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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 ; the ratio of the parallelogram AC to the parallelogram CF...
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Side 166
af Euclides - 1816 - 528 sider
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Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 672 sider
...a circle for the base and the vertex on the circumference, determine that which is the greatest. 2. Equiangular parallelograms have to one another the ratio which is compounded of the ratio of their sides AB, AD, the sides of a rectangle, are 8 and 6, parallelograms are described about...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1860 - 334 sider
...to CD, so is EF to PR, and because PR is equal to GH, AB is to CD, as EF to GH. PROP. XXIII. THEOR. Equiangular parallelograms have to one another the...angle ECG; the ratio of the parallelogram AC to the paral lelogram CF, is the same with the ratio which is compounded of the ratiot of their sides. 1 M...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 sider
...squares are proportional, and conversely. For squares are similar figures. PROPOSmOS XXIII. THEOREM. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. Given AC and CF two equiangular parallelograms, having the angle BCD equal to the angle ECG ; to prove...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 380 sider
...parallelograms are proportional to the squares of their homologous sides. 36. How is it s.hewn 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 compounded of...
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 sider
...similarly situated. fThey are to one another as -j the rectangles under their ( bases and altitudes. They have to one another the ratio which is compounded of the ratios of their sides. Their sides about the eqnal angles are reciprocally proportional. They are equal to one another. .They...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 714 sider
...that is, to divide it into two equal parts. VOLUNTARY PORTION. 1. Define compound ratio. Prove that equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. 2. Define a plane. When is a straight line perpendicular to a plane ? Draw a straight line perpendicular...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 sider
...DFalso = fig. AC; — which is impossible : .-. EF not ф BC ; ,. e., EF = BC. QED PÜOP. 23. — THEOR. Equiangular parallelograms have to one another the ratio which is compounded of the ratio of their sides. CON. 14, 1. 31, I. 12, VI. DEM. Def. AV of Compound Ratio. When there arc any...
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Lessons on plane trigonometry

Edward Butler (A.M.) - 1862 - 154 sider
...triangles, a and a' homologous sides. Then, T= )rf , and T'=j . smA " smA Whence, J_£ 70. 7%« areas of equiangular parallelograms have to one another, the ratio which is compounded of the ratios iff the sides. (B. vi., Prop, xxiii.) Let P and P' be equiangular parallelograms, a and b two adjacent...
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The Propositions of the Fifth Book of Euclid Proved Algebraically: with an ...

George Sturton Ward - 1862 - 104 sider
...the ratio) compounded of 'the ratios of their sides." The same parallelopipeds may also be shewn to have to one another the ratio which is compounded of the ratios of their edges. When a ratio is compounded of several ratios, all of •which are the same, it is termed a duplicate...
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An elementary treatise on mensuration

Benjamin Theophilus Moore - 1863 - 320 sider
...area of a rectangle. In Euclid's Elements of Geometry, Book VI. Proposition 23, it is proved that " Equiangular parallelograms have to one another the...ratio which is compounded of the ratios of their sides ;" and therefore rectangles, which are equiangular parallelograms, have to one another this same ratio....
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