## 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 |

### Inni boken

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 ... 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 ... 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 ... 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 ...### Andre utgaver - Vis alle

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,