The Elements of Euclid for the Use of Schools And Colleges Comprising the Fir
The Elements of Euclid for the Use of Schools And Colleges Comprising the Fir
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To quickly assess the difficulty of the text, read a short excerpt:
In the same manner it may be shewn that HK is [double of BK.
And because BK is equal to CK, as was shewn, md that HK is double of BK, and LK double of CK, herefore HKis equal to LK. [Axiom 6.
In the same manner it may be shewn that GH, txM, ML are each of them equal to HK or LK; therefore the pentagon GHKLM is equilateral.
It is also equiangular.
128 EUCLID'S ELEMENTS.
For, since the angle FKC is equal to the angle FLO^ and that the angle HKL is double of the angle FKC, and the angle KLM double... of the angle FLC, as was shewn, therefore the angle HKL is equal to the angle KLM. [Axiom 6.
In the same manner it may bo shewn that each of the angles KHG, HGM, GML is equal to the angle HKL or KLM ; therefore the pentagon GHKLM is equiangular. And it has been shewn to be equilateral.
Wherefore an equilateral and equiangular pentagon has been described about the given circle, q. E. F.
PROPOSITION 13. PROBLEM.
To inscribe a circle in a given equilateral and equi- angular pentagon.
Let ABCDE be the given equilateral and equiangular pentagon: it is required to inscribe a circle in the pen- tagon ABCDE.
What to read after The Elements of Euclid for the Use of Schools And Colleges Comprising the Fir?
You can find similar books in the "Read Also" column, or choose other free books by Todhunter, I. (Isaac), 1820-1884 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
In the same manner it may be shewn that HK is [double of BK.
And because BK is equal to CK, as was shewn, md that HK is double of BK, and LK double of CK, herefore HKis equal to LK. [Axiom 6.
In the same manner it may be shewn that GH, txM, ML are each of them equal to HK or LK; therefore the pentagon GHKLM is equilateral.
It is also equiangular.
128 EUCLID'S ELEMENTS.
For, since the angle FKC is equal to the angle FLO^ and that the angle HKL is double of the angle FKC, and the angle KLM double... of the angle FLC, as was shewn, therefore the angle HKL is equal to the angle KLM. [Axiom 6.
In the same manner it may bo shewn that each of the angles KHG, HGM, GML is equal to the angle HKL or KLM ; therefore the pentagon GHKLM is equiangular. And it has been shewn to be equilateral.
Wherefore an equilateral and equiangular pentagon has been described about the given circle, q. E. F.
PROPOSITION 13. PROBLEM.
To inscribe a circle in a given equilateral and equi- angular pentagon.
Let ABCDE be the given equilateral and equiangular pentagon: it is required to inscribe a circle in the pen- tagon ABCDE.
What to read after The Elements of Euclid for the Use of Schools And Colleges Comprising the Fir?
You can find similar books in the "Read Also" column, or choose other free books by Todhunter, I. (Isaac), 1820-1884 to read onlineMoreLess
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