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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: Viz. the First Six Books, Together with the Eleventh ... - Side 329
av Euclid, Robert Simson - 1821 - 516 sider
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - 349 sider
...are together equal to four times the quadrilateral figure. PROPOSITION XXVI. THEOREM. (Eucl. vi. 23.) Equiangular parallelograms have to one another the ratio, which is compounded of the ratios of their sides. B. JI \ \. K. ZM Let AC and CF be equiangular Os, baving L BCD = L ECG. Then must LJ AC...
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Five Years in an English University

Charles Astor Bristed - 1874 - 572 sider
...of gravity. SENATE-HOUSE EXAMINATION. FRIDAY, Jan. 3, 1845. 9 . . . ll£. 1. DEFINE compound ratio. Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. 2. Draw a straight line perpendicular to a plane from a given point above it. a. Show...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...to a similar and similarly described triangle upon the second, PROP. XIV.— THEOREM. (Eoo. VI. 23.) Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let ABCD and CHGF be two equiangular parallelograms, having the angles BCD and HCP equal,...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...is to CD, as EF to GH (V. 7). If therefore, four straight lines, &c. QED PROPOSITION 23. —Theorem. Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG....
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Recent military, naval, and civil service examination papers in mathematics ...

Braithwaite Arnett - 1874
...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 - 403 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
...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 - 413 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
...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, New ed., revised

James McDowell - 1878
...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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