 | Education, Higher - 1884 - 538 pages
...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... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...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... | |
 | Euclides - 1884 - 434 pages
...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... | |
 | 1885 - 608 pages
...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... | |
 | George Bruce Halsted - Geometry - 1885 - 389 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 2=75 so that HC and CB are in one line ; then, by 109, DC and CF... | |
 | 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... | |
 | 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... | |
 | 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... | |
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Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. 
