 | Euclides - 1861 - 464 pages
...the scalene д ABC. QEF PROP. 16. — Тнnoв. (Very Important.) If four st. 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 equal to the rectangle contained by... | |
 | Euclides - 1865 - 402 pages
...reciprocally proportional, are equal to one another. Prop. 16. 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 equal to the rectangle contained by... | |
 | Robert Potts - 1865 - 528 pages
...Therefore, equal triangles, &o. QED PROPOSITION XVI. THEOREM. If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained l»j the means : and conversely, if the rectangle contained by the extremes be equal to the rectangle... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...Wherefore, 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 if the rectangle contained by the' extremes be equal to the rectangle contained by the means, the... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...Wherefore, equal triangles &c. QF.D. PROPOSITION 16. THEOREM. If four straight lines be proportionals, Hie rectangle contained by the extremes is equal to the rectangle contained by the means; and if the rectangle contained liy the' extremes be equal to the rectangle contained by the means,... | |
 | James Maurice Wilson - Geometry - 1868 - 150 pages
...sides reciprocally proportional, are equal. COR. 4. Hence, if four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means, and conversely. COR. 5. If three straight lines are in continued proportion, that is, if the first... | |
 | Cambridge univ, exam. papers - 1870 - 272 pages
...between the corresponding angles of the original triangle. 4. If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means ; and if the rectangle contained by the extremes be equal to the rectangle contained by the means,... | |
 | Thomas Steadman Aldis - 1872 - 84 pages
...equal to the rectangle contained by the means; and conversely, if we have four straight lines such that the rectangle contained by the extremes is equal to the rectangle contained by the means, these four straight lines shall be proportional. Let AB be to BG as FB is to BG. Then shall the rectangle... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...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 that AB is to CD as EF is to GH. Then... | |
 | William Alexander Myers - Circle-squaring - 1873 - 238 pages
...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 to the rectangle contained by B and... | |
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If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means. 
