This classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. Several hundred theorems and corollaries are formulated and proved completely; numerous others remain unproved, to be used by students as exercises. 1929 edition.
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52 of 52 people found the following review helpful:
4.0 out of 5 stars
A Classic on Euclidean geometry,
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This review is from: Advanced Euclidean Geometry (Dover Books on Mathematics) (Paperback)
Recently Dover has reissued two classics on Euclidean geometry, College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle (Dover Books on Mathematics) and this book. Both books were originally issued in the first half of the 20th century and both were aimed at a college level audience. Both of them also have a considerable amount of so called triangle geometry. As triangle geometry has seen a large upsurge the last years, especially during the last two decennia, there is certainly a need for an English book that gives an overview of the subject including the recent results. These books are useful in this respect but as they are both from the first half of the 20th century, they are out of date. Until a modern treatment of the subject will be available, these two books and the resources on the www will have to do. Altshiller Courts' book has a great set of exercises that can be used as a training ground for geometric problem solving. The problems in Johnsons' book mostly ask for proofs of theorems that are ommited in the text (that's why I give 4 stars). Another drawback of Johnsons' book is that there is no attention paid to geometric constructions. If you are interested in the subject, buy both, its certainly value for money.
The book assumes that you are familiar with simple geometrical concepts like congruence of triangles, parallelograms, circles and the most elementary theorems and constructions as can be found in Kiselev's book Kiselev's Geometry / Book I. Planimetry. The table of contents: I Introduction Prerequisites Points at infinity Notation Directed angles II Similar Figures Homothetic figures Centers of similitude of two circles Similar figures in general III Coaxal circles and inversions The radical axis Coaxal circles Inversions IV Triangles and Polygons Ratios in the triangle Quadrangles and quadrilaterals The theorem of Ptolemy Triangle and quadrangle theorems Polygon theorems and exercises Theorems concerning areas V Geometry of Circles The power theorem of Casey Circles of antisimilitude Poles and polars Stereographic projection VI Tangent Circles Circles tangent to two circles Steiner chains; the arbelos The problem of Apollonius Four circles touching a circle VII The theorem of Miquel The Miquel theorem Pedal triangles and circles; Simson lines VII Theorems of Ceva and Menelaos Theorems of Ceva and Menelaos; applications Isogonal conjugates IX Three Notable Points Fundamental properties of orthocenter and circumcenter The orthocentric system Properties of the median point The polar circle X Inscribed and Escribed Circles Fundamental properties Algebraic formulas; principle of transformation XI The nine point circle Properties of the nine point circle The theorem of Feuerbach Further properties of Simson lines XII Symmedian Point and Other Notable Points Symmedians and the symmedian point The isogonic centres Nagel point, Spieker circle, Fuhrmann circle XIII Triangles in Perspective The theorem of Desargues The theorems of Pascal and Brianchon XIV Pedal Triangles and Circles Pedal triangles and circles of a quadrangle Fontené's theorems; the theorem of Feuerbach The orthopole XV Shorter Topics Statical theorems: center of gravity, resultant of vectors The cyclic quadrangle and its orthocenters The theorem of Morley Circles of Droz-Farny Miscellaneous exercises XVI The Brocard Configuration The Brocard points and their properties The Tucker circles The Brocard triangles and the Brocard circle Steiner point and Tarry point Related triangles XVII Equibrocardal Triangles The Neuberg circles Vertical projection of triangles Circles of Appolonius and isodynamic points The circles of Schoute Generalizations of Brocard geometry XVIII Three Similar Figures Similar figures on the sides of a triangle Three similar figures in general Index
1 of 18 people found the following review helpful:
5.0 out of 5 stars
The House Of Alexander!,
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This review is from: Advanced Euclidean Geometry (Dover Books on Mathematics) (Paperback)
Aristotle Onassis, arrived as a young man,at the New York City port's; He had $.06 in his pocket as he looked at the Statue of Liberty...He said one word ....."Alexander!"....He took the City in a very short time.....Your coffee or sugar might come from one of his Ships!
Euclid was born in Alexandria....300 B.C.-A city that Alexander founded-It is located in Egypt!....Euclid was Alexander's..."Golden Child"... Euclid Is the Father of Geometry.... Almost every-man Who has Built a building,of any note-on the Earth...Knows Euclid's name.... Euclid dwells in side the Book you sent Me...You don't realize-Thank's!!!!!!!!!!!!!!!!!!!!!!
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