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" Any two rectangles are to each other as the products of their bases by their altitudes. "
Elements of Geometry and Conic Sections - Page 60
by Elias Loomis - 1857 - 226 pages
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1887 - 342 pages
...Corollary. Two rectangles having equal bases are to each other as their altitudes. PROPOSITION III. Any two rectangles are to each other as the products of their bases by their altitudes. PROPOSITION IV. The area of a rectangle is equal to the product of its base and altitude. PROPOSITION...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...Corollary. Two rectangles having equal bases are to each other as their altitudes. PROPOSITION III. Any two rectangles are to each other as the products of their bases by their altitudes. PROPOSITION IV. The area of a rectangle is equal to the product of its base and altitude. PROPOSITION...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 332 pages
...rectangle" is to be understood " surface of the rectangle." ' I '*•-'. - PROPOSITION III.— THEOREM. 7. Any two rectangles are to each other as the products of their loses by their altitudes. Let It and R' be two rectangles, k and It their bases, h and h' their altitudes...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 272 pages
...From (1) and (2) rect. AF AE Ax. 1 PLANE GEOMETRY. BOOK IV. PROPOSITION II. THEOREM. 362. The areas of two rectangles are to each other as the products of their bases by their altitudes. b b. b Let R and R' be two rectangles, having for their bases b and b', and for their altitudes a and...
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Exercise Manuals, Issue 3

George Albert Wentworth - 1889 - 276 pages
...as their altitudes; and two rectangles having equal altitudes are to each other as their bases. 177. Theorem. Any two rectangles are to each other as the products of their bases and altitudes. 178. Theorem. Area of a rectangle = base X altitude. 179. Theorem. Area of a square...
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Wentworth & Hills's Exercise Manuals: Geometry, Issue 3

George Albert Wentworth - 1889 - 264 pages
...as their altitudes; and two rectangles having equal altitudes are to each other as their bases. 177. Theorem. Any two rectangles are to each other as the products of their bases and altitudes. 178. Theorem. Area of a rectangle = base X altitude. 179. Theorem. Area of a square...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 418 pages
...yards and whose altitude is the same as that of the first ? Proposition 2. Theorem. 358. The areas of any two rectangles are to each other as the products of their bases by their altitudes. Hyp. Let R and R' be two rectangles, b and b' their bases, a and a' their altitudes, „ R a X b To...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 414 pages
..." area of the triangle," etc. EXERCISES. PLANE GEOMETRY. Proposition 2.. Theorem. 358. The areas of any two rectangles are to each other as the products of their bases by (heir altitudes. Hyp. Let R and R' be two rectangles, b and V their bases, a and a' their altitudes,...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...equivalent, because they are all equivalent to the same rectangle. 365. COR. 2. Any two parallelograms are to each other as the products of their bases by their altitudes; therefore parallelograms having equal bases are to each other as their altitudes, and parallelograms...
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Educational Review, Volume 3

Nicholas Murray Butler, Frank Pierrepont Graves, William McAndrew - Education - 1892 - 544 pages
...equal to the product of its base and altitude, reference is made to the proposition that " the areas of two rectangles are to each other as the products of their bases by their altitudes" making the former proposition depend upon the latter. To expose the fallacy of the proof it is necessary...
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