 | Euclides - 1860 - 288 pages
...squares are proportional, and conversely. For squares are similar figures. PROPOSmOS XXIII. THEOREM. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. Given AC and CF two equiangular parallelograms, having the angle BCD equal to the angle ECG ; to prove... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...parallelograms are proportional to the squares of their homologous sides. 36. How is it s.hewn 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... | |
 | Eucleides - 1860 - 396 pages
...similarly situated. fThey are to one another as -j the rectangles under their ( bases and altitudes. They have to one another the ratio which is compounded of the ratios of their sides. Their sides about the eqnal angles are reciprocally proportional. They are equal to one another. .They... | |
 | War office - 1861 - 714 pages
...that is, to divide it into two equal parts. VOLUNTARY PORTION. 1. Define compound ratio. Prove that equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. 2. Define a plane. When is a straight line perpendicular to a plane ? Draw a straight line perpendicular... | |
 | Euclides - 1861 - 464 pages
...DFalso = fig. AC; — which is impossible : .-. EF not ф BC ; ,. e., EF = BC. QED PÜOP. 23. — THEOR. Equiangular parallelograms have to one another the ratio which is compounded of the ratio of their sides. CON. 14, 1. 31, I. 12, VI. DEM. Def. AV of Compound Ratio. When there arc any... | |
 | Edward Butler (A.M.) - 1862 - 154 pages
...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... | |
 | George Sturton Ward - Geometry, Algebraic - 1862 - 104 pages
...the ratio) compounded of 'the ratios of their sides." The same parallelopipeds may also be shewn to have to one another the ratio which is compounded of the ratios of their edges. When a ratio is compounded of several ratios, all of •which are the same, it is termed a duplicate... | |
 | Benjamin Theophilus Moore - Measurement - 1863 - 320 pages
...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.... | |
 | Henry White - 1864 - 156 pages
...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 - Mathematics - 1864 - 234 pages
...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... | |
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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... 
