 | 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... | |
 | George Bruce Halsted - Geometry - 1885 - 389 pages
...composition of two equal ratios is called the Duplicate Ratio of either. THEOREM XVII. 542. Mutually equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. \ \ PROOF. Place the 2=75 so that HC and CB are in one line ; then, by 109, DC and CF... | |
 | 1885 - 608 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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Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. 
