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

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Side 77

Upon the same straight line , and on the same side of it , there cannot be two

similar

the two similar

the ...

Upon the same straight line , and on the same side of it , there cannot be two

similar

**segments**of circles , not coinciding with one another . If it be possible , letthe two similar

**segments**of circles , viz . , ACB , A DB , be upon the same side ofthe ...

Side 81

the angle in a

the centre , BC a diameter , and consequently BAC a semicircle ; and let the ...

the angle in a

**segment**greater than a semicircle is acute ; and ( 3. ) the angle in a**segment**less than a semicircle is obtuse . 1 B Let ABC be a circle , of which F isthe centre , BC a diameter , and consequently BAC a semicircle ; and let the ...

Side 315

Then BD or DC is half the sum of the

difference : and BD is to DH , or twice BD to twice DH , as tan DEB to tan DEH .

Now it is easy to show that BED is half the sum of the angles ABC , ACB , and

HED half ...

Then BD or DC is half the sum of the

**segments**BH , HC , and DH half theirdifference : and BD is to DH , or twice BD to twice DH , as tan DEB to tan DEH .

Now it is easy to show that BED is half the sum of the angles ABC , ACB , and

HED half ...

Side 332

D L a given straight line , and that it may divide the other into

containing angles equal to given angles . Let it be required to draw a straight line

cutting the circles AB , CD , so that the part of it within AB may be equal to a given

straight ...

D L a given straight line , and that it may divide the other into

**segments**containing angles equal to given angles . Let it be required to draw a straight line

cutting the circles AB , CD , so that the part of it within AB may be equal to a given

straight ...

Side 386

such that one

right angle , may be equal to the sum of the ... If BD , CE , in the figure in page

250 , be joined , the interior figure contained by the

a ...

such that one

**segment**of the hypotenuse made by the perpendicular , from theright angle , may be equal to the sum of the ... If BD , CE , in the figure in page

250 , be joined , the interior figure contained by the

**segments**of the diagonals , isa ...

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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...