Plane and solid geometry . Q E. Given lune NASB with the number of degrees in its Z. denotedby N, its area denoted by L, and the area of the surface of thesphere denoted by 5; let O EQ be the great O whose pole is N. To prove - = S 360 I. If arc AB and circumference EQ are commensurable(Fig. 1). 1. Argument Let m be a common measure of arc ABand circumference EQ^ and supposethat m is contained in arc AB r timesand in circumference EQ t times,arc AB r t 2. Then circumference EQ 3. Through the several points of division on circumference EQ pass semicir-cumferences of great circles from Nto S. 4.

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Plane and solid geometry . Q E. Given lune NASB with the number of degrees in its Z. denotedby N, its area denoted by L, and the area of the surface of thesphere denoted by 5; let O EQ be the great O whose pole is N. To prove - = S 360 I. If arc AB and circumference EQ are commensurable(Fig. 1). 1. Argument Let m be a common measure of arc ABand circumference EQ^ and supposethat m is contained in arc AB r timesand in circumference EQ t times,arc AB r t 2. Then circumference EQ 3. Through the several points of division on circumference EQ pass semicir-cumferences of great circles from Nto S. 4. Then lune NASB is divided into r lunes and the surface of the sphere into tlunes, each equal to lune NCSB, 1. Reasons§335. 2. §341. 3. § 908, h. 4. §984. BOOK IX 453 L SL S r —• t Argument arc AB circumference EQ 7. But arc AB is the measure of ; it contains iV degrees. 8. And circumference EQ contains 360°. L N 9. S 360 Reasons 5. §341. 6. §54,1. 7. §918. 8. §297. 9. §309. II. If arc AB and c

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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912