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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: Also the Book of Euclid's Data ...cor. viz. The ... - Side 323
av Robert Simson - 1804
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Recent Military, Naval, and Civil Service Examination Papers in Mathematics ...

Braithwaite Arnett - 1874 - 130 sider
...AE, AD will be equal to the rectangle AB, AC. 8. Parallelograms which are equiangular to one another have to one another the ratio which is compounded of the ratios of their sides. 9. ABCD is a rectangle, and E, F, G, and H are the feet of the perpendiculars let fall...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 446 sider
...parallelograms are proportional to the squares of their homo-' logons sides. 36. How is it shewn that equiangular parallelograms have to one another the ratio which is compounded of the ratios of their bases and altitudes? 37. To find two lines which shall have to each other, the ratio com. pounded...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 sider
...four straight lines be proportionals, those straight lines shall be proportionals. .. .. .. 215 23. Equiangular parallelograms have to one another the ratio which is compounded of the ratio of their sides. . . . . ' . . . . . . 215 24. The parallelograms about the diagonal of any parallelogram...
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Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics ...

Samuel H. Winter - 1877 - 452 sider
...through A in the points D,E respectively, prove that BD ; DA ; ; CE : EA. 12. Define compound ratio. Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. 13. Prove that every equilateral polygon inscribed in a circle must be equiangular. Is...
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Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1877 - 562 sider
...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 sider
...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 - 1879 - 412 sider
...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 sider
...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 sider
...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 - 1881 - 258 sider
...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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