 | Adrien Marie Legendre - Geometry - 1822 - 394 pages
...: : A : B, we shall have A2 : B2 : : BA : BC ; or(Cor. 2. Theor. 11.) A2 : B2 : : A : C. Hence in a continued proportion, the first is to the third as the square of the first is to the square of the second. The ratio which A bears to C is sometimes called the duplicate... | |
 | George Lees - 1826 - 276 pages
...equivalent to the triangle DEFe. Again, e 10- 4because BC : EF : : EF : BG, and that, if three quantities be in continued proportion, the first is to the third as the square of the first to the square of the second? ; therefore, BC : BG : : t 121. Alg. BC2 : EF2 ; but, BC : BG :... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...the circle suggested a considerable improvement in the form of astronomical angular instruments. 6. If three lines be in continued proportion, the first...square of the difference between the second and third. 7. If a line bisect the angle adjacent to the vertical angle of a triangle, and meet the base produced,... | |
 | James Elliot - 1860 - 252 pages
...ratio of 8 to 12, and what the Subtriplicate ratio of 3 to 81 ? THEOREM XIII. When three Quantities are in continued Proportion, the first is to the third as the Square of the first to the Square of the second ; and the first is to the second as the square Root of the first... | |
 | Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...two quantities is equal to the square root of their product. PROPOSITION XIV. — If three quantities be in continued proportion, the first is to the third, as the square of the first is to the square of the second ; that ù, in the duplicate ratio of the first and second. Let... | |
 | Benjamin Greenleaf - Algebra - 1864 - 420 pages
...fractional ; whence, 11 11 a" : 6" : : c" : dn, and a" : b" : : c" : rf". 32 1, If three quantities be in continued proportion, the first is to the third as the square of the first is to the square of the second. If a : b : : b : c, then a : c : : a2 : b1. „ ab ... . . ,... | |
 | Horatio Nelson Robinson - Conic sections - 1865 - 474 pages
...Hence the theorem ; if four magnitudes are in proportion, etc. THEOREM XIV. If three magnitudes are in proportion, the first is to the third as the square of the first is to the square of the second. Let A, B, and C, be three proportionals. Then we are to prove... | |
 | James Pryde - Navigation - 1867 - 506 pages
...since ac — №, IP = ac, and taking the square root of both sides, b = Jaf. 50. If three quantities be in continued proportion, the first is to the third as the square of the first to the square of the second. Let a : b = b : c; to prove that a : c= az \№. Since -т = -,... | |
 | Horatio Nelson Robinson - 1868 - 430 pages
...quantities is equal to the square riiot of their product. PROPOSITION XIV. — If three quantifies le in continued proportion, the first is to the third, as the square of the first is to the xijuare of the second ; that is, in the <lnp!icute ratio of theßrst and second. Let... | |
 | Horatio Nelson Robinson - 1869 - 276 pages
...the theorem; if four magnitudes are in proportion, etc. • THEOREM XIV. If three magnitudes are in proportion, the first is to the third as the square of the first is to the square of the second. Let A, B, and (7, be three proportionals. Then we are to prove... | |
| |
If three quantities are in continued proportion, the first is to the third as the square of the first is to the square of the second. Let a : b = b : c. Then, 2=*. b с Therefore, ^xb. = ^x± b с bb Or °r 
