The elements of geometry, in eight books; or, First step in applied logic1874 |
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Σελίδα 2
... coincide with each other . Or , the place of a figure is the portion of space in which we conceive it to exist . As geometrical figures are mere conceptions of our mind , they may penetrate each other , and partly , or wholly , coincide ...
... coincide with each other . Or , the place of a figure is the portion of space in which we conceive it to exist . As geometrical figures are mere conceptions of our mind , they may penetrate each other , and partly , or wholly , coincide ...
Σελίδα 3
... coincide with each other , and become indivisible ; therefore , if all the points of a line should touch each other , the whole line would be reduced to a point : there must be consequently some distance between the points of a line ...
... coincide with each other , and become indivisible ; therefore , if all the points of a line should touch each other , the whole line would be reduced to a point : there must be consequently some distance between the points of a line ...
Σελίδα 5
... coincide ; and , again that the magnitudes of figures which cannot partly coincide , have no common measure , and conse- quently no common unit . 16. Incommensurable lines are lines which have no other common measure than their ...
... coincide ; and , again that the magnitudes of figures which cannot partly coincide , have no common measure , and conse- quently no common unit . 16. Incommensurable lines are lines which have no other common measure than their ...
Σελίδα 6
... coincide in all their parts , and also that equal figures which coincide in all their parts , form but one figure and are not distinct from one another : they have consequently the same properties.1 THE ELEMENTS OF GEOMETRY .
... coincide in all their parts , and also that equal figures which coincide in all their parts , form but one figure and are not distinct from one another : they have consequently the same properties.1 THE ELEMENTS OF GEOMETRY .
Σελίδα 7
... coincide in all their parts , they are equal . Again , two figures , each of which is equal to a third , are obviously equal to each other , for they may both be made to coincide with the third , and consequently with each other . 19 ...
... coincide in all their parts , they are equal . Again , two figures , each of which is equal to a third , are obviously equal to each other , for they may both be made to coincide with the third , and consequently with each other . 19 ...
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...