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" Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Side 329
av Euclid, Robert Simson - 1821 - 516 sider
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First Public Examination in Literis Graecis Et Latinis

University of Oxford - 1879
...shall be greater than the other two together. 10. Parallelograms which are equiangular to one another have to one another the ratio which is compounded of the ratios of their sides. V. Elements of Mechanics. I. 1. Prove the parallelogram offorees for direction. Find the...
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Military examinations. Mathematical examination papers, set for entrance to ...

Woolwich roy. military acad, Walter Ferrier Austin - 1880
...intersection A', B', C', D', E', F. Show that the hexagon A'B'C'D'E'F' is three times as great as ABCDEF. 10. Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Two circles touch one another externally at A. A straight line touches the circles at...
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Military examinations. Mathematical examination papers, set at entrance to ...

Sandhurst roy. military coll - 1880
...parallelograms have to one another the ratio which is compounded of the ratios of their sides. Show that any two parallelograms have to one another the ratio which is compounded of the ratios of their bases and altitudes. 7. Each of three circles cuts the other two; prove that the three common...
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AN ELEMENTARY TREATISE ON MENSURATION

GEORGE BRUCE HALSTED - 1881
...assigned whenever we speak of the product of one line by another. GENEKAL PKOOF. Eectangles, being equiangular parallelograms, have to one another the ratio which is compounded of the ratios of their sides. Ww. 315; (Eu. VI 23 . QV. IV. 5). f represent the surfaces or areas of two recand o! represent...
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The Cambridge Examiner, Volum 4

1884
...to two right angles. 15. Triangles which have one angle of the one equal to one angle of the other, have to one another the ratio which is compounded of the ratios of their sides. Algebra. Junior, Senior, and Higher Local. Junior Work, Nos. 1 — 9 inclusive. Senior...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 400 sider
...Therefore PR is equal to GH. triangles which have one angle of tlie one equal to one angle of tht other, have to one another the ratio which is compounded of the ratios of their sides. Then VI. 19 ig an immediate consequence of this theorem. For let ABC and DBF he similar...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884
...EF: OH, then A&> : CD* = EF* : Off*. 2. If two ratios be equal, their duplicates are equal. Mutually equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.* AF G' Let ||m AB be equiangular to l|m BC, having L DBF = L GBE: it is required to prove...
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THE ELEMENTS OF GEOMETRY.

GEORGE BRUCE HALSTED - 1885
...composition of two equal ratios is called the Duplicate Ratio of either. THEOREM XVII. 542. Mutually equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. \ \ PROOF. Place the 2=75 so that HC and CB are in one line ; then, by 109, DC and CF...
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Annual Report of the Chief Superintendent of Education

1885
...proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means. 6. Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. NB— Female Candidates for Class I. will receive credit for any work correctly done in...
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The Elements of Geometry

George Bruce Halsted - 1886 - 366 sider
...composition of two equal ratios is called the Duplicate Ratio of either. THEOREM XVII. 542. Mutually equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. PROOF. Place the ZK so that HC and CB are in one line ; then, by 109, DC and CF are in...
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