 | Euclid - 1822 - 222 pàgines
...XVII. THEOR. If three right lines be proportional (A to B as B to Fig, 24. CJ the rectangle under the extremes is equal to the square of the mean. And if...three right lines are proportional. Part 1. Assume a line D equal to B, and A is to (i)Pro;'.n. B as D to C (1), therefore the rectangle under A and^-5C... | |
 | Charles Hutton - 1822 - 616 pàgines
...rectangle of the two extremes is equal to the square of the mean ; and, conversely, if the rectangle of the extremes be equal to the square of the mean, the three lines are proportionals. Carol, t. Since it appears, by the rules of proportion In Arithmetic and Algebra,... | |
 | Peter Nicholson - 1825 - 1046 pàgines
...EUCLID. £69 PROP. XVII. THEOR. Iflkree straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean : And if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are projwrlionals.... | |
 | Euclides - 1826 - 226 pàgines
...PROPOSITION XVII.* THEOREM. If three right lines be proportional, the rectangle contained under the extremes is equal to the square of the mean ; and if the rectangle contained under the extremes be equal to the square of the mean, the three right lines will be proportional.... | |
 | Euclid - 1826 - 234 pàgines
...PROPOSITION XVII.* THEOREM. If three right lines be proportional, the rectangle contained under the extremes is equal to the square of the mean ; and if the rectangle contained under the extremes be equal to the square of the mean, the three right lines will be proportional.... | |
 | Euclid, John Playfair - 1826 - 326 pàgines
...&e. QED PROP. XVII. THEOR. If three straight lines be proportionals, the reetangle eontained by the extremes is equal to the square of the mean : And if the reetangle eontained by the extremes be equal to the square of the mean, the three straight lines are... | |
 | Robert Simson - 1827 - 546 pàgines
...&c. QED PROP. XVII. THEOR. If three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean : and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals.... | |
 | Euclid, Dionysius Lardner - 1828 - 542 pàgines
...proportional (A to B as B to C) the rectangle under the extremes is equal to the square of the mean. 2°. And if the rectangle under the extremes be equal to...right lines are proportional. Part 1°. — Assume a line D equal to B, and A is to B as D to C (hyp.), therefore the rectangle under A and C is equal to... | |
 | Pierce Morton - 1830 - 584 pàgines
...proportionals, the rectangle under the extremes shall be equal to the square of the mean ; and, conversely, if the rectangle under the extremes be equal to the square of the mean, the three straight lines shall be proportionals. Cor. 4. It appears from the proposition that rectangles which... | |
 | Euclid - 1833 - 216 pàgines
...three right lines be proportional (A to B as B to C), the rectangle under the extremes is equal tothe square of the mean. And if the rectangle under the...three right lines are proportional. Part 1. Assume a line D equal to B, and A is to (i)Prop.i4. B as D to C(1); therefore the rectangle under A and ™\5A... | |
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IF three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean ; and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals. 
