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 Βιβλία Βιβλία If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means. For, if ad = bc, then, divide by bd. т~, - г~;« bd bd а с 01 6 = 5 New School Algebra - Σελίδα 310
των G.A. Wentworth - 1901
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο ## A treatise on the elements of algebra, by G. Ainsworth and J. Yeats

G. Ainsworth - 1854
...d, then -=-, and multiplying both sides by ac, —= — , Л С ' <to . • . bc=ad. And conversely, if the product of two quantities is equal to the product of two other quantities, the four are proportional. For (by hyp.) ad=bc, and dividing both sides by bd, we... ## A Treatise on Algebra

Elias Loomis - 1855 - 316 σελίδες
...expression becomes abd bcd ~b~=~d' or ad=bc. Thus, if 3 : 4 : : 9 : 12, .hen 3X12=4X9. (213.) Conversely, if the product of two quantities is equal to the product of two others, the first two quantities may be made the extremes, and the other two the means of a proportion. Let-... ## Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - 1855 - 592 σελίδες
...definition, that the product of the extremes is equal to the product of the menus ; and conversely, if the product of two quantities is equal to the product of two others, the first two may be taken as the structed with a groove in each leg, so that extremes, and the last... ## The Popular Educator, Τόμος 6

1855
...means in both cases is the same. So, if na : Ь : : x : y, then a : Ь : : x : ny. On the other hand, if the product of two quantities is equal to the product of two others, the four quantities will form a proportion, if they are so arranged that those on one side of the equation... ## Elementary Treatise on Algebra

Thomas Sherwin - 1855 - 300 σελίδες
...product of the extremes. 2. Suppose we have ad=bc. Dividing both members by b XLIX. PROPORTIONS. 221 If the product of two quantities is equal to the product of two otner quantities, the two factors of either product may be made the means, and the two factors of the... ## Common School Algebra

Thomas Sherwin - 1855 - 238 σελίδες
...ad=bc. If we divide both members by b and d, we have — = —, or bdi a : b = c : d. Therefore, •• If the product of two quantities is equal to the product of two other quantities, the two factors of one product may be made the means, and the two factors of the... ## The Elements of Algebra

Elias Loomis - 1856 - 268 σελίδες
...the equation of fractions, we have ad— bc. Thus, if 3:4:: 9:12, then 3x12=4x9. (184.) Conversely, if the product of two quantities is equal to the product of two others, the first two quantities may be made the extremes, and the other two the means of a proportion. Let... ## Elements of Geometry and Conic Sections

Elias Loomis - 1857 - 226 σελίδες
...by the proposition, A xC=B xB, which is equal to B'. PROPOSITION ii. THEOEEM (Converse of Prop. /.). If the product of two quantities is equal to the product of twc other quantities, the first two may be made the extremes, and the other two the means of a proportion.... ## Elements of Geometry and Conic Sections

Elias Loomis - 1858 - 234 σελίδες
...by the proposition, AXC = BXB, which is equal to B1. PROPOSITION n. THEOREM (Converse of Prop. /.). If the product of two quantities is equal to the product of twc other quantities, the first two may be made the extremes, and the other two the means of a proportion.... ## New Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - 1859 - 299 σελίδες
...other, that A x D = В x (7, we shall also have, -j = -~ ; А ъ and hence, A : В : : С : D. That is : If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion....