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XI.—Researches on Malfatti's Problem

Published online by Cambridge University Press:  17 January 2013

H. F. Talbot Esq.
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Extract

The problem which bears the name of the Italian geometer Malfatti, by whom it was first proposed and solved, has long attracted the attention and exercised the ingenuity of mathematicians, and has been made the subject of many careful and elaborate researches.

The great attention which has been bestowed upon this problem has arisen partly from its intrinsic difficulty, but chiefly on account of the extreme simplicity of the solution finally obtained by Malfatti, which seemed to open new views of geometrical research, and gave reason to hope that simple solutions might in like manner be found of many other geometrical problems usually accounted very difficult or insoluble.

Type
Transactions
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 24 , Issue 1 , 1865 , pp. 127 - 138
Copyright
Copyright © Royal Society of Edinburgh 1865

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References

page 127 note * See Gergonne, vol. i. p 347.

page 128 note * See Gergonne, vol. i. p 343.

page 128 note † Ibid. vol. ii. p. 60.

page 130 note * Vol. xi. p. 126.

page 130 note † Die einleitenden Worte des Verfassers; “Um die Fruchtbarkeit,” &c. &c., könnten demjenigen, der, wie ich von mir bekennen muss, keine Idee davon hat, wie die Construction, &c., &c…. . den Gedanken aufdrängen, dass die gegebene Construction nicht bewiesen sei.

page 136 note * I have called it α, because it stands opposite to the angle A of the original triangle. Similarly for the names of β and γ. I have called, α, β, and γ the secondary circles.