## 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 5

Side 13

to CA, and AF is common; therefore the two sides BA, AF are

AF, each to each, and the contained ... Let ABC be a triangle having the angle

ABC

...

to CA, and AF is common; therefore the two sides BA, AF are

**equal**to the two CA,AF, each to each, and the contained ... Let ABC be a triangle having the angle

ABC

**equal**to the angle ACB ; the side A B is also**equal**to the side**A.C.**For, if AB...

Side 50

to

complements AG, GE are

CB, for GC is

to

**AC**; therefore HF, CK are the squares of**AC**, CB. And because 5–F– (I. 43.) thecomplements AG, GE are

**equal**, and that AG is the rectangle contained by**AC**,CB, for GC is

**equal**to CB; therefore GE is also**equal**to the rectangle**AC**. Side 55

in D : the squares of AD, DB are together double of the squares of AC, CD. From

C draw (I. 11.) CE at right angles to AB, and make it

EA, EB : through D draw (I. 31.) DF parallel to CE, and through F draw FG parallel

...

in D : the squares of AD, DB are together double of the squares of AC, CD. From

C draw (I. 11.) CE at right angles to AB, and make it

**equal to AC**or CB, and joinEA, EB : through D draw (I. 31.) DF parallel to CE, and through F draw FG parallel

...

Side 141

equal to one another, because they are respectively equal to the A L. F. equal

angles DAC, DAE; and conse- P quently (I. 6.) A F is

because A D is parallel to FC, a p-d-: d side of the triangle BCF, BD: DC :: BA : AF

; but ...

equal to one another, because they are respectively equal to the A L. F. equal

angles DAC, DAE; and conse- P quently (I. 6.) A F is

**equal to AC**. Then (VI. 2.)because A D is parallel to FC, a p-d-: d side of the triangle BCF, BD: DC :: BA : AF

; but ...

Side 186

Let ABC, DEF, GHK be three plane angles, every two of which are greater than

the third : then, if AB, BC, DE, EF, GH, HK be all

joined; a triangle may be made of

...

Let ABC, DEF, GHK be three plane angles, every two of which are greater than

the third : then, if AB, BC, DE, EF, GH, HK be all

**equal**, and if**AC**, DF, GK bejoined; a triangle may be made of

**AC**, DF, GK: that is, every two of these lines are...

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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...