Legendre, A. M. (Adrien Marie), 1752-1833, Brewster, David, Sir, 1781-1868, Davies, Charles, 1798-1876 · New York, Wiley & Long · leaf 138
refore suppose the solid angle S tobe formed by three plane angles ASB,ASC, BSC, whereof the angle ASB isthe greatest ; we are to show thatASB<ASC + BSC. In the plane ASB make the angle BSD = BSC, draw thestraight line ADB at pleasure; and having taken SC = SD,draw AC, BC. The two sides BS, SD,… … BOOK VI. 130 mains AD<AC. The two sides AS, SD, are equal lo thetwo AS, SC ; the third side AD is less than the third side AC ;Ihereture the an;rle ASD<ASC (Book I. Prop. IX. Sch.).Adding BSl) = BSC, we shall have ASD + BSD or ASB<ASC + B«C.
Trigonometry · Geometry
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