Plane and solid geometry . and altitude AB, and letU be the chosen unit of surface, whose side is u. To prove the area of ABCD = AD • AB. I. If AD and AB are each commensurable with u,(a) Suppose that u is contained in AD and AB each an in-tegral number of times. Argument 1. Lay off u upon AD and AB, respectively. Suppose that it is contained in AD rtimes, and in AB s times. 2. At the points of division on AD and onAB erect Js to AD and AB, respectively. 3. Then rectangle ABCD is divided into unit squares. 4. There are ?- of these unit squares in a row on AD, and s rows of thesesquares in rect
Plane and solid geometry . and altitude AB, and letU be the chosen unit of surface, whose side is u. To prove the area of ABCD = AD • AB. I. If AD and AB are each commensurable with u,(a) Suppose that u is contained in AD and AB each an in-tegral number of times. Argument 1. Lay off u upon AD and AB, respectively. Suppose that it is contained in AD rtimes, and in AB s times. 2. At the points of division on AD and onAB erect Js to AD and AB, respectively. 3. Then rectangle ABCD is divided into unit squares. 4. There are ?- of these unit squares in a row on AD, and s rows of thesesquares in rectangle ABCD. 5. .-. the area of ABCD = r • 5. 6. But r and s are the measure-numbers oi AD and AB, respectively, referredto the linear unit u. 7. .-. the area of ABCD = ADAB. Reasons 1. § 335. 2. § 63. 3. § 466. 4. Arg. 1. 5. § 467. 6. Arg. 1. 7. § 309. 214 PLANE GEOMETRY (b) If u is not a measure of AD and AB, respectively, butff some aliquot part of u is such a measure. The proof is left to the student. I.
Size: 2091px × 1195px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
