| Education - 1918 - 990 pages
...and not a vague largeness. It is a very common inconsistency a little later to attempt to prove that **"Two rectangles having equal altitudes are to each other as their bases"** in the following manner: Call the two rectangles R and S, respectively. Assuming the bases commensurable,... | |
| Isaac Newton Failor - Geometry - 1906 - 440 pages
...triangle, rectangle, etc., are frequently used for area of triangle, etc. PROPOSITION I. THEOREM 395 **Two rectangles having equal altitudes are to each other as their bases.** DE HYPOTHESIS. The rectangles ABCD and EFGH have equal altitudes, AB and EF. CONCLUSION. ABCD : EFGH... | |
| Isaac Newton Failor - Geometry - 1906 - 431 pages
...triangle, rectangle, etc., are frequently used for area of triangle, etc. PROPOSITION I. THEOREM 395 **Two rectangles having equal altitudes are to each other as their bases.** DE HYPOTHESIS. The rectangles ABCD and EFGH have equal altitudes, AB and EF. CONCLUSION. ABCD : EFGH... | |
| Webster Wells - Geometry, Plane - 1908 - 206 pages
...the radical sign ; then, 2x=mV5—m; and x (or AC) = BOOK IY ABBAS OP POLYGONS PROP. I. THEOREM 275. **Two rectangles having equal altitudes are to each other as their bases.** The words "rectangle," "parallelogram," "triangle," etc., in the propositions of Book IV, mean the... | |
| Webster Wells - Geometry - 1908 - 338 pages
...the radical sign ; then, 2a;=mV5-m; and x (or AC) = BOOK TY AREAS OF POLYGONS PROP. I. THEOREM 275. **Two rectangles having equal altitudes are to each other as their bases.** The words "rectangle," "parallelogram," "triangle," etc., in the propositions of Book IV, mean the... | |
| William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...equal. § 275 EFGH EH ABCD AD' QED 417. COE. Because any side of a rectangle may be taken as the base, **two rectangles having equal altitudes are to each other as their bases.** Ex. 347. Find the bisectors of the triangle whose sides are, respectively, 18, 20, and 22 ft. Ex. 348.... | |
| George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...identically equal," the word equal is often used to mean "equivalent." PROPOSITION I. THEOREM 316. **Two rectangles having equal altitudes are to each other as their bases.** A x BAX F Given the rectangles AC and AF, having equal altitudes AD. To prove that D AC: D AF = base... | |
| Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 328 pages
...~^-- 480. Cor. m. (a) Two rectangles having equal bases are to each other as their altitudes, and (6) **two rectangles having equal altitudes are to each other as their bases.** — . — — OUTLINE OF PROOF — fr ' ft _ ft ~ ^ ' ft Sf~bh'~h'- ~B>~V~^h~VEx. 803. Draw a rectangle... | |
| David Eugene Smith - Geometry - 1911 - 358 pages
...the vicinity offers all the outdoor work that is needed to make Book IV seem very important. THEOREM. **Two rectangles having equal altitudes are to each other as their bases.** Euclid's statement (Book VI, Proposition 1) was as follows: Triangles and parallelograms which are... | |
| Geometry, Plane - 1911 - 192 pages
...circle the product of the segments of one chord is equal to the product of the segments of the other. 5. **Two rectangles having equal altitudes are to each other as their bases.** 6. Two similar polygons are to each other as the squares of their homologous sides. 7. The line joining... | |
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