# The first six books of the Elements of Euclid, and propositions i.-xxi. of book xi

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### Inhalt

 INTRODUCTION 1 BOOK II 76 BOOK III 106 BOOK V 180 BOOK VI 210
 BOOK XI 267 Prism Pyramid Cylinder Sphere and Cone 283 NOTES 299 E MCullaghs proof of the minimum property 305

### Beliebte Passagen

Seite 295 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.
Seite 182 - 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...
Seite 9 - LET it be granted that a straight line may be drawn from any one point to any other point.
Seite 102 - 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.
Seite 122 - 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...
Seite 226 - 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.
Seite 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.
Seite 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.
Seite 126 - 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.
Seite 194 - If there be any number of proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.