 | Euclid - Geometry - 1845 - 218 pages
...; 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... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...&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)... | |
 | Euclides - 1846 - 292 pages
...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... | |
 | Euclides - 1848 - 52 pages
...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... | |
 | John Playfair - Euclid's Elements - 1849 - 332 pages
...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... | |
 | 1851 - 268 pages
...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... | |
 | Sir James Kay-Shuttleworth - Church and education - 1853 - 554 pages
...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... | |
 | Sir James Kay-Shuttleworth - Church and education - 1853 - 524 pages
...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.... | |
 | Euclides - Geometry - 1853 - 334 pages
...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... | |
 | Euclides - Geometry - 1853 - 176 pages
...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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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 CF... 
