The First Six Books of the Elements of Euclid: And Propositions I-XXI of Book XI, and an Appendix on the Cylinder, Sphere, Cone, Etc., with Copious Annotations and Numerous ExercisesHodges, Figgis, & Company, 1885 - 312 sider |
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Side 9
... circumference of a circle according as its distance from the centre is less than , greater than , or equal to , the radius . POSTULATES . Let it be granted that— 1. A right line may be drawn from any one point to any other point . When ...
... circumference of a circle according as its distance from the centre is less than , greater than , or equal to , the radius . POSTULATES . Let it be granted that— 1. A right line may be drawn from any one point to any other point . When ...
Side 107
... figure bounded by a chord and one of the arcs into which it divides the circumference . VI . Chords are said to be equally distant from the centre when the perpendiculars drawn to them from the centre are equal . VII . The angle ...
... figure bounded by a chord and one of the arcs into which it divides the circumference . VI . Chords are said to be equally distant from the centre when the perpendiculars drawn to them from the centre are equal . VII . The angle ...
Side 115
... equal lines cannot be drawn from P to the circumference . Cor . 1. - If two equal lines PD , PF be drawn from a point P to the circumference of a circle , the diameter through P bisects the angle DPF formed by these lines . Cor . 2 ...
... equal lines cannot be drawn from P to the circumference . Cor . 1. - If two equal lines PD , PF be drawn from a point P to the circumference of a circle , the diameter through P bisects the angle DPF formed by these lines . Cor . 2 ...
Side 260
... on L. 51. The sum of the squares of lines drawn from any system of points A , B , C , D , & c . , to any point P , exceeds the sum of the squares of lines from the same points to their centre of mean position O by nOP2 . 52. If a point be ...
... on L. 51. The sum of the squares of lines drawn from any system of points A , B , C , D , & c . , to any point P , exceeds the sum of the squares of lines from the same points to their centre of mean position O by nOP2 . 52. If a point be ...
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The First Six Books of the Elements of Euclid: And Propositions I-XXI of ... Euclid,John Casey Uten tilgangsbegrensning - 1885 |
The First Six Books of the Elements of Euclid John Casey,Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
ABCD AC is equal AD² adjacent angles altitude angle ABC angle ACB angle BAC angular points Axiom bisector centre chord circles touch circumference circumscribed circle collinear concurrent lines const coplanar cyclic quadrilateral Dem.-Let diagonals diameter divided draw equal angles equal to AC equiangular equilateral triangle escribed circles Euclid Exercises exterior angle Geometry given circle given line given point greater Hence the angle hypotenuse inscribed less line AC line joining locus manner meet middle points multiple nine-points circle opposite sides parallel parallelogram parallelopiped perpendicular plane points of intersection prism PROP Proposition prove radii radius rectangle contained rectilineal figure regular polygon respectively equal right angles right line segments semicircle sides AC similar square on AC tangent theorem triangle ABC vertex vertical angle
Populære avsnitt
Side 299 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.
Side 186 - When of the equimultiples of four magnitudes (taken as in the fifth definition) the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the fourth...
Side 9 - LET it be granted that a straight line may be drawn from any one point to any other point.
Side 104 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Side 124 - The diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less. Let ABCD be a circle, of which...
Side 230 - If from any angle of a triangle, a straight line be drawn perpendicular to the base ; the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle.
Side 29 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Side 63 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Side 128 - The diagonals of a quadrilateral intersect at right angles. Prove that the sum of the squares on one pair of opposite sides is equal to the sum of the squares on the other pair.
Side 22 - ACB, DB is equal to AC, and BC common to both ; the two sides DB, BC, are equal to the two AC, CB, each to each, and the angle DBC is equal to the angle ACB : therefore, the base DC is equal to the base AB, and the triangle DBC (Mr. Southey) is equal to the triangle ACB, the less to the greater, which is absurd,
Bibliografisk informasjon
| Tittel | The First Six Books of the Elements of Euclid: And Propositions I-XXI of Book XI, and an Appendix on the Cylinder, Sphere, Cone, Etc., with Copious Annotations and Numerous Exercises |
| Forfattere | Euclid, John Casey |
| Redaktør | John Casey |
| Utgave | 3 |
| Utgiver | Hodges, Figgis, & Company, 1885 |
| Original fra | University of Michigan |
| Digitalisert | 12. jun 2007 |
| Lengde | 312 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |