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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... "
The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick - Σελίδα 128
των Royal Military Academy, Woolwich - 1853
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 12 σελίδες
...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...

Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...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...

Lessons on plane trigonometry

Edward Butler (A.M.) - 1862
...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...

The Propositions of the Fifth Book of Euclid Proved Algebraically: with an ...

George Sturton Ward - 1862 - 79 σελίδες
...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...

An elementary treatise on mensuration

Benjamin Theophilus Moore - 1863 - 278 σελίδες
...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....

Solutions of the Problems and Riders Proposed in the Senate-house ...

William Walton - 1864 - 212 σελίδες
...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...

Guide to the Civil service

Henry White - 1864
...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)...

Register

University of Cambridge - 1864
...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...

The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...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...

The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865
...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,...




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