The elements of geometry, in eight books; or, First step in applied logic1874 |
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Σελίδα 3
... direction of a line is its position relatively to each of its points . In the extension of a line there is an infinity of points , for between two points , however close to each other , it is always possible to conceive a third one ...
... direction of a line is its position relatively to each of its points . In the extension of a line there is an infinity of points , for between two points , however close to each other , it is always possible to conceive a third one ...
Σελίδα 37
... direction of a straight line is the same throughout its extension . 1 Whenever in The Elements the joining of two points is spoken of , the meaning is that one point is to be joined to the other by a straight line . 2 Let the student ...
... direction of a straight line is the same throughout its extension . 1 Whenever in The Elements the joining of two points is spoken of , the meaning is that one point is to be joined to the other by a straight line . 2 Let the student ...
Σελίδα 43
... definition of the straight line that its position in rela- tion to one of its points is the same relatively to every other of them [ 1 i ] ; whence , the direction of a straight line is determined BOOK I. - CHAPTER I. 43 On Perpendiculars.
... definition of the straight line that its position in rela- tion to one of its points is the same relatively to every other of them [ 1 i ] ; whence , the direction of a straight line is determined BOOK I. - CHAPTER I. 43 On Perpendiculars.
Σελίδα 44
... direction , since they have not the same position relatively to the point of section ; thus , the direction of a straight line distinguishes it from any other line cutting it . It is also evident that if one straight line cutting ...
... direction , since they have not the same position relatively to the point of section ; thus , the direction of a straight line distinguishes it from any other line cutting it . It is also evident that if one straight line cutting ...
Σελίδα 45
... directions ; each of them is called a perpendicular . That is when no portion of one is inclining towards any portion of the other . 16. Two straight lines are said to be oblique to or on one another , when they have not the same direction ...
... directions ; each of them is called a perpendicular . That is when no portion of one is inclining towards any portion of the other . 16. Two straight lines are said to be oblique to or on one another , when they have not the same direction ...
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...