 Three quantities are in proportion when the first has the same ratio to the second, that the second has to the third ; and then the middle term is said to be a mean proportional between the other two.  The Elements of Algebra - Page 225by Elias Loomis - 1856 - 268 pagesFull view - About this book
 | John Playfair - Euclid's Elements - 1844 - 338 pages
...said to be continual proportionals. 9. When three magnitudes are continual proportionals, the second is said to be a mean proportional between the other two. For example, if A, B, C, D, be four magnitudes of the same kind, the first A is said to have to the last D, the... | |
 | Charles Davies - Algebra - 1845 - 382 pages
...last is said to be a fourth proportional to the other three taken in order. 171. Three quantities are in proportion when the first has the same ratio to...said to be a mean proportional between the other two. 172. Quantities are said to be in proportion by inversion, or inversely, when the consequents are made... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...second the same ratio that the third has to the fourth. 6. Magnitudes are said to be proportionals, when the first has the same ratio to the second that the third has to the fourth ; and the third to the fourth the same ratio which the fifth has to the sixth,... | |
 | Charles Davies - Algebra - 1848 - 300 pages
...quantities, what are the first and third called ' What the second and fourth ? 147. Three quantities are in proportion when the first has the same ratio to...mean proportional between the other two. For example, 3 : 6 : : 6 : 12; and 6 is a mean proportional between 3 and 12. 1 48. Quantities are said to be in... | |
 | Algebra - 1848 - 394 pages
...proportional to the other three taken in order. 171. Three quantities are in proportion when the first lias the same ratio to the second that the second has to...said to be a mean proportional between the other two. 172. Quantities are said to be in proportion by inversion, or inversely, when the consequents are made... | |
 | Joseph Ray - Algebra - 1848 - 250 pages
...a fourth proportional to the other three, taken in their order. ART. 243. — Three quantities are in proportion, when the first has the same ratio to the second, that the second has to the third. In this case, the middle term is called a mean proportional between the other two. Thus, if we have... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...last is said to be a fourth proportional to the other three taken in order. 4. Three quantities are in proportion, when the first has the same ratio to...said to be a mean proportional between the other two. 5. Magnitudes are said to be in proportion by inversion, or inversely, when the consequents are taken... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...the second to the third; thus, if A, B, and C are in proportion, then A : B : : B : C. In this case the middle term is said to be a mean proportional between the other two. Def. 4. Two magnitudes are said to be equimultiples of two others, when they contain those others the... | |
 | Charles Davies - Geometry - 1850 - 238 pages
...last proportion, A and C are the antecedents, and B and D the consequents. 4. Three quantities are in proportion when the first has the same ratio to...mean proportional between the other two. For example, 3 : 6 : : 6 : 12 ; and 6 is a mean proportional between 3 and 12. 5. Quantities are said to be in proportion... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...last proportion, A and C are the antecedents, and B and D the consequents. 4. Three quantities are in proportion when the first has the same ratio to...mean proportional between the other two. For example, 3 : 6 : : 6 : 12 ; and 6 is a mean proportional between 3 and 12. 5. Quantities are said to be in proportion... | |
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