| Adrien Marie Legendre - Geometry - 1822 - 367 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 - 266 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 - 240 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 - 472 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 - 508 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... | |
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