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" Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. "
Elements of Geometry: Containing the First Six Books of Euclid with a ... - Strona 140
autor: John Playfair - 1855 - Liczba stron: 318
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The English Journal of Education, Tomy 11-13

1857
...shall be equiangular, and shall have those angles equal about which the sides are proportional. 2. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. 3. If the sides of any polygon be produced to meet the alternate sides, also produced, the angles formed...
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Manual of Euclid: books iv., v., vi., by J.A. Galbraith and S. Haughton

Euclides - 1859
...Ta "taoyúvia rrapaXXqXóypa/i/ia irpоçâXXqXa Xóyov ÉXC* Tоv ffvyKtípívov ¿K TÜV ir\ivpwv. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. Statement — Let AC and CF be equiangular parallelograms, having the angle BCD equal to the angle...
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Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - Liczba stron: 1869
...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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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...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 - Liczba stron: 361
...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
...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 - Liczba stron: 12
...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
...nowfig, 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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The Propositions of the Fifth Book of Euclid Proved Algebraically: with an ...

George Sturton Ward - 1862 - Liczba stron: 79
...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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Lessons on plane trigonometry

Edward Butler (A.M.) - 1862
...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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