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" K hag to M the ratio which is compounded of the ratios of the sides ; therefore also the parallelogram AC has to the parallelogram CF the ratio which is compounded of the ratios of the sides. COR. Hence, any two rectangles are to each other as the products... "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Page 139
by Euclid, John Playfair - 1846 - 317 pages
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...parallelogram CF: ex fequalif, K is to M, as the pa- *22. S. rallelogram AC to the parallelogram CF : But K has to M the ratio which is compounded of the ratios of...ratio which is compounded of the ratios of the sides. Wherefore equiangular parallelograms, &c. QED PROP. XXIV. THEOR. THE parallelograms about the diameter...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...parallelogram CF ; ex zequali (22. 5.), K is to M, as the parallelogram AC to the parallelogram CF ; but K has to M the ratio which is compounded of the ratios of...ratio which is compounded of the ratios of the sides. Wherefore equiangular paralle-* lograms, &c'. Q, ED • PROP. XXIV. THEOR. The parallelograms about...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...parallelogram CF ; ex aequali (22. 5.), K is to M, as the parallelogram AC to the pawllelogram CF ; but K has to M the ratio which is compounded of the ratios of...the ratio which is compounded of the ratios of the sidss. Wherefore equiangular, paralle^ lograms, &c. Q, ED PROP. XXIV. THEOR, The parallelograms about...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...parallelogram CF; ex trquali, ('22. 5.) К is to M, as the parallelogram AC to the parallelogram CF : but E has to M the ratio which is compounded of the ratios of...ratio which is compounded of the ratios of the sides. Wherefore equiangular parallelograms, &c. Q. Б. D. PROP. xxiv. TH"EOR. The parallelograms about Ihc...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...to M, as the parallelogram AC to the parallelogram CF ; but K has to M the ratie whieh is eompounded of the ratios of the sides; therefore also the parallelogram AC has to the parallelogram CF the ratio whieh is eompounded of the ratios of the sides. Wherefore equiangular parallelograms, &e. QED A- PROP....
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...CF; ex aequali*, • **• 5K is to M, as the parallelogram AC to the parallelogram CF : but K has to M the ratio which is compounded of the ratios of...ratio which is compounded of the ratios of the sides. Wherefore equiangular parallelograms, &c. QBD See N. PROP. XXIV. THEOR. Parallelograms about the diameter...
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 218 pages
...its height, and CE X CG is the product of the base of the rectangle CEFG by its height. Therefore — Two rectangles are to each other as the products of their bases by their heights. 159. It is usual to estimate areas by square feet, square yards, square rods, &c....
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...angles and the same sides containing them, these parallelograms (36. Cor. 1.) will be to one another in the ratio which is compounded of the ratios of the sides ; therefore the triangles, which are their halves, will be to one another in the same ratio. (17. Cor. 1.) Otherwise:...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...CF ; ex a-quali *, K is * 22. 5. to M, as the parallelogram AC to the parallelogram CF : but K has to M the ratio which is compounded of the ratios of...parallelogram CF the ratio which is compounded of the rutios of the sides. Wherefore, equiangular parallelograms, &c. QED 12. 6. • 12. 6. • Def. A. 5....
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...parallelogram CF; ex cnqvali*, f 22. 5. K is to M as the parallelogram AC to the parallelogram CF : But K has to M the ratio which is compounded of the ratios of...ratio which is compounded of the ratios of the sides. Wherefore, " equiangular parallelograms" &c. QED PROP. XXIV. THEOR. The parallelograms about the diameter...
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