| Great Britain. Education Department. Department of Science and Art - 1877 - 564 pages
...their angles proportional, the triangles will be similar. 2. Prove that the areas of two rectangles **have to one another the ratio which is compounded of the ratios of** their sides ; and thence show that, if a perpendicular be drawn from one of the angles of a rectangle... | |
| James McDowell - 1878 - 310 pages
...we may concisely express it, as AB3 : CD3. Euclid has proved (YI. 23) that rectangles (for they are **equiangular parallelograms) have to one another the ratio which is compounded of the ratios of** their sides. If, therefore, BC, CD and CG, CE be the adjacent sides of two rectangles, Therefore the... | |
| University of Oxford - Greek language - 1879 - 414 pages
...shall be greater than the other two together. 10. Parallelograms which are equiangular to one another **have to one another the ratio which is compounded of the ratios of** their sides. V. Elements of Mechanics. I. 1. Prove the parallelogram offorees for direction. Find the... | |
| Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 pages
...intersection A', B', C', D', E', F. Show that the hexagon A'B'C'D'E'F' is three times as great as ABCDEF. 10. **Equiangular parallelograms have to one another the ratio which is compounded of the ratios of** their sides. Two circles touch one another externally at A. A straight line touches the circles at... | |
| Sandhurst roy. military coll - 1880 - 68 pages
...parallelograms have to one another the ratio which is compounded of the ratios of their sides. Show that any two **parallelograms have to one another the ratio which is compounded of the ratios of** their bases and altitudes. 7. Each of three circles cuts the other two; prove that the three common... | |
| George Bruce Halsted - Measurement - 1881 - 258 pages
...assigned whenever we speak of the product of one line by another. GENEKAL PKOOF. Eectangles, being **equiangular parallelograms, have to one another the ratio which is compounded of the ratios of** their sides. Ww. 315; (Eu. VI 23 . QV. IV. 5). f represent the surfaces or areas of two recand o! represent... | |
| Education, Higher - 1884 - 538 pages
...to two right angles. 15. Triangles which have one angle of the one equal to one angle of the other, **have to one another the ratio which is compounded of the ratios of** their sides. Algebra. Junior, Senior, and Higher Local. Junior Work, Nos. 1 — 9 inclusive. Senior... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...Therefore PR is equal to GH. triangles which have one angle of tlie one equal to one angle of tht other, **have to one another the ratio which is compounded of the ratios of** their sides. Then VI. 19 ig an immediate consequence of this theorem. For let ABC and DBF he similar... | |
| Euclides - 1884 - 434 pages
...EF: OH, then A&> : CD* = EF* : Off*. 2. If two ratios be equal, their duplicates are equal. Mutually **equiangular parallelograms have to one another the ratio which is compounded of the ratios of** their sides.* AF G' Let ||m AB be equiangular to l|m BC, having L DBF = L GBE: it is required to prove... | |
| 1885 - 604 pages
...proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means. 6. **Equiangular parallelograms have to one another the ratio which is compounded of the ratios of** their sides. NB— Female Candidates for Class I. will receive credit for any work correctly done in... | |
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