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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 ... - Pagina 130
door John Playfair - 1855 - 318 pagina’s
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A Treatise on Arithmetic: Through which the Entire Science Can be Most ...

Noble Heath - 1856 - 472 pagina’s
...multiplying the base by its perpendicular height or altitude, (103,) it is evident that the areas of any two parallelograms have to one another the ratio which is compounded of the ratios of their bases and altitudes. Hence we deduce the following properties : 1. Parallelograms of equal base and...
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The English Journal of Education, Volumes 11-13

1857 - 1266 pagina’s
...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.

Euclid - 1859 - 136 pagina’s
...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 - 672 pagina’s
...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 - 288 pagina’s
...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 pagina’s
...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 pagina’s
...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 pagina’s
...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 pagina’s
...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 - 104 pagina’s
...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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