 | George Bruce Halsted - Geometry - 1886 - 394 pages
...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... | |
 | E. J. Brooksmith - Mathematics - 1889 - 356 pages
...and produced to meet in C: prove that AC and BC are bisected at E and D. 10. Define compound ratio. Equiangular parallelograms have to one another the ratio which is compounded of the ratio of their sides. 1 1 . The rectangle contained by the diagonals of a quadrilateral figure inscribed... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...student to enunciate generally the proposition assumed, and to demonstrate it. PROPOSITION 23. THEOREM. Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangr. ||gms such that L BCD= L ECG ; then ||gm AC : jgm CF in the ratio... | |
 | Queensland. Department of Public Instruction - Education - 1890 - 526 pages
...the external bisector ? 8. 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 the sides about the equal angles. 9. The three external bisectors of the angles of a triangle cut the sides in... | |
 | Euclid - Geometry - 1890 - 442 pages
...CD = P : Q, = X:Y, = dupl. ratio of LM to NO. .-. AB : CD = LM : NO. 272 Proposition 23. THEOREM — Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let ABCD, CEFG be equiang. Os, in which AA BCD = EGG. Place them so that a pair of the... | |
 | 1891 - 718 pages
...diagonal is parallel to a side. 3. The areas of parallelograms which are equiangular to one another have to one another the ratio which is compounded of the ratios of their sides. Hence deduce that the areas of similar parallelograms are to one another in the duplicate... | |
 | 1898 - 830 pages
...externally their common tangent is a mean proportional between their diameters (4 marks). 8. Prove that equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides (10 marks). Show also that triangles which have one angle of the one equal or supplemental... | |
 | Edinburgh Mathematical Society - Electronic journals - 1899 - 340 pages
...:NH =(EF : GH)2 But KAB:LCD= MF : NH (AB : CD)2 = (EF : GH)2 AB :CD = EF : GH EUCLID VI. 23. Mutually equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let parallelogram BE be equiangular to parallelogram CD, and let _ to prove / / / .|pBE:||-CD... | |
 | Eldred John Brooksmith - Mathematics - 1901 - 368 pages
...on the diagonal of the rectangle. 11. Prove that parallelograms which are equiangular to one another have to one another the ratio which is compounded of the ratios of their sides. 12. Prove that, in any right-angled triangle, any rectilineal figure described on the... | |
 | 1903 - 188 pages
...together equal to two right angles. (c) Shew that parallelograms which are equiangular to one another have to one another the ratio which is compounded of the ratios of their sides. 3. Describe a circle which shall pass through a given point and touch two given straight... | |
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Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. 
