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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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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Tom 5

John Mason Good - 1819
...similarly described upon four straight lines be proportionals, those straight lines shall be proportionals. Prop. XXIII. Theor. Equiangular parallelograms have...which is compounded of the ratios of their sides. Prop. XXIV. Theor. The parallelograms about the diameter of any parallelogram, are similar to the whole,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1821 - Liczba stron: 516
...PR, and that PR is equal to GH; AB is to CD, as EF to GH. If, therefore, four straight lines, &c. QED PROP. XXIII. THEOR. EQUIANGULAR parallelograms have...which is compounded of the ratios of their sides.* Lot AC, CF be equiangular parallelograms, having the angle BCD ^qual to the angle ECG: the ratio of...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - Liczba stron: 372
...PR is equal to GH ; AB is to CD, as EF to GH. If therefore four straight lines, &c. QED PROP. XXJIL THEOR, Equiangular parallelograms have to one another...is compounded of the ratios of their sides. Let AC, С F be equiangular parallelograms, baring the angle BCD CEOMETRV. logram CF, is the same with the...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - Liczba stron: 180
...QED Deduction, PROPOSITION XXIII. THEOREM. Equiangular parallelograms are to one another in a ratio compounded of the ratios of their sides. Let AC, CF,...equiangular parallelograms having the angle BCD equal to ECG, then the parallelogram AC is to the parallelogram CF in a ratio compounded of the ratios of their...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...QED Deduction. PROPOSITION XXIII. THEOREM. Equiangular parallelograms are to one another in a ratio compounded of the ratios of their sides. Let AC, CF,...equiangular parallelograms having the angle BCD equal to ECG, then the parallelogram AC is to the parallelogram CF in a ratio compounded of the ratios of their...
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Alma Mater, Or, Seven Years at the University of Cambridge, Tom 1

John Martin Frederick Wright - 1827
...which the other sides of the triangle have to one another. Shew that the converse is also true. 2. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. 3. The rectangle contained by the diagonals of any quadrilateral figure inscribed in a circle is equal...
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Alma mater; or, Seven years at the University of Cambridge. By a Trinity-man ...

John Martin F. Wright - 1827
...which the other sides of the triangle have to one another. Shew that the converse is also true. 2. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. 3. The rectangle contained by the diagonals of any quadrilateral figure inscribed in a circle is equal...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - Liczba stron: 513
...the sides. And with this demonstration agrees the enunciation which is at present in the text, viz. equiangular parallelograms have to one another the ratio which is compounded of the ratios of the sides; for the vulgar reading, " which is compounded of their sides," is absurd. But, in this edition,...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - Liczba stron: 186
...duplicate ratio of that which their homologous sides have to each other. ED. PROPOSITION XXIII. THEOREM. Equiangular parallelograms have to one another the...ratio which is compounded of the ratios of their sides about the equal angles ; " that is, they are to one another as the rectangles contained by the sides...
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A Collection of Cambridge Mathematical Examination Papers: Papers in the ...

John Martin Frederick Wright - 1831
...axis intercepted between the origin and the normal. TRINITY COLLEGE, 1829. 1 . EQUIANGULAR / — 73 have to one another the ratio which is compounded of the ratios of their sides. 2. If two straight lines be J_ to the same plane, they are || to one another. 3. Required the value...
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