The elements of geometry, in eight books; or, First step in applied logic1874 |
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Αποτελέσματα 1 - 5 από τα 18.
Σελίδα vi
... quantities , which has been the subject of such endless discussions , is a purely arithmetical one . The ratio of two geometrical quantities may always be re- placed by that of two straight lines , which have at least , accord- ing to ...
... quantities , which has been the subject of such endless discussions , is a purely arithmetical one . The ratio of two geometrical quantities may always be re- placed by that of two straight lines , which have at least , accord- ing to ...
Σελίδα xvii
... Quantities ' . V. Arithmetical Theorems I. Lines PLANE GEOMETRY . ' BOOK I. ON LINES . PRELIMINARY DEFINITIONS . II . Surfaces III . Divisions of Geometry CHAPTER I. ON STRAIGHT LINES . SECTION I. On Straight Lines generally II . On ...
... Quantities ' . V. Arithmetical Theorems I. Lines PLANE GEOMETRY . ' BOOK I. ON LINES . PRELIMINARY DEFINITIONS . II . Surfaces III . Divisions of Geometry CHAPTER I. ON STRAIGHT LINES . SECTION I. On Straight Lines generally II . On ...
Σελίδα 5
... quantities ; their study is the province of Arithmetic.2 In Arithmetic , form is indeterminate ; the magnitude may be that of a figure of any form . In Geometry , on the contrary , it is magnitude which is indeterminate ; a figure may ...
... quantities ; their study is the province of Arithmetic.2 In Arithmetic , form is indeterminate ; the magnitude may be that of a figure of any form . In Geometry , on the contrary , it is magnitude which is indeterminate ; a figure may ...
Σελίδα 14
... and the diagrams themselves ; he must also accustom himself to demonstrating without the use of any diagram . IV . GENERAL THEOREMS ON QUANTITIES . To facilitate the 14 THE ELEMENTS OF GEOMETRY . On the Representation of Geometrical ...
... and the diagrams themselves ; he must also accustom himself to demonstrating without the use of any diagram . IV . GENERAL THEOREMS ON QUANTITIES . To facilitate the 14 THE ELEMENTS OF GEOMETRY . On the Representation of Geometrical ...
Σελίδα 15
... quantities will have to be demonstrated here which properly belong to General Mathematics . These theorems and their ... quantities is another quantity equal to all of them together ; the sum of two equal quantities is the double of each ...
... quantities will have to be demonstrated here which properly belong to General Mathematics . These theorems and their ... quantities is another quantity equal to all of them together ; the sum of two equal quantities is the double of each ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 202 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Σελίδα 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.
Σελίδα 43 - The projection of a point on a plane is the foot of the perpendicular drawn from the point to the plane.
Σελίδα 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...
Σελίδα 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...