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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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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 332 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. 1.); complete...
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## Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 sider
...to CD, as EF to GH. (v. 7-) If, therefore, four straight lines, &c. QED PROPOSITION XXIII. THEOREM. Equiangular parallelograms have to one another the...parallelograms, having the angle BCD • equal to the angle ECG. Then the ratio of the parallelogram AC to the parallelogram CF, shall be the same with the ratio which...
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## Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 218 sider
...; AB is to CD, as EF to GH. If therefore four straight lines, &c. QED PROPOSITION XXIII. THEOB. — Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. BOOK VI. PROP. XXIV. • 14. 1. t 12. 6. t 12. 6. A. Def. 5. V 11.5. Let BC, CG be placed in a straight...
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## The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclides, James Thomson - 1845 - 382 sider
...&c.* Cor. Triangles which have one angle of the one equal, or supplemental, to one angle of the other, have to one another the ratio which is compounded of the ratios of the sides containing those angles. For, if BD and EG be joined, the triangles BCD, ECG bemg (I. 34)...
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## The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 sider
...having the angle BCD equal to the angle ECG : the parallelogram AC shall be to the parallelogram CF in the ratio which is compounded of the ratios of their sides. Let BC, CG be placed in a straight line ; therefore DC and CE will be also in a straight line : complete...
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## The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 sider
...straight lines be proportionals, those straight lines shall be proportionals. PROP. XXIII. THEOREM. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. PROP. XXIV. THEOREM. The parallelograms about the diameter of any parallelogram, are similar to the...
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## Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1849 - 332 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...parallelograms having the angle BCD equal to the angle ECG ; tbe ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded...
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## Papers for the Schoolmaster, Bind 1

1851 - 268 sider
...have their sides about their equal angles reciprocally proportional. .3. Equiangular paralellograms have to one another the ratio which is compounded of the ratios of their sides. SECTION IV. 1. Upon a given base to describe an isosceles triangle equal to a given rectangle. 2. To...
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## Public Education: As Affected by the Minutes of the Committee of Privy ...

Sir James Kay-Shuttleworth - 1853 - 554 sider
...to one angle of the other, have their sides about their equal angles reciprocally proportional. 3. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. Section 4. 1. Upon a given base to describe an isosceles triangle equal to a given rectangle. 2. To...
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## Public Education: As Affected by the Minutes of the Committee of Privy ...

Sir James Kay-Shuttleworth - 1853 - 524 sider
...their sides about their equal angles reciprocally proportional. 3. Equiangular parallelograms hare to one another the ratio which is compounded of the ratios of their sides. Section 4. 1. Upon a given base to describe an isosceles triangle equal to a given rectangle. . 2....
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