Artículos relacionados a The Mathematical repository Volume 3
Sinopsis
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1804 Excerpt: ...and five equal angles, is a regular pentagon: and the most regular inscribed curve will be a circle. Then, as S. of A»B: S. of ABo:: AB: Ao = 42-5332, also as, Rad.: AB:: S. of EBA: A/j =r 29390; hence Ao--Ab. = 13-1432 the radius of the circle. The content of which is 542-697 square yards; and this at 6d. per yard amounts to 13I. 11s. 4d. the expence of digging the pond. Tit same, answered by Tyro Philomatheticus. Let ABCDE represent the garden, &c. Then it is evident that the pond must be a circle, the centre of which is the centre of the pentagon; it is likewise manifest ihat Xko Is a right angle, and ihat DA =: AB, and from the nature of the figure »Di =18' and ACD = 54; therefore as, Rad.: DC (50) S: S. of /ECH (54) ' D = 4"4/)85« and 40-45085 X 10= 404.5085, the sum ofthe lengths of all the walks; and as, S. of Dei (72 ): D4 40-45085):: S osoDA (18 ): ok s= 131432 the radius of the pond; consequently its area is 542-697 square yards, which at 6d per yard amounts to 13I. 11s. 4d. the expence of digging. The sane, answered by Mr. John Whitley. Let ABCDEA represent the pentangular garden, AD, BE, AC, DB, and CE, the walks intersecting each other in the points i, c, d, e,a; then, by Emtrsoris Geometry IV. 43, DEiC, DEAe, EABa, ABC/), and BCDc, are parallelograms, and therefore the angles CÆ, CDE, DrA, DEA, &c. are equal, and consequently abedea is a pentagon, and the curve which touches all its sides will be a circle, the centre of which will be, the centre of that circle vhich circumscribes the given pentagon. Let 0 be the centre and draw og _L to AD, and through 0 draw AoH meeting DC in H. Then, by Cor. 3. of the above quoted proposition, we have as, Thrsamt, answered by Tyro PhilomatheticuJ. By the question, y--= x + y,...
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Reseña del editor
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1804 Excerpt: ...and five equal angles, is a regular pentagon: and the most regular inscribed curve will be a circle. Then, as S. of A»B: S. of ABo:: AB: Ao = 42-5332, also as, Rad.: AB:: S. of EBA: A/j =r 29390; hence Ao--Ab. = 13-1432 the radius of the circle. The content of which is 542-697 square yards; and this at 6d. per yard amounts to 13I. 11s. 4d. the expence of digging the pond. Tit same, answered by Tyro Philomatheticus. Let ABCDE represent the garden, &c. Then it is evident that the pond must be a circle, the centre of which is the centre of the pentagon; it is likewise manifest ihat Xko Is a right angle, and ihat DA =: AB, and from the nature of the figure »Di =18' and ACD = 54; therefore as, Rad.: DC (50) S: S. of /ECH (54) ' D = 4"4/)85« and 40-45085 X 10= 404.5085, the sum ofthe lengths of all the walks; and as, S. of Dei (72 ): D4 40-45085):: S osoDA (18 ): ok s= 131432 the radius of the pond; consequently its area is 542-697 square yards, which at 6d per yard amounts to 13I. 11s. 4d. the expence of digging. The sane, answered by Mr. John Whitley. Let ABCDEA represent the pentangular garden, AD, BE, AC, DB, and CE, the walks intersecting each other in the points i, c, d, e,a; then, by Emtrsoris Geometry IV. 43, DEiC, DEAe, EABa, ABC/), and BCDc, are parallelograms, and therefore the angles CÆ, CDE, DrA, DEA, &c. are equal, and consequently abedea is a pentagon, and the curve which touches all its sides will be a circle, the centre of which will be, the centre of that circle vhich circumscribes the given pentagon. Let 0 be the centre and draw og _L to AD, and through 0 draw AoH meeting DC in H. Then, by Cor. 3. of the above quoted proposition, we have as, Thrsamt, answered by Tyro PhilomatheticuJ. By the question, y--= x + y,...
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