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

### Inni boken

Side 13

OTHERWISE Let the straight line AF divide the angle BAC into two equal parts .

Then , in the triangles ... Let ABC be a triangle having the angle ABC equal to the

angle ACB ; the side AB is also equal to the side AC . For , if AB be not

OTHERWISE Let the straight line AF divide the angle BAC into two equal parts .

Then , in the triangles ... Let ABC be a triangle having the angle ABC equal to the

angle ACB ; the side AB is also equal to the side AC . For , if AB be not

**equal to**... Side 50

For the same reason HF also is a square , and it is upon the side HG , which is

because ( 1. 43. ) the complements AG , GE are

rectangle ...

For the same reason HF also is a square , and it is upon the side HG , which is

**equal**( 1. 34. ) to**AC**; therefore HF , CK are the squares of**AC**, CB . Andbecause ( 1. 43. ) the complements AG , GE are

**equal**, and that AG is therectangle ...

Side 55

E F 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

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

...

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

...

Side 141

equal to one another , because they are respectively equal to the equal angles

DAC , DAE ; and consequently ( I. 6. ) AF is

AD is parallel to FC , a side of the triangle BCF , BD : DC :: BA : AF : but AF is ...

equal to one another , because they are respectively equal to the equal angles

DAC , DAE ; and consequently ( I. 6. ) AF is

**equal to AC**. Then ( VI . 2. ) becauseAD is parallel to FC , a side of the triangle BCF , BD : DC :: BA : AF : but AF is ...

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...

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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 base bisected called centre chord circle circumference coincide common cone consequently const construction contained continual cylinder demonstrated describe diagonal diameter difference divided double draw equal equal angles extremities figure fore four fourth given given circle given point given straight line greater half Hence inscribed join less magnitudes manner means meet method multiple opposite parallel parallelepiped parallelogram pass perpendicular plane polygon prism PROB produced proof PROP proportional proposition proved pyramid radius ratio reason rectangle remaining respectively right angles Schol segments semicircle shown sides similar square straight line taken THEOR third touching triangle triangle ABC twice vertical wherefore whole

### 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...