 | 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 ratio 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... | |
 | 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... | |
 | George Sturton Ward - Geometry, Algebraic - 1862 - 104 pages
...it is clear that a technical use of the term was intended in the Enunciation of Prop. 23, Bk. vi , "Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides," — \oyov TOV avy/ceip,evov ¿к Ttav TT\evpwv. It may easily be seen that the ratio... | |
 | 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... | |
 | 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... | |
 | 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 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... | |
 | 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 ratio which is compounded of the ratios of their sides. If one parallelogram have to another parallelogram the ratio which is compounded of the... | |
 | University of Cambridge - 1864 - 694 pages
...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 ratio which is compounded of the ratios of their sides. If one parallelogram have to another parallelogram the ratio which is compounded of the... | |
 | Euclides - 1864 - 448 pages
...is to CD, as EFto GH. (v. 7.) If therefore, four straight lines, &c. QED PROPOSITION XXIII. THEOREM. 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 B CD equal to the angle ECG.... | |
 | Robert Potts - 1865 - 528 pages
...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... | |
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Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. 
