| George Albert Wentworth - Geometry - 1877 - 426 pages
...uв ' 5' EB = FС ' TF' Ax. 1 CASE. II. — When AE and EB (Fig. 2) are incommensurable. Divide AE **into any number of equal parts, and apply one of these parts to** EB as often as it will be contained in E B. Since AE and EB are incommensurable, a certain number of.... | |
| George Albert Wentworth - 1881 - 266 pages
..._ 3 TF~ 5But AE EB AE , 5 FC CASE. II. — When AE and ЕВ (Fig. 2) are incommensurable. Divide AE **into any number of equal parts, and apply one of these parts to** EB as often as it will be contained in E B. Since AE and EB are incommensurable, a certain number of... | |
| George Albert Wentworth - Geometry - 1888 - 264 pages
...transversal). Compare (1) and (2), < 2 > CASE II. When AE and EB (Fig. 2) are incommensurable. Divide AE **into any number of equal parts, and apply one of these parts** as a unit of measure to EB as many times as it will be contained in EB. Since AE and EB are incommensurable,... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...Comparing, angle O Arc AB Ax. i QED CASE II. When the arcs arc incommensurable. Suppose AB to be divided **into any number of equal parts and apply one of these parts to** A'B' as a measure as often as it will go. Since AB and A'B' are incommensurable, there will be a remainder... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...A'B' angle O arc AB §180 Ax. i CASE II. When the arcs are incommensurable. Suppose AB to be divided **into any number of equal parts and apply one of these parts to** A'B' as a measure as often as it will go. Since AB and A'B' are incommensurable, there will be a remainder... | |
| Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...In the A ABC, DE is drawn II to BC, and AD and DB are incommensurable. Conclusion. AD :DB:: AE : EC. **Proof. Divide AD into any number of equal parts, and apply one of these parts to** DB as a unit of measure. It will be contained a certain number of times with a remainder FB, which... | |
| Webster Wells - Geometry - 1899 - 450 pages
...Case H. When the angles are incommensurable. C\E'\ (Prove as in §§ 189 or 244. Let Z CAD be divided **into any number of equal parts, and apply one of these parts to** Z CAE as a unit of measure.) 626. Cor. I. The surface of a lune is to the surface of the sphere as... | |
| George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...A). . Z A'C'B' 4 Z.ACB CASE 2. When the arcs are incommensurable (Figs. 2 and 3). Proof. Divide AB **into any number of equal parts, and apply one of these parts to** A'B' as many times as A'S ' will contain it. Since AB and A'B' are incommensurable, a certain number... | |
| George Albert Wentworth - Geometry - 1899 - 498 pages
...= m:n. .-.EB:AE=FC:AF. Ax. 1 CASE 2. When AE and EB (Fig. 2) are incommensurable. Proof. Divide AE **into any number of equal parts, and apply one of these parts to** EB as many times as EB will contain it. Since AE and EB are incommensurable, a certain number of these... | |
| Webster Wells - Geometry - 1899 - 424 pages
...rect. parallelopipeds, with equal bases, and incommensurable altitudes, AA' and BB'. Proof. Divide AA' **into any number of equal parts, and apply one of these parts to** BB' as a unit of measure. Since AA' and BB' are incommensurable, a certain number of the parts will... | |
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