A Sequel to the First Six Books of the Elements of Euclid: Containing an Easy Introduction to Modern Geometry, with Numerous ExamplesHodges, Figgis, 1895 - 168 sider |
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A Sequel to the First Six Books of the Elements of Euclid John Casey Ingen forhåndsvisning tilgjengelig - 2008 |
A Sequel to the First Six Books of the Elements of Euclid John Casey Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
ABCD angular points anharmonic ratio bisected bisectors centre of mean centre of similitude chord circle touching circumference circumscribed coaxal system common tangent concurrent concurrent lines conjugate points cut orthogonally Dem.-Let denoted diameter divided double points draw equiangular equianharmonically fixed point form a harmonic four points given circles given in position given in species given line given point Given the base harmonic conjugates harmonic mean harmonic system Hence the Proposition homographic inverse involution joining the points let fall limiting points line of collinearity locus meet middle point monic Nine-points Circle orthogonally passes pencil perpendicular point of intersection points of contact polar pole polygon Prop Proposition is proved Ptolemy's Theorem quadrilateral radical axis radii radius rays rectangle contained respect right line Section semicircle square subtend system of points theorem three given transversal
Populære avsnitt
Side 24 - A, and the adjacent angular points of the squares joined, the sum of the squares of the three joining lines is equal to three times the sum of the squares of the sides of the triangle.
Side 53 - E2. Hence the Proposition is proved. Cor. 1. — If the point P be in the circumference of the O, we have the following theorem : — The Bum of the squares of the lines drawn from any point in the circumference of a circle to the angular points of an inscribed polygon is equal to 2»E2.
Side 132 - L' in the points a, b. Join Pi, and from Q draw Q,«' making the required angle C with Pi ; the two points a, a' will form two homographic divisions on L, the double points of which will give two solutions of the required question. (4). To inscribe in a circle a triangle whose sides shall pass through three given, points.
Side 7 - It is a most comprehensive work, and quite as exhaustive as any ordinary student will require. Dr. Casey shows his usual mastery of detail, due to thorough acquaintance, from long teaching, with all the cruces of the subject. He has embraced in his pages all the usual topics, and has introduced several points of extreme interest from the best foreign text-books.
Side 14 - EC shall be = to the sum of the as CQ, CP. 21. If a square be inscribed in a A , the rectangle under its side and the sum of base and altitude = twice the area of the A . 22. If a square be escribed to a A, the rectangle under its side and the difference of the base and altitude = twice the area of the A . 23. Given the difference between the diagonal and side of a square : construct it. 24. The sum of the squares of lines joining any point in the plane of a rectangle to one pair of opposite angular...
Side 60 - O, together with the square of the side of a decagon, is equal to the square of the side of a pentagon. 6. Any diagonal of a pentagon is divided by a consecutive diagonal into two parts, such that the rectangle contained by the whole and one part is equal to the square of the other part. 7. Divide an L of an equilateral A into five equal parts. 8. Inscribe a O in a given sector of a circle.
Side 163 - The preface states that this book 'is intended to supply a want much felt by Teachers at the present day — the production of a work which, while giving the unrivalled original in all its integrity, would also contain the modern conceptions and developments of the portion of Geometry over which the elements extend.' " The book is all, and more than all, it professes to be. . . . The propositions suggested are such as will be found to have most important applications, and the methods of proof are...
Side 18 - The sum of the squares of the four sides of a quadrilateral is equal to the sum of the squares of its diagonals plus four times the square of the line joining the middle points of the diagonals.
Side 28 - HEFQ is a en; .-. the Z PEF = PHQ = right angle ; .-. EF is a tangent at E ; and since Z EFQ = EHQ = right angle, EF is a tangent at F. The tangent EF is called a direct common tangent. If with P as centre, and a radius equal to the sum of the radii of the two given...
Side 24 - AC* +2EB* +2-ED* = AC* + 4BF*+4FE* = AC* + BD* + 4FE*. (38.) In any trapezium, if two opposite sides be bisected ; the sum of the squares of the two other sides, together with the squares of the diagonals, is equal to the sum of the squares of the bisected sides together with four times the square of the line joining those points of bisection.