The Elements of Geometry [Euclid Book 1-3] in General Terms, with Notes and C. and C. Also a Variety of Problems and Theorems. [Ed. by J. Luby. With] the Elem PDF Download
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Author: Euclides Publisher: Theclassics.Us ISBN: 9781230211022 Category : Languages : en Pages : 76
Book Description
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1821 edition. Excerpt: ... A VARIETY OS THE MOST IMPORTANT DEDUC1BLE FROM THE SECOND & THIRD BOOKS. PP&B ANALYTICALLY. PROP. 1. THEOR. The difference between the hypothenuse BC and rum of the sides BA, AC of a right angled triangle ABC it equal to tmo radii of the inscribed circle. Fig. 14, ANALYSIS, Suppose it to be the case;. then since BC with FG, GE is = to BA, AC together, BC with FA, AE is j= to BA, AC; for it is evident that FA, AE are respectively ac to Geji'gj since each of the. angles F, A, E, is a right angle,.": BC is'=: to BF and CE together, if this can, be. proved the. proposition is evident. Join BG; then since in the triangles BGD, BGF the sides BG and GD are respectively = to BG and GF, and the angles BDG, BFG are = as being right and the angles DBG, FBG of the same affection, the triangles are =5 in every way, .-, BD is = to BF; for tie same reason CD is = to CE, .. BC is = to the sum of BF and CE, -. &c. PROP. 2, PROB. To produce a given right line AB so that the rectangle under the whole and-produced part may he equul ta a given quantity. Fig-15. ANAlYSls. Suppose it done, and that AC is the line produced. Jet F be sr to a side of the Q of the given quantity; then it is evident from. prop. 37, b. 3, that CA shalJ be = to the secant drawn from the extremity of the tangent (= to F, ) through the centre of the circle, the diameter of which is = to the given line. Describe a circle of which the diameter is the givea line AB, draw to it a tangent IA--s to the given quantity, and from its extremity I draw through the centre the secant ID, it is evidently = to the whole produced line, .-. make BC == to GI, and the rect. ACB is = to the given quantity. Cor. 1. By being given the tangent and internal part of the secant passing in any way, we can find the secan
Author: Euclides Publisher: Theclassics.Us ISBN: 9781230211022 Category : Languages : en Pages : 76
Book Description
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1821 edition. Excerpt: ... A VARIETY OS THE MOST IMPORTANT DEDUC1BLE FROM THE SECOND & THIRD BOOKS. PP&B ANALYTICALLY. PROP. 1. THEOR. The difference between the hypothenuse BC and rum of the sides BA, AC of a right angled triangle ABC it equal to tmo radii of the inscribed circle. Fig. 14, ANALYSIS, Suppose it to be the case;. then since BC with FG, GE is = to BA, AC together, BC with FA, AE is j= to BA, AC; for it is evident that FA, AE are respectively ac to Geji'gj since each of the. angles F, A, E, is a right angle,.": BC is'=: to BF and CE together, if this can, be. proved the. proposition is evident. Join BG; then since in the triangles BGD, BGF the sides BG and GD are respectively = to BG and GF, and the angles BDG, BFG are = as being right and the angles DBG, FBG of the same affection, the triangles are =5 in every way, .-, BD is = to BF; for tie same reason CD is = to CE, .. BC is = to the sum of BF and CE, -. &c. PROP. 2, PROB. To produce a given right line AB so that the rectangle under the whole and-produced part may he equul ta a given quantity. Fig-15. ANAlYSls. Suppose it done, and that AC is the line produced. Jet F be sr to a side of the Q of the given quantity; then it is evident from. prop. 37, b. 3, that CA shalJ be = to the secant drawn from the extremity of the tangent (= to F, ) through the centre of the circle, the diameter of which is = to the given line. Describe a circle of which the diameter is the givea line AB, draw to it a tangent IA--s to the given quantity, and from its extremity I draw through the centre the secant ID, it is evidently = to the whole produced line, .-. make BC == to GI, and the rect. ACB is = to the given quantity. Cor. 1. By being given the tangent and internal part of the secant passing in any way, we can find the secan
Author: Euclides Publisher: Palala Press ISBN: 9781357523022 Category : Languages : en Pages : 286
Book Description
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Author: Euclides![The Elements of Geometry [Euclid Book 1-3] in General Terms, with Notes and C. and C. Also a Variety of Problems and Theorems. [Ed. by J. Luby. With] the Elem PDF](https://books.google.com/books/content/images/frontcover/eH1NnwEACAAJ?fife=w80-h100)
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Author: Euclides![The Elements of geometry [Euclid book 1-3] in general terms, with notes &c. &c. Also a variety of problems & theorems. [Ed. by J. Luby. With] The elements of plane geometry, comprising the definitions of the fifth book, and the sixth book in general terms, with notes [&c.] by J. Luby [described as] Pt. 3 PDF](https://books.google.com/books/content/images/frontcover/Chh6ksCQ3dYC?fife=w80-h100)
Author: Euclides![The Elements of Geometry [Euclid Book 1-3] in General Terms, with Notes &C. &C. Also a Variety of Problems & Theorems. [Ed. by J. Luby. With] the Elements of Plane Geometry, Comprising the Definitions of the Fifth Book, and the Sixth Book in General Terms PDF](https://books.google.com/books/content/images/frontcover/IPoGDQEACAAJ?fife=w80-h100)
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