## 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

Resultat 1-5 av 5

Side 24

But it has been

are BA , AC greater than BD , DC . Again , the exterior angle BDC of the triangle

CDE is greater ( I. 16. ) than CED ; for the same reason , the exterior angle CEB

of ...

But it has been

**shown**that BA , AC are greater than BE , EC : much more thenare BA , AC greater than BD , DC . Again , the exterior angle BDC of the triangle

CDE is greater ( I. 16. ) than CED ; for the same reason , the exterior angle CEB

of ...

Side 112

For , the same construction being made , it may be

is greater than FG , but that it is not greater than EG : and L is a multiple of D ; and

FG , EG are like multiples of CB , AB ; therefore ( V. def . 7. ) D has a greater ...

For , the same construction being made , it may be

**shown**, in like manner , that Lis greater than FG , but that it is not greater than EG : and L is a multiple of D ; and

FG , EG are like multiples of CB , AB ; therefore ( V. def . 7. ) D has a greater ...

Side 118

GH is greater than HK ; but KO is not greater than KH , wherefore GH is greater

than Ko . In like manner it may be

if KO be not 1 2 3 H ot M 0 р pet P H HT M M NA K B K B DN + N E Ft B G A G L A

...

GH is greater than HK ; but KO is not greater than KH , wherefore GH is greater

than Ko . In like manner it may be

**shown**, that LM is greater than NP . Therefore ,if KO be not 1 2 3 H ot M 0 р pet P H HT M M NA K B K B DN + N E Ft B G A G L A

...

Side 121

E bas to F a greater ratio than C to B. And because B : C :: D : Ě , by inversion , C :

B :: E : D : and E was

13. cor . ) E has to F a greater ratio than E to D : but the magnitude to which the ...

E bas to F a greater ratio than C to B. And because B : C :: D : Ě , by inversion , C :

B :: E : D : and E was

**shown**to have to F a greater ratio than C to B ; therefore ( V.13. cor . ) E has to F a greater ratio than E to D : but the magnitude to which the ...

Side 282

In the same manner , it may be

line DE , the rectangle AC.AD is equal to the given space . Therefore ( APP . II .

def . 1. ) DE is the locus of D ; and its position is given from that of the point E.

In the same manner , it may be

**shown**, that wherever Ď is taken in the straightline DE , the rectangle AC.AD is equal to the given space . Therefore ( APP . II .

def . 1. ) DE is the locus of D ; and its position is given from that of the point E.

### 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 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...