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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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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Bog 1

Euclides - 1853 - 334 sider
...THEOE. If two parallelograms have one angle of the one equal to one angle of the other : then they shall have to one another the ratio which is compounded of the ratios of each pair of sides about the equal angles. Let ABCD, EFGH be two parallelograms, having the angle ABC...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853 - 400 sider
...equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. Let BC, CG be placed in a straight line ; therefore DC and CE are also in a straight line (14. i.) ; and...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 176 sider
...the angle e С g '• the ratio of the parallelogram a С to the parallelogram. С fis the same with the ratio which is compounded of the ratios of their sides. Let bС, С g be placed in a straight line ; therefore d С and С e are also in a straight line (i. 14)...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 270 sider
...described upon them, are also continual proportionals ; and amversely. PROP. XXIIL THEOREM. taugu/ar parallelograms have to one another the ratio which is compounded of the ratios of their sides Let AC and CF be equiangular parallelograms, having the angle BCD equal to the angle EC G. The ratio of the...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855 - 1050 sider
...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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A Treatise on Arithmetic ...

Noble Heath - 1855 - 468 sider
...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 Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855 - 230 sider
...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: Through which the Entire Science Can be Most ...

Noble Heath - 1856 - 472 sider
...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, Bind 11–13

1857 - 1266 sider
...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 - 150 sider
...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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