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" Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Page 323
by Robert Simson - 1781 - 466 pages
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Examination Papers for Science Schools and Classes

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...
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Exercises on Euclid and in Modern Geometry

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...
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First Public Examination in Literis Graecis Et Latinis

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...
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Military examinations. Mathematical examination papers, set for entrance to ...

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...
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Military examinations. Mathematical examination papers, set at entrance to ...

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...
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Metrical Geometry: An Elementary Treatise on Mensuration

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...
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The Cambridge Examiner, Volume 4

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...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

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...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

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...
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Annual Report of the Chief Superintendent of Education

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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