 | Edward Butler (A.M.) - 1862 - 154 pągines
...triangles, a and a' homologous 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 - 1863 - 320 pągines
...area of a rectangle. In 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 ratio.... | |
 | University of Cambridge - 1864 - 694 pągines
...its angular points on the same circle and all its angles equal, then shall all its sides be equal. 5. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. If one parallelogram have to another parallelogram the ratio which is compounded of the ratios of their... | |
 | Henry White - 1864 - 156 pągines
...extremities of the base have the same ratio which the other sides of the triangle have to one another. 7. Equiangular parallelograms have to one another the...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 (1)... | |
 | William Walton - 1864 - 234 pągines
...sideAB = CD = EF=...= ZA = BC=..., the number of sides being odd. So that all the sides are equal. 5. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. If one parallelogram have to another parallelogram the ratio which is compounded of the ratios of their... | |
 | Euclides - 1864 - 448 pągines
...parallelograms are 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... | |
 | Euclides - 1865 - 402 pągines
...is to CD, as EF to OH. (T. 7.) If, therefore, four straight lines, &c. QED PROP. XXIII.— THEOREM. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides, (References— Prop. i. U ; v. 11, 22, def. A ; VI. 1, 12.) Let AC, CF be eqniangolar parallelograms,... | |
 | Robert Potts - 1865 - 528 pągines
...parallelograms, are 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 pągines
...extremities of the base have the same ratio which the other sides of the triangle have to one another. 7. Equiangular parallelograms have to one another the...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 (1)... | |
 | Euclid, Isaac Todhunter - 1867 - 426 pągines
...the following theorem, triangles which have one angle of tJie one equal to one angle of the •other, have to one another the ratio which is compounded of the ratios of their sides. Then VI. ig is an immediate consequence of this theorem. For let ABC and DEF be similar triangles,... | |
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Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. 
