 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...EF, so EF to BG ; and that if three straight lines be proportionals, the first is said (10 Def. v.) to have to the third the duplicate ratio of that which it has lo the second ; BC therefore has to BG the duplicate ratio of that which BC has to EF : But as BC to... | |
 | Euclides - 1855 - 270 pages
...the second haa to the third. X. When three magnitudes are continual proportionals, the first is said to have to the third, the duplicate ratio of that which it has to the second. When three magnitudes are continual proportionals, the ratio of the first to the third is compounded... | |
 | Elias Loomis - Algebra - 1855 - 356 pages
...213, a : b : : a+c+e : b+d+f. (225.) If three quantities are in continued proportion, the first will have to the third the duplicate ratio of that which it has to the second. Let a : b : : b : c. Then a : c : : a' : &'. For since a : b : : b : c, by Art. 212, ac=b*.... | |
 | Euclides - 1855 - 230 pages
...extremes, and all the others the mean terms. 10. When three magnitudes are proportionals, the first is said to have to the third the duplicate ratio of that which it second. litudes are proportionals, the first is said duplicate ratio of that which it has to the 11.... | |
 | Samuel Alsop - Algebra - 1856 - 152 pages
...: с : d, ma : nb : : me : nd. § 97. If three quantities be in continual proportion, the first has to the third the duplicate ratio of that which it has to the second. Thus, if a : Ъ : : Ъ : с, а : с is the duplicate ratio of a : b. For (§ 88) the ratio... | |
 | Elias Loomis - Algebra - 1858 - 394 pages
...213, a : b : : a+c+e : b+d+f. (225.) If three quantities are in continued proportion, ttu first will have to the third the duplicate ratio of that which it has to tht second. Let a : b : : b : c Then a : c : : a" : V. For since a : b : : b : c, by Art. 212, ac=b*.... | |
 | Eucleides - 1860 - 396 pages
...and that if three >e);v. bef.' 10. straight lines he proper- (/) VI. 1. tionals, the first is said to have to the third the duplicate ratio of that which it has to the second (e) ; therefore BC has to BG the duplicate ratio of that which BC has to EF. But as BC is to... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...because as BC is to EF, so EFto BG ; and that if three straight lines be proportionals, the first is said to have to the third, the duplicate ratio of that which it has to the second : (v. def. 10.) therefore B Chots to SG the duplicate ratio of that which .B Chaste EF: but... | |
 | Euclides - 1860 - 288 pages
...because BC is to EF as EF to BG ; and that if three straight lines be proportionals, the first has to the third the duplicate ratio of that which it has to the second ; BC therefore has to BG the duplicate ratio of that which BC has to EF. But as BC to BG, so... | |
 | Euclides - 1861 - 464 pages
...thus, a : b :: 6 : c, or 2 : 4 : : 4 X. — When three magnitudes are proportionals, the first is said to have to the third the duplicate ratio of that which it has to the second. A duplicate, or two-fold ratio is a ratio compounded of two equal ratios ; n Л thus if a :... | |
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When three magnitudes are proportionals, the first is said to have to the third the duplicate ratio of that which it has to the second. 
