 | Edward Butler (A.M.) - 1862 - 154 pages
...sides. Then, T= )rf , and T'=j . smA " smA Whence, J_£ 70. 7%« areas of equiangular parallelograms have to one another, the ratio which is compounded of the ratios iff the sides. (B. vi., Prop, xxiii.) Let P and P' be equiangular parallelograms, a and b two adjacent... | |
 | Benjamin Theophilus Moore - Measurement - 1863 - 320 pages
...Euclid's Elements of Geometry, Book VI. Proposition 23, it is proved that " Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides ;" and therefore rectangles, which are equiangular parallelograms, have to one another this same... | |
 | Henry White - 1864 - 156 pages
...same ratio which the other sides of the triangle have to one another. 7. Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. 8. Trisect a given straight line. 9. Construct a rectangle which shall be equal to a given square... | |
 | William Walton - Mathematics - 1864 - 234 pages
...same circle and all its angles equal, then shall all its sides be equal. v. Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. If one parallelogram have to another parallelogram the ratio which is compounded of the ratios... | |
 | Euclides - 1864 - 448 pages
...proportional to the squares of their homologous sides. 36. How is it shewn that equiangular parallelograms have to one another the ratio which is compounded of the ratios of their bases and altitudes ? 37. To find two lines which shall have to each other, the ratio compounded of... | |
 | University of Cambridge - 1864 - 694 pages
...same circle and all its angles equal, then shall all its sides be equal. 5. Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. If one parallelogram have to another parallelogram the ratio which is compounded of the ratios... | |
 | Euclides - 1865 - 402 pages
...be proportionals, those straight lines shall be proportionals. Prop. 23. Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Prop. 24. Parallelograms about the diameter of any parallelogram, are similar to the whole,... | |
 | Robert Potts - 1865 - 528 pages
...proportional to the squares on their homologous sides. 36. How is it shewn that equiangular parallelograms have to one another the ratio which is compounded of the ratios of their bases and altitudes ? 37. To find two lines which shall have to each other, the ratio compounded of... | |
 | Civil service - 1866 - 270 pages
...same ratio which the other sides of the triangle have to one another. 7. Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. 8. Trisect a given straight line. 9. Construct a rectangle which shall be equal to a given square... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...straight lines &c. QED PROPOSITION 23. THEOREM. Parallelograms which are equiangular to one another have to one another the ratio which is compounded of the ratios of their sides. Let the parallelrgram AC be equiangular to the parallelogram CF, having the angle BCD equal... | |
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Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. 
