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" 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 "
Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ... - Page 73
by Euclides - 1860
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Elements of Geometry and Trigonometry: With Notes

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...
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Elements of Arithmetic, Algebra, and Geometry

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 :...
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Elements of Plane Geometry According to Euclid

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,...
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An elementary course of practical mathematics, Part 1

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...
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

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 ¨, in the duplicate ratio of the first and second. Let...
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New Higher Algebra: An Analytical Course Designed for High Schools ...

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 ... . . ,...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

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...
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Navigation

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 = -,...
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New University Algebra: A Theoretical and Practical Treatise Containing Many ...

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 the▀rst and second. Let...
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Elements of Geometry, Plane and Spherical: With Numerous Practical Problems

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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