The elements of geometry, in eight books; or, First step in applied logic1874 |
From inside the book
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... reasoning . If Euclid himself could live once more and re - edit his Elements , and give to them a form more in harmony with modern science , it is probable that a number of teachers would continue to prefer the accustomed bonds of the ...
... reasoning . If Euclid himself could live once more and re - edit his Elements , and give to them a form more in harmony with modern science , it is probable that a number of teachers would continue to prefer the accustomed bonds of the ...
Page v
... Reasoning ; and in doing so , he has followed the example of the ancients . In order to succeed in the treatment of any science , it is first of all necessary to clear it , not of that which is unconnected with it , for all sciences are ...
... Reasoning ; and in doing so , he has followed the example of the ancients . In order to succeed in the treatment of any science , it is first of all necessary to clear it , not of that which is unconnected with it , for all sciences are ...
Page x
... reasoning , the admirable ac- curacy of thought and expression , which are the immortal glory of the great Geometer ; he has adhered to the spirit of Euclid's fabric , if not to its letter . 1 The often repeated praise given to Euclid ...
... reasoning , the admirable ac- curacy of thought and expression , which are the immortal glory of the great Geometer ; he has adhered to the spirit of Euclid's fabric , if not to its letter . 1 The often repeated praise given to Euclid ...
Page xi
... reasoning . Hitherto , mathe- matics in general , and Geometry in particular , have been a sealed book for " the million " ; it is only of late years that the tendency to keep the profanum vulgus at a respectful distance , has somewhat ...
... reasoning . Hitherto , mathe- matics in general , and Geometry in particular , have been a sealed book for " the million " ; it is only of late years that the tendency to keep the profanum vulgus at a respectful distance , has somewhat ...
Page xiii
... reasoning and inventive powers of his pupils , by proposing them new theorems to be demon- strated , and problems to be solved and discussed , by means of the theorems and corollaries previously read . And last , not least , he should ...
... reasoning and inventive powers of his pupils , by proposing them new theorems to be demon- strated , and problems to be solved and discussed , by means of the theorems and corollaries previously read . And last , not least , he should ...
Common terms and phrases
A B and C D A B C and D E F adjacent angles adjacent sides altitude angle A B C angle ABC angles formed apothem bisect bisectrix centre angle centre line chord circular segment coincide Const Conversely COROLLARY II diagonals diameter divided equal angles equal circumferences equal to half equally distant equilateral equilateral polygon equivalent Eucl extremities given straight line greater homologous hypothenuse inscribed angle intercepts intersection isosceles trapezium isosceles triangle Let A B C magnitude middle line middle perpendicular middle point parallel parallelogram perimeter plane figure point H point of tangence points of section portions produced quadrangle quantities radii radius reasoning would prove rectangle regular polygon right-angled triangle Scholium segment sides A B square straight angle symmetric points tangent THEOREM transversal trapezium triangle A B C unequal vertex W. W. T. B. D. COROLLARY W. W. T. B. D. Inversely
Popular passages
Page 226 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 202 - Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 230 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 143 - When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of the angles is called a, right angle ; and the straight line which stands on the other is called a perpendicular to it. 11. An obtuse angle is that which is greater than a right angle. 12. An acute angle is that which is less than a right angle. 13. A term or boundary is the extremity of any thing.
Page 218 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 202 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Page 268 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 43 - The projection of a point on a plane is the foot of the perpendicular drawn from the point to the plane.
Page 335 - Assuming that the areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles...
Page 382 - FLC, there -are two angles -of the one equal to two angles of the other, each to each ; and the side FC which is adjacent to the equal...