 | Robert Simson - Trigonometry - 1806 - 546 pages
...EF, so EF to BG ; and that if three straight lines be proportionals, the first is f 10.def.5. said f to have to the third the duplicate ratio of that which it h»s to the second ; BC therefore has to BG the duplicate ratio of 1 6 that which BC has to EF : but... | |
 | Euclid - Geometry - 1810 - 554 pages
...BG ; and- that if three x / ix straight lines be pro- T> portionals, the first is . s-iidi' to hiive to the third the duplicate ratio of that which it has to the second; BC therefore has to BG the duplicate ratio of gl. 6. that which BC nas to EF: but as BC to... | |
 | Euclides - 1816 - 588 pages
...to EF, so EF to BG ; and that if three 'lOJiet. 5 straight lines he proportional, the first is saidf to have to the third the duplicate ratio of that which it has to the second ; BC therefore has to BG the duplicate ratio of that • 1-6 which BC has to EF : But as BC... | |
 | James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...the equality of ratios. I A. Omitted. 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. XI. When four magnitudes are continued proportionals, the first is said to have to the fourth... | |
 | James Ryan - Algebra - 1824 - 550 pages
...equality of ratios. rA. ' , Omitted. 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. XI. When four magnitudes ate couVxwyfc&v J first is said to have Xo VVve fo\«\.YiVJaft ratio... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...to BG; and that if three straight lines be proportionals, the first is said (10 def. «.). to hare 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 BÜ,... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...Proportion consists in three terms at least. 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. XL See N. When four magnitudes are continual proportionals, the first is said to have to the... | |
 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...there will be three terms in all. (453) 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. (454) The proportion in this case is said to be continued. Any number of magnitudes are said... | |
 | John Playfair - Euclid's Elements - 1832 - 358 pages
...because that BC is to EF,asEFtoBG;andthat if three straight lines be proportionals, the first has Tito 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... | |
 | Euclid - 1835 - 540 pages
...Proportion consists in three terms at least. 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. XL See N. When four magnitudes are continual proportionals, the first is said to have to the... | |
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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. 
