Books Books If four quantities are in proportion, they are in proportion by composition; that is, 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. Solid Geometry - Page 254
by John H. Williams, Kenneth P. Williams - 1916 - 162 pages ## Catalogue of the Officers and Students

Trinity College (Hartford, Conn.) - 1870 - 1010 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... ## A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...antecedent into parts. The quotient of  divided by  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'... ## A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...dividing this by , A + B A' + B' A ~ A' '  results which are briefly expressed by the theorem, if four quantities are in proportion, they are in proportion by composition ; the term composition being employed to express the addition of antecedent and consequent in each... ## 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... ## Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 394 pages
...alternation, a : b : : c : d, and a : b :: e : f, and consequently, c : d : : e : f. PROPOSITION V. THEOREM. If four quantities are in proportion, they are in proportion by composition. Assume the proportion, a : b : : c : d, whence - = - ; . . . (1) adding each member of the preceding... ## Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. 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 —... ## University Algebra

Webster Wells - Algebra - 1879 - 468 pages
...: d then, ad = b с Whence, b : a = d : c. 347. If four quantities are in proportion, they will be in proportion by COMPOSITION ; that is, the sum of the first two terms will be to the first term, as the sum of the last two terms is to the third term. Thus, if a : b =... ## The Dictionary of Education and Instruction: a Reference Book and Manual on ...

Alexander Jacob Schem - Education - 1881 - 374 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... ## 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... 