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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 ... - Strona 140
autor: John Playfair - 1855 - Liczba stron: 318
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The Cambridge University Magazine, Tom 1,Wydanie 1

1840
...the Moon's rotation exactly equal to the motion in its orbit. WEDNESDAY. Jan. 8 ...... 9 to llj. 1. EQUIANGULAR parallelograms have to one another the...which is compounded of the ratios of their sides. 2. Every solid angle is contained by plane angles which are together less than four right angles. 3....
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - Liczba stron: 351
...having the angle BCD equal to the angle ECG: the parallelogram AC shall have to the parallelogram CF, 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;* and complete...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...that is, if A, B, c, D be four straight lines, and if л : в : : c : D, then A* : B* : : c* : D*. PROP. XXIII. THEOR. EQUIANGULAR parallelograms have...to one another the ratio which is compounded of the ratio of their sides. Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - Liczba stron: 317
...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
...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 - Liczba stron: 199
...; 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 ...

Euclid, James Thomson - 1845 - Liczba stron: 352
...&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
...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
...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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Papers for the Schoolmaster, Tom 1

1851
...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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