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" If four quantities are in proportion, they are in proportion by composition, ie the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term. "
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... - Page 99
by William Chauvenet - 1875 - 368 pages
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Catalogue of the Officers and Students

Trinity College (Hartford, Conn.) - 1870 - 1008 pages
...the ratio of 4 to 3; and if 8 be subtracted from each they will be in the ratio of 0 to 4. Prove that if four quantities are in proportion, they are in proportion by composition. 8. Find three numbers in geometrical progression such that their sum shall be 42, and the sum of the...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...unity from both members of [1], we should have found A — B A' — B' B A — B A B' A' — B' A' [3] results which are briefly expressed by the theorem,...quantities are in proportion, they are in proportion by division; where the term division is employed to express the subtraction of consequent from antecedent...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...antecedent into parts. The quotient of [2] divided by [3] is A + B A — B A' + B' A' — B''' that is, if four quantities are in proportion, they are in proportion by composition and division. 11. Definition. A continued proportion is a series of equal ratios, as A : B = A' : B'...
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Catalogue - Harvard University

Harvard University - 1874 - 668 pages
...If two parallel lines are cut by a third straight line, the alternate interior angles are equal. 8. If four quantities are in proportion, they are in proportion by composition and division. 4. An inscribed angle is measured by one-half its intercepted arc. 5. A parallel to the...
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 376 pages
...inversion, a + b : a :: c + d : c, and a + b : b :: c + d : d, which was to be proved. PROPOSITION VI. THEOREM. If four quantities are in proportion, they are in proportion by division. Assume the proportion, a : b :: c : d, whence - = -, ... (1) subtracting each member of the...
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Elements of Geometry: And the First Principles of Modern Geometry

William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...dividing this by the given equation, we have, ^JT- = - ~tD, or, A + B : A = C + D : C. .A. \_> Hence, if four quantities are in proportion, they are in proportion by composition. 9. Subtracting unity from both members of — = T~, we obtain, in like manner, AB CD BD , or, A —...
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The Dictionary of Education and Instruction: a Reference Book and Manual on ...

Henry Kiddle, Alexander Jacob Schem - Education - 1881 - 378 pages
...vitiate the proportion, is not brought to light at all. For example, suppose we are to prove that, If four quantities are in proportion, they are in proportion by composition, ie, if a : b : : a : d, then a : a-\-b : : a : c-{-d. The common method is to pass from the given proportion...
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Elements of Plane Geometry

Franklin Ibach - Geometry - 1882 - 208 pages
...d : c. Take the form — = — • о а Divide 1 by each member. Then 1-1, а с THEOREM VII. 162. If four quantities are in proportion, they are in proportion by composition. Let a : b :: с : d. To prove that a .\- b : b : : с -fd : d. Take the form .7- = -=-• о а To...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...have, I = -g, or A : B :: C : D; in like manner, we have, £ = £, or B : A :: D | C; PROPOSITION III. THEOREM. If four quantities are in proportion, they are in proportion by alternation. • Assume the proportion, BD A : B : : C : D ; whence, T" = ~C" Q Multiplying each member...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1888 - 826 pages
...members of [1] ; then or, reducing, A + B ^ A' + B' B B' and dividing this by [1], A + B A' + B' A' [2] results which are briefly expressed by the theorem,...members of [1], we should have found A — BA — B' B B' [3] A— B A' — B' ' AA ' results which are briefly expressed by the theorem, if four quantities...
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