The elements of geometry, in eight books; or, First step in applied logic1874 |
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Σελίδα 34
... distance between these points be imagined to be infinitely small , the idea of a line may thus be conceived which will ... equally from the same , that a curved line consists of infinitely small straight lines . II . SURFACES . " A plane ...
... distance between these points be imagined to be infinitely small , the idea of a line may thus be conceived which will ... equally from the same , that a curved line consists of infinitely small straight lines . II . SURFACES . " A plane ...
Σελίδα 41
... equal to the line A NB : that is , AN B is not less than AN'B ; therefore ... same reasoning would prove that if ANB were partly to coincide , and partly not to coincide ... distance between two points is the length BOOK I. - CHAPTER I. 41.
... equal to the line A NB : that is , AN B is not less than AN'B ; therefore ... same reasoning would prove that if ANB were partly to coincide , and partly not to coincide ... distance between two points is the length BOOK I. - CHAPTER I. 41.
Σελίδα 42
L J V. Gerard. Scholium . The distance between two points is the length of the straight line joining them ( Gen. Def . 8 ) ... equal straight lines which cut each other is greater than each of equal lines joining their opposite extremities ...
L J V. Gerard. Scholium . The distance between two points is the length of the straight line joining them ( Gen. Def . 8 ) ... equal straight lines which cut each other is greater than each of equal lines joining their opposite extremities ...
Σελίδα 49
... equal to D C , and let the points C ' and E be joined ; now let the plane containing the figure be folded upon AB as ... distance from a point to a straight line is the length of the perpendicular drawn from the point to the line . ( Gen. Def ...
... equal to D C , and let the points C ' and E be joined ; now let the plane containing the figure be folded upon AB as ... distance from a point to a straight line is the length of the perpendicular drawn from the point to the line . ( Gen. Def ...
Σελίδα 51
... equal straight lines . COROLLARY III . If a point is equally distant from the extremities of a straight line , it is less distant from any other point of the same line . THEOREM 14 . Each point of the middle perpendicular on BOOK I ...
... equal straight lines . COROLLARY III . If a point is equally distant from the extremities of a straight line , it is less distant from any other point of the same line . THEOREM 14 . Each point of the middle perpendicular on BOOK I ...
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...