...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....

..._ 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...

...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,...

...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...

...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...

...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...

...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...

...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...

...= 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...

...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...