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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 - Σελίδα 128
των Royal Military Academy, Woolwich - 1853
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...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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...equal to GH ; AB is to CD, as EF to GH. If, therefore, four straight lines, &c. QED PROP. XXIII. THEOR. EQUIANGULAR parallelograms have to one another the...which is compounded of the ratios of their sides. • See Note. Let BG, CG, be placed in a straight line ; therefore DC and CE are also in a straight...

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...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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...37. Cor. 4.) ; therefore, the ratio which is compounded of the ratios of С D* to QN= and N A2 to PT1 is the same with the ratio which .is compounded of the ratios of CP- to CNa — С P1 and С N - to С Р-, the same, that is, with the ratio of С N * to С N - —...

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...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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...and join AB and DE. The parallelograms CF and CO are evidently equiangular ; they have, therefore, to one another the ratio which is compounded of the ratios of their sides (23 of VI); that is, the ratio which is IMPROVED MODE OF PRESERVING BEBH FROM SOCRINC. of the ratios...

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...equal to GH, AB is to CD, as EF to GH. If therefore four straight lines, &c. QED PROP. XXIII. THEOR. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. Let AC,CF be equiangular parallelograms having the angle BCDequal to the angle ECG; the ratio of the parallelogram...

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

John Playfair - 1833 - 333 σελίδες
...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 EC, CG be placed in a straight line ; therefore DC and CE are also in a straight line (14. 1.) ; complete...

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...ratios that are the same with the ratios of the sides. And to this demonstration agrees the enunciation 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, iu this...

The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - 1835 - 513 σελίδες
...AB is to CD, as EF to GH. " If, therefore, four straight lines, &c. QED PROP. XXIII. THEOR. See N. Equiangular parallelograms have to one another the...the same with the ratio which is compounded of the ratio of their sides. Let BC, CG be placed in a straight line ; therefore DC Book vI. and'CE are also...




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