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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 - Σελίδα 60
των Elias Loomis - 1858 - 234 σελίδες
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Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 416 σελίδες
...0'. T, J_ i] . ' И Л AСB ABХ CO AB v CO /\ Д A' C'B' A' HX C' 0' A' B' " С" 0' ' (two ÊÎ are to each other as the products of their bases by their altitudes). AB = CO A'B' "" C7^' 326 But § 297 (¿Ae homologous altitudes of similar A have the same ratio as...

Elements of Geometry: And the First Principles of Modern Geometry

William Henry Harrison Phillips - 1878 - 236 σελίδες
...parallelopipeds having equal altitudes are to each other as their bases. VI. Theorem. Any two parallelopipeds are to each other as the products of their bases by their altitudes. HYPOTII. P and p are two parallelopipeds whose bases are B and &, and whose altitudes are A and a respectively....

New Elementary Algebra: Designed for the Use of High Schools and Academies

Benjamin Greenleaf - 1879 - 322 σελίδες
...= 57. 5. If a -f- x : a — x : : 11 : 7, what is the ratio of a to xl Ans. 9 : 2. 6. Triangles are to each other as the products of their bases by their altitudes. The bases of two triangles are to each other as 17 to 18, and their altitudes as 21 to 23 ; required...

Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1880 - 452 σελίδες
...employed in B. Ill, Pr. 14. Therefore two rectangles, etc. PROPOSITION IV. THEOREM. BOOK IV. C gle ABCD to the rectangle AEGF is the same with the ratio of the product of AB by AD to the product of AE by AF ; that is, ABCD : AEGF : : AB x AD : AE x AF. Having placed the two rectangles...

Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1880 - 456 σελίδες
...the same method employed in B. Ill, Pr. 14. Therefore two rectangles, etc. PROPOSITION IV. THEOREM. Any two rectangles are to each other as the products of their bases by their altitudes. gle ABCD to the rectangle AEGF is the same with the ratio of the product of AB by AD to the product...

An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - 1880 - 260 σελίδες
...Scholium. By rectangle in these propositions is meant surface of the rectangle. ' THEOREM XV. v 38. Any two rectangles are to each other as the products of their bases by their altitudes. LetABCD,DJ£FGbe two rectangles ; then A BCD :DEFG=AD XD Place the two rectangles so that „ the angles...

Elements of Geometry

George Albert Wentworth - 1881 - 266 σελίδες
...Euclid's Def., § 272 QED 1 1 1 Í j L t. AC We ar г to ) ¡rove TCC PROPOSITION II. THEOREM. 315. Two rectangles are to each other as the products of their bases by their altitudes. _____ J b b' Ь Let Л and R' be two rectangles, having for their bases b and b', and lor their altitudes...

Elements of Geometry, After Legendre, with a Selection of Geometrical ...

Charles Scott Venable - 1881 - 380 σελίδες
...part of the prism having the same base and the same altitude. COR. 2. First. — Any two pyramids are to each other as the products of their bases by their altitudes. Secondly. — Two pyramids having the same altitude are to each other as their bases. Thirdly. —...

Essentials of Geometry

Alfred Hix Welsh - 1883 - 326 σελίδες
...one-half of any parallelogram having an equal base and an equal altitude. Cor. II.—Any two triangles are to each other as the products of their bases by their altitudes. For, let T and T' denote two triangles whose bases are b and b', and whose altitudes are a and a'....

Wentworth & Hill's Exercise Manuals: Geometry, Τεύχος 3

George Albert Wentworth - 1884 - 264 σελίδες
...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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