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" Any two rectangles are to each other as the products of their bases by their altitudes. "
Elements of Geometry - Σελίδα 165
των George Albert Wentworth - 1881
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 368 σελίδες
...(III. 15). 4. Corollary. Since AD may be called the base, and AB and AE the altitudes, it follows that two rectangles having equal bases are to each other as their altitudes. Note. In these propositions, by " rectangle" is to be understood " surface of the rectangle." PROPOSITION...

A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1872 - 368 σελίδες
...(III. 15). 4. Corollary. Since AD may be called the base, and AB and AE the altitudes, it follows that two rectangles having equal bases are to each other as their altitudes. Note. In these propositions, by " rectangle" is to be understood "surface of the rectangle." PROPOSITION...

Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 σελίδες
...approach their limits ; rect. AF are always equal .'. their limits are equal, namely, AE rect. AC §199 AB QED 314. COROLLARY. Two rectangles having equal...two rectangles, with the same base, or equal bases, aro to each other as their altitudes. GEOMETRY. BOOK ANOTHER DEMONSTRATION. Let A С and A' C' be two...

Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 σελίδες
...near they approach their limits ; rect. AF .-. their limits are equal, namely, AE rect, AC AB §199 QED 314. COROLLARY. Two rectangles having equal bases...two rectangles, with the same base, or equal bases, aro to each other as their altitudes. GEOMETRY. — BOOK IV. ANOTHER DEMONSTRATION. Let A С and A'...

Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 σελίδες
...approach their limits ; rect. AF are always equal .'. their limits are equal, namely, AE rect. AC AB §199 QED 314. COROLLARY. Two rectangles having equal bases...rectangles AD and AD, the altitudes will be AB and AE But we have just shown that these two rectangles are to each, other as AB is to A E. Hence two rectangles,...

Elements of Plane and Solid Geometry

George Albert Wentworth - 1882 - 398 σελίδες
...they approach their limits ; rect. AF .'. their limits are equal, namely, AE rect. AC AB §199 ''a. ED 314. COROLLARY. Two rectangles having equal bases...equal bases, are to each other as their altitudes. I ii I i 176 GEOMETRY. BOOK IV. ANOTHER DEMONSTRATION. Let AC and A' C' be two rectangles of equal...

Elements of Plane and Solid Geometry

George Albert Wentworth - 1884 - 406 σελίδες
...their limits ; rect. AF are always equal .'. their limits are equal, namely, 199 = AE rect. A~C ~~ ТB' QED 314. COROLLARY. Two rectangles having equal bases...equal bases, are to each other as their altitudes. ANOTHER DEMONSTRATION. Let A С and A' C" be two rectangles of equal altitudes. P С О PI D' £' F'...

The Elements of Geometry

Webster Wells - 1886 - 371 σελίδες
..._ AD 153 317. COROLLARY. Since either side of a rectangle may be taken as the base, it follows that Two rectangles having equal bases are to each other as their altitudes. PROPOSITION II. THEOREM. 318. Any two rectangles are to each other as the products of their bases by...

Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - 1887 - 322 σελίδες
...AE Therefore, by II., Theorem, Doctrine of Limits, ABCD AB AEFD AE' (v. II., 42, and III., 14.) 6. COROLLARY. Two rectangles having equal bases are to each other as their altitudes. Note. In these propositions, by " rectangle" is to be understood " surface of the rectangle." PROPOSITION...

CHAUVENETS TREATISE ON ELEMENTARY GEOMETRY

W. E. BYERLY - 1887
...equivalent. PROPOSITION II. Two rectangles having equal altitudes are to each other as their bases. 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....




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