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" Any two rectangles are to each other as the products of their bases by their altitudes. "
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... - Σελίδα 127
των William Chauvenet - 1872 - 368 σελίδες
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 368 σελίδες
...(I. 120), of which AEFD will contain 4; consequently, we have ABCD = 7 AEFD ~~ 4and therefore ABCD AB AEFD ~~ AE The demonstration is extended to the...the altitudes, it follows that two rectangles having 9qual bases are to each other as their altitudes. Note. In these propositions, by " rectangle" is to...

Elements of Plane and Solid Geometry

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

Elements of Geometry

George Albert Wentworth - 1881 - 250 σελίδες
...their limits ; rect. AF .-. their limits are equal, namely, = ., § 199 rect. AC AB QED 314. COROLLARY. Two rectangles having equal bases are to each other as their altitudes. By considering the bases of these two rectangles AD and AD, the altitudes will be AB and A E. But we...

The Elements of Geometry

Webster Wells - 1886 - 371 σελίδες
...equal. Hence, ABCD _ 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 - 1887
...its limit. Therefore, by II., Theorem, Doctrine of Limits, (-II-, 42, and III., 14.) 6. COROLLARY. Two rectangles having equal bases are to each other...understood " surface of the rectangle." PROPOSITION III.— THEOREM. 7. Any two rectangles are to each other as the products of their bases by their altitudes....

Chauvenet's Treatise on Elementary Geometry

William Chauvenet - 1887 - 322 σελίδες
...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....

CHAUVENETS TREATISE ON ELEMENTARY GEOMETRY

W. E. BYERLY - 1887
...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....

Chauvenet's Treatise on Elementary Geometry

William Chauvenet - 1888 - 322 σελίδες
...to the case in which the bases are incommensurable, by the process already exemplified in (II. 61) and (III. 15). 4. Corollary. Since AD may be called...understood " surface of the rectangle." PROPOSITION IL— THEOREM. 5. Any two rectangles are to each other as the products of their bases by their altitudes....

A Text-book of Geometry

George Albert Wentworth - 1888 - 386 σελίδες
...are constantly equal, and each approaches a limit, the limits arc equal). a ED 361. COB. The areas of two rectangles having equal bases are to each other as their altitudes. For AB and AE may be considered as the altitudes, AD and AD as the bases. PROPOSITION II. THEOREM....

Exercise Manuals, Τεύχος 3

George Albert Wentworth - 1889
...Definitions. Equivalent figures, area of a figure, units of area, transformation of a figure. 176. Theorem. Two rectangles having equal bases are to each other as their altitudes; and two rectangles having equal altitudes are to each other as their bases. 177. Theorem. Any two rectangles...




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