 | Euclides, James Hamblin Smith - 1872 - 376 σελίδες
...AP, respectively. Shew that the triangle ANM is equal to the triangle ABC. PROPOSITION XVI. THEOREM. If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means. M. oLet the four st. lines AB, CD, EF, GH be proportionals, so... | |
 | William Alexander Myers - 1873 - 238 σελίδες
...B as B is to C, [Hypothesis.} and that B is equal to D; therefore A is to B as D is to C. [ V. 7.] But if four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means ; [VI. 16.] therefore the rectangle contained by A and C is equal... | |
 | William Alexander Myers - 1874 - 207 σελίδες
...B as B is to C, [Hypothesis.] and that B is equal to D', therefore A is to B as D is to C. [7. 7.] But if four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means ; [ VI. 16.] therefore the rectangle contained by A and C is equal... | |
 | Euclides - 1874 - 342 σελίδες
...equal to the triangle ADE (V. 9). Therefore, equal triangles, &c. QED PROPOSITION 16. — Theorem. If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means; and conversely, if the rectangle contained by the extremes be... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 σελίδες
...straight line, and therefore the angles are vertically opposite. PROP. XII.— THEOREM. (Euc. VI. 16, 17.) If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means; and conversely. Let AB, CD, E and P be four straight lines which... | |
 | Robert Potts - 1876 - 446 σελίδες
...pqual to B. And because as A to B, so 11 to C, and that B is equal to D; A is to B, as D to C: (v. 7.) but if four straight lines be proportionals, the rectangle...is equal to that which is .contained by the means; (VI. 16.) .therefore the rectangle. contained by .<4, 0 is equal to that contained by B, D : but the... | |
 | Richard Wormell - 1876 - 268 σελίδες
...Because А В : FE = DB BE, and В С : FE = GB BF; therefore А В : FE = В С FE; THEOREM LXXVI. // four straight lines be proportionals the rectangle contained by the extremes is equal to the rectangle contained by the means. Сonversely, if the rectangle contained by the extremes be equal... | |
 | D. Tierney - 1877 - 126 σελίδες
...two triangles BDE and EFC are similar, and therefore BD : EF :: BE : EC, which was to be proved. 9. If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means. On a given straight line describe an isosceles triangle equal... | |
 | Samuel H. Winter - 1877 - 452 σελίδες
...the diameters of these circles are to each other in the same ratio as the segments of the base. 9. If four straight lines be proportionals, the rectangle contained by the extremes shall be equal to the rectangle contained by the means. On a given straight line describe an isosceles... | |
 | London univ, exam. papers - 1878 - 164 σελίδες
...xl -yl. (e)x2+2x-i. 9. (i) 26. (2)5. (3)^ = 8,^ = 6. (4)^ = 4,^ = 3,2=2. 10. (a) TA, Art. 359. (b) If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means ; and conversely (Euc. VI. 16). (f) Now T = -> hence -£x-,=-xr.... | |
| |
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. 
