 | E. J. Brooksmith - 1889 - 356 σελίδες
...whether four magnitudes are proportionals ? Find a fourth proportional to three given straight lines. 10. 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 means be equal to the... | |
 | New Brunswick. Board of Education - 1889 - 1004 σελίδες
...Show that in a parallelogram the diagonals do not bisect the angles unless their sides art; equal. 5. If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means. fi. Equal triangles which have one angle of the one equal to... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 σελίδες
...the figure of VI. 15, A and the mid points of BD and CE nre collinear. PROPOSITION 16. THEOREM. (1) If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means. (2) Conversely : — If the rectangle contained by the extremes... | |
 | Queensland. Department of Public Instruction - 1892 - 508 σελίδες
...equiangular ; and the equal angles shall be those which are opposite to the homologous sides. 14. If three straight lines be proportionals, the rectangle contained by the extremes is equal to the square on the mean, and conversely. ACOUSTICS, LIGHT AND HEAT. (FntsT PAPKB.) 21«/ December —... | |
 | Henry Martyn Taylor - 1893 - 486 σελίδες
...therefore the triangles ABC, DEF are equal in area. Wherefore, if two triangles &c. PROPOSITION 16. PART 1. If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means. Let the straight lines AB, CD, EF, GH be proportionals, so that... | |
 | Henry Martyn Taylor - 1895 - 708 σελίδες
...therefore the triangles ABC, DEF are equal in area. Wherefore, if two triangles &c. PROPOSITION 16. PART 1. If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means. Let the straight lines AB, CD, EF, GH be proportionals, so that... | |
 | 1861 - 806 σελίδες
...any quadrilateral figure [escribed in a circle, are together equal to two right angles. 11. If three straight lines be proportionals, the rectangle contained by the extremes is equal to the 10. Describe an isosceles triangle, having each f the angles at the base double the third angle.... | |
 | Sir Thomas Little Heath - 1921 - 482 σελίδες
...figure, Euclid is able to apply VI. 1. From 14 are directly deduced 1 6, 1 7 (that, if four or three straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the two means or the square on the one mean, and the converse). 18-22 deal... | |
 | Sir Thomas Little Heath - 1921 - 474 σελίδες
...figure, Euclid is able to apply VI. 1. From 14 are directly deduced 16, 17 (that, if four or three straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the two means or the square on the one mean, and the converse). 18-22 deal... | |
 | Sir Thomas Little Heath - 1921 - 474 σελίδες
...figure, Euclid is able to apply VI. 1. From 14 are directly deduced 16, 17 (that, if four or three straight lines be proportionals, the rectangle contained by the extremes is equal !<• the rectangle contained by the two means or the square on throne mean, and the converse). 18-22... | |
| |
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. 
