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

John Playfair - 1846 - 332 Seiten
...which is compounded of the ratios of the solid AF to the solid GS, and of the solid GS to the solid GO, is the same with the ratio which is compounded of the ratios of the base AC to the base GK, and of the altitude AE to the altitude GM (F. 5.). But the ratio of the...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 Seiten
...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 Seiten
...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 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...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, Band 1

1851 - 268 Seiten
...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 Seiten
...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 - 516 Seiten
...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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The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New ..., Bücher 1

Euclides - 1853 - 334 Seiten
...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 first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 176 Seiten
...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 - 258 Seiten
...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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