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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... "
The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick - Seite 128
von Royal Military Academy, Woolwich - 1853
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855 - 1050 Seiten
...angles to each of them in that point; these three straight lines are in cue and the same plane. 14. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. Draw a straight line perpendicular to the plane of a triangle such that if any point in it be joined...
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855 - 226 Seiten
...similarly situated. They are to one another as 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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A Treatise on Arithmetic ...

Noble Heath - 1855 - 468 Seiten
...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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A Treatise on Arithmetic: Through which the Entire Science Can be Most ...

Noble Heath - 1856 - 472 Seiten
...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, Bände 11-13

1857 - 1266 Seiten
...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 - 132 Seiten
...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 Seiten
...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 - 332 Seiten
...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 - 286 Seiten
...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 - 361 Seiten
...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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