## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illus., and an Appendix in Five Books |

### Inni boken

Resultat 1-5 av 6

Side 70

X.

, let the circle FAB cut the circle DEF in more than two points, viz., in B, G, F : take

(III. 1.) the centre H, of the circle ABC, and join HB, HG, H.F. Then, because ...

X.

**THEOR**. ONE circle cannot cut another in more than two points. If it be possible, let the circle FAB cut the circle DEF in more than two points, viz., in B, G, F : take

(III. 1.) the centre H, of the circle ABC, and join HB, HG, H.F. Then, because ...

Side 71

which joins their centres passes through that point. Let the two circles ABC, A DE

touch each other externally in the point A ; and let F and G be their centres: the ...

**THEOR**. If two circles touch each other externally in any point, the straight linewhich joins their centres passes through that point. Let the two circles ABC, A DE

touch each other externally in the point A ; and let F and G be their centres: the ...

Side 130

1.) AD = BC; whence by dividing by C and D we get § – #. Therefore, if four

numbers, &c. PROP. W.

same number; and the same has the same ratio to equal numbers. Let A and B

be equal ...

1.) AD = BC; whence by dividing by C and D we get § – #. Therefore, if four

numbers, &c. PROP. W.

**THEOR**. EQUAL numbers have the same ratio to thesame number; and the same has the same ratio to equal numbers. Let A and B

be equal ...

Side 131

IX.

multiples have. Let A and B be two magnitudes; then, n being a whole number, A

: B : : n A : n B. mA For (No. 10.) *= nB' Therefore, magnitudes, &c. PROP. X.

IX.

**THEOR**. MAGNITUDEs have the same ratio to one another that their likemultiples have. Let A and B be two magnitudes; then, n being a whole number, A

: B : : n A : n B. mA For (No. 10.) *= nB' Therefore, magnitudes, &c. PROP. X.

**THEOR**. Side 176

three straight lines which meet one another, not in the same point. Let two

straight lines AB, CD, cut one another in E.; AB, CD are in one plane: so also are

three ...

**THEOR**. Two straight lines which cut one another, are in one plane: so also arethree straight lines which meet one another, not in the same point. Let two

straight lines AB, CD, cut one another in E.; AB, CD are in one plane: so also are

three ...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Ingen forhåndsvisning tilgjengelig - 2016 |

### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol segments semicircle sides similar similar triangles solid angles square of AC straight lines drawn tangent THEOR third triangle ABC triplicate ratio vertex vertical angle wherefore

### Populære avsnitt

Side 94 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Side 53 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.

Side 143 - 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.

Side 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.

Side 57 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.

Side 138 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...

Side 43 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.

Side 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 40 - 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 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...