## 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 101

If there be four magnitudes , and if any like multiples whatever be taken of the first

and third , and any whatever of the second and

multiple of the first is greater than the multiple of the second , equal to it , or less ...

If there be four magnitudes , and if any like multiples whatever be taken of the first

and third , and any whatever of the second and

**fourth**; and if , according as themultiple of the first is greater than the multiple of the second , equal to it , or less ...

Side 103

Alternately : † this word is used when there are four proportionals of the same

kind : and it is inferred , that the first has the same ratio to the third , which the

second has to the

: as ...

Alternately : † this word is used when there are four proportionals of the same

kind : and it is inferred , that the first has the same ratio to the third , which the

second has to the

**fourth**; or that the first is to the third , as the second to the**fourth**: as ...

Side 106

F H K If the first be the same multiple of the second , which the third is of the

; and if of the first and third there be taken like multiples , these will be like

multiples of the second and

multiple ...

F H K If the first be the same multiple of the second , which the third is of the

**fourth**; and if of the first and third there be taken like multiples , these will be like

multiples of the second and

**fourth**, each of each . Let A the first be the samemultiple ...

Side 109

than the

the third can be proved to be equal to the

magnitudes , & c . PROP . B. THEOR . If four magnitudes be proportionals , they ...

than the

**fourth**. In like manner , if the first be equal to the second , or less than it ,the third can be proved to be equal to the

**fourth**or less than it . Therefore , if fourmagnitudes , & c . PROP . B. THEOR . If four magnitudes be proportionals , they ...

Side 123

Let AB : C :: DE : F ; and let BG the fifth have to C the second , the same ratio

which EH the sixth has to F the

has to C the second , the same ratio which DH , the sum of the third and sixth ,

has to F ...

Let AB : C :: DE : F ; and let BG the fifth have to C the second , the same ratio

which EH the sixth has to F the

**fourth**: then , AG , the sum of the first and fifth ,has to C the second , the same ratio which DH , the sum of the third and sixth ,

has to F ...

### 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...