its side. 479. Cor. II. Any two rectangles are to each other as the products of their bases and their altitudes. OUTLINE OF PROOF. Denote the two rectangles by R and R', their bases by b and... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Solid - 1912 - 220 pages
...diameter adjacent to the chord. 478. The area of a square is equal to the square of its side. 479. Any two rectangles are to each other as the products of their bases and their altitudes. 480. (a) Two rectangles having equal bases are to each other as their altitudes,... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...are the altitude and base respectively of the rectangle whose area is B, then R = 322. COROLLARY 1. Two rectangles are to each other as the products of their bases and altitudes. For if R = a6, and R' = a'b'. then — = -- B' a'b' 323. COROLLARY 2. Two rectangles... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...altitude and base respectively of the rectangle whose area is B, then R = ab gquare 322. COROLLARY 1. Two rectangles are to each other as the products of their bases and altitudes. For if E = ab, and R' = a'b', then — = —^ . 323. COROLLARY 2. Two rectangles having... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...approaches AB as a limit. OAF as AP varies in value and Case1 QED are to PROPOSITION II. THEOREM 318. Two rectangles are to each other as the products of their bases by their altitudes. b' b Given the rectangles R and R', having for the numerical measure of their bases... | |
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K hag to M the ratio which is compounded of the ratios of the sides ; therefore also the parallelogram AC has to the parallelogram CF the ratio which is compounded of the ratios of the sides. COR. Hence, any two rectangles are to each other as the products... 
