Abhandlungen Zur Geschichte Der Mathematischen Wissenschaften Mit Einschluss Ihrer Anwendungen Volume 30 (Paperback)
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Von Händler/Antiquariat, BuySomeBooks [52360437], Las Vegas, NV, U.S.A.
This item is printed on demand. Paperback. 128 pages. Dimensions: 9.7in. x 7.4in. x 0.3in.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. 1913 Excerpt: . . . with the ellipse. It is our great regret that we have no material for describing the processes or analysis by which these formulae were calculated. We shall try in the following lines to say something of Hsus process of calculating the altitude of a circular segment in terms of the chord. 3) The formula we have to explain is yersin x Tx Ta Tj i where the successive terms are of the forms For the purpose of deriving this expression, the considerations are started from a figure as annexed. The rectangle is so constructed 1) Chus Third Part of Biographical Collections, Book 4. 2) Hsus Measurement of the Sphere, appendix. Tings reprint. 3) Hsus Ko-yiian Chui-shu or the Analysis of Circle-Measurement, Book 2, commented by Wu Chia-shan and supplemented by Tso Chien. Published by Ting, 1874. that EK the sagitta, KA the supplemental sagitta or the difference of the diameter and the given sagitta, while KG is equal to KE. Here the rectangle AC is the product of the sagitta and the supplemental sagitta, namely, equal to sin8 a: But CD AC C3 AD, . -. AD ainx, so that we get, after the division by the diameter d, the length of ED, which we write Tv Thus T, -Bmxd. Next constructing the figure as shown here, we have OKN CD NHCD BG. ButDXiV--T, and so we write Tjd DG T2. Next drawing the figure as annexed, where the ruled area is intended to become a square, we have LN (Tx Tt- DG, where G We have also a MM TtTx, . -. o ZG MM (2Tt T2)T2. Again DM and so (2 J, ) r2 niTff JBG, . : Ts d GG. In this way the expansion as we have mentioned above may be obtained. But Hsu goes further to transform it. Thus it will be seen that . . . This item ships from La Vergne,TN.

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Von Händler/Antiquariat, Amazon.com.
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. 1913 Excerpt: ...with the ellipse. It is our great regret that we have no material for describing the processes or analysis by which these formulae were calculated. We shall try in the following lines to say something of Hsu's process of calculating the altitude of a circular segment in terms of the chord.3) The formula we have to explain is yersin x = Tx + Ta + Tj + i where the successive terms are of the forms For the purpose of deriving this expression, the considerations are started from a figure as annexed. The rectangle is so constructed 1) Chu's "Third Part of Biographical Collections", Book 4. 2) Hsu's "Measurement of the Sphere", appendix. Ting's reprint. 3) Hsu's Ko-yiian Chui-shu or the "Analysis of Circle-Measurement", Book 2, commented by Wu Chia-shan and supplemented by Tso Ch'ien. Published by Ting, 1874. that EK = the sagitta, KA = the supplemental sagitta or the difference of the diameter and the given sagitta, while KG is equal to KE. Here the rectangle AC is = the product of the sagitta and the supplemental sagitta, namely, equal to sin8 a: But CD AC = C3 AD,.-. □ AD = ainx, so that we get, after the divis'ion by the diameter d, the length of ED, which we write Tv Thus T,-Bmx/d. Next constructing the figure as shown here, we have OKN = CD NH=CD BG. ButDXiV--T, and so we write Tjd = DG = T2. Next drawing the figure as annexed, where the ruled area is intended to become a square, we have □ LN' = (Tx + Tt-□ DG', where G' We have also a MM' =TtTx,.-. o ZG' + □ MM' = (2Tt + T2)T2. Again □ DM' = □ and so (2 + J,) r2 = niTff = □ JB'G",.: Ts d = GG". In this way the expansion as we have mentioned above may be obtained. But Hsu goes further to transform it. Thus it will be seen that ... Paperback, Label: RareBooksClub.com, RareBooksClub.com, Produktgruppe: Book, Publiziert: 2012-05-14, Studio: RareBooksClub.com.

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Von Händler/Antiquariat, The Book Depository US [58762574], London, United Kingdom.
Language: English Brand New Book ***** Print on Demand *****. 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. 1913 Excerpt: .with the ellipse. It is our great regret that we have no material for describing the processes or analysis by which these formulae were calculated. We shall try in the following lines to say something of Hsu s process of calculating the altitude of a circular segment in terms of the chord.3) The formula we have to explain is yersin x = Tx + Ta + Tj + i where the successive terms are of the forms For the purpose of deriving this expression, the considerations are started from a figure as annexed. The rectangle is so constructed 1) Chu s Third Part of Biographical Collections, Book 4. 2) Hsu s Measurement of the Sphere, appendix. Ting s reprint. 3) Hsu s Ko-yiian Chui-shu or the Analysis of Circle-Measurement, Book 2, commented by Wu Chia-shan and supplemented by Tso Ch ien. Published by Ting, 1874. that EK = the sagitta, KA = the supplemental sagitta or the difference of the diameter and the given sagitta, while KG is equal to KE. Here the rectangle AC is = the product of the sagitta and the supplemental sagitta, namely, equal to sin8 a: But CD AC = C3 AD, .-. AD = ainx, so that we get, after the divis ion by the diameter d, the length of ED, which we write Tv Thus T, -Bmx/d. Next constructing the figure as shown here, we have OKN = CD NH=CD BG. ButDXiV--T, and so we write Tjd = DG = T2. Next drawing the figure as annexed, where the ruled area is intended to become a square, we have LN = (Tx + Tt- DG , where G We have also a MM =TtTx, .-. o ZG + MM = (2Tt + T2)T2. Again DM = and so (2 + J, ) r2 = niTff = JB G, : Ts d = GG. In this way the expansion as we have mentioned above may be obtained. But Hsu goes further to transform it. Thus it will be seen that .

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Von Händler/Antiquariat, The Book Depository [54837791], London, United Kingdom.
Language: English Brand New Book ***** Print on Demand *****.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. 1913 Excerpt: .with the ellipse. It is our great regret that we have no material for describing the processes or analysis by which these formulae were calculated. We shall try in the following lines to say something of Hsu s process of calculating the altitude of a circular segment in terms of the chord.3) The formula we have to explain is yersin x = Tx + Ta + Tj + i where the successive terms are of the forms For the purpose of deriving this expression, the considerations are started from a figure as annexed. The rectangle is so constructed 1) Chu s Third Part of Biographical Collections, Book 4. 2) Hsu s Measurement of the Sphere, appendix. Ting s reprint. 3) Hsu s Ko-yiian Chui-shu or the Analysis of Circle-Measurement, Book 2, commented by Wu Chia-shan and supplemented by Tso Ch ien. Published by Ting, 1874. that EK = the sagitta, KA = the supplemental sagitta or the difference of the diameter and the given sagitta, while KG is equal to KE. Here the rectangle AC is = the product of the sagitta and the supplemental sagitta, namely, equal to sin8 a: But CD AC = C3 AD, .-. AD = ainx, so that we get, after the divis ion by the diameter d, the length of ED, which we write Tv Thus T, -Bmx/d. Next constructing the figure as shown here, we have OKN = CD NH=CD BG. ButDXiV--T, and so we write Tjd = DG = T2. Next drawing the figure as annexed, where the ruled area is intended to become a square, we have LN = (Tx + Tt- DG , where G We have also a MM =TtTx, .-. o ZG + MM = (2Tt + T2)T2. Again DM = and so (2 + J, ) r2 = niTff = JB G, : Ts d = GG. In this way the expansion as we have mentioned above may be obtained. But Hsu goes further to transform it. Thus it will be seen that .