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" Zbafy + 3cxif + dif into its canonical form, = (\x + p.yf + (\.'x + ii!y)*. 6. State, and prove analytically, the general theorem obtainable by projection from the theorem " the middle points of the three diagonals of a complete quadrilateral lie in a... "
Oxford, Cambridge and Dublin Messenger of Mathematics - Page 113
1864
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Calendar

University of Cambridge - 1864 - 694 pages
...% + w = Q. 6. State, and prove analytically, the general theorem obtainable by projection from the theorem " the middle points of the three diagonals of a complete quadrilateral lie in a line"." 7. Explain the meaning of the expressions, (1) polar of a point in relation to a conic ;...
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Mathematical Questions and Solutions

Mathematics - 1868 - 126 pages
...mnp'q'—m'n'pq ptf-p's r'4-Pi If m = m! and n = n', it is evident from the above that ER = FR; which shows that the middle points of the three diagonals of a complete quadrilateral lie in a straight line, as is well known from other considerations. 2662. (Proposed by the Rev. J. WOLSTENHOLME,...
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Mathematical Questions and Solutions, from the "Educational Times ..., Volume 10

W. J. C. Miller - Mathematics - 1868 - 130 pages
...pq'-p'q " p'q'-pq If «> = m' and n = n', it is evident from the above that ER = FR; which shows tbat the middle points of the three diagonals of a complete quadrilateral lie in a straight line, as is well known from other considerations. 2662. (Proposed by the Rev. J. WOLSTBNHOLMB,...
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Memoires, Volume 6

Société des sciences physiques et naturelles de Bordeaux - Science - 1868 - 562 pages
...Thus AA'OG' has a greater area and a less altitude than AAOC, and .-. a fortiori A'C' > AC. * §H. THEOREM. — The middle points of the three diagonals of a complete quadrilateral ABGD lie in direclum. 1,43, ex absurdo) A'A" passes through C. Now the middle of BD is also the middle...
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Jahrbuch über die Fortschritte der Mathematik, Volume 1

Electronic journals - 1871 - 472 pages
...regelnlässigen Fünf-, Sechs- und Zehnecks gebildete Dreieck rechtwinklig sei. No. A. -HALL. Gauss' proof tfrat the middle - points of the three diagonals of a complete quadrilateral lie in a right line. Messenger IV. 137. Im Ganzen kommen 9 Punkte in Betracht: die 6 Ecken des Vierseits und...
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Jahrbuch über die Fortschritte der Mathematik, Volume 1

1871 - 478 pages
...regelnlässigen Fünf-, Sechs- und Zehnecks gebildete Dreieck rechtwinklig sei. No. A. HALL. Gauss' proof that the middle - points of the three diagonals of a complete quadrilateral lie in a right line. Messenger IV. 137. Im Ganzen kommen 9 Punkte in Betracht: die 6 Ecken des Vierseits und...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...simple manner, whether three points lie in the same straight line. For example, take the following theorem : The middle points of the three diagonals of a complete quadrilateral are in a straight line. A complete quadrilateral is the figure formed by four straight lines intersecting...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...simple manner, whether three points lie in the same straight line. For example, take the following theorem: The middle points of the three diagonals of a complete quadrilateral are in a straight line. A complete quadrilateral is the figure formed by four straight lines intersecting...
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Exercises on Euclid and in Modern Geometry

James McDowell - 1878 - 310 pages
...position, and the sum or difference of their areas, find the locus of the common vertex. NB DBF 12 22. The middle points of the three diagonals of a complete quadrilateral lie in the same straight line 17 23. Given the base and the difference of the two sides of a triangle ; find the locus of the foot...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1882 - 286 pages
...harmonically in P and Q. The same may be proved of either of the diagonals AC, BD. Proposition 13. Theorem. — The middle points of the three diagonals of a complete quadrilateral are in the game line. Let L, M, N be the three middle points of the diagonals AC, BD, EF. LMN is a...
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