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

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Side 101

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

and

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

the ...

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,

the ...

Side 102

kind, such that the ratios of the first to the second, of the second to the

so on, whatever may be their number, are all equal; the magnitudes are said to

be continual proportionals. * 9. The second of three continual proportionals is

said ...

kind, such that the ratios of the first to the second, of the second to the

**third**, andso on, whatever may be their number, are all equal; the magnitudes are said to

be continual proportionals. * 9. The second of three continual proportionals is

said ...

Side 106

If the first be the same multiple of the second, which the

if of the first and

the second and fourth, each of each. Let A the first be the same multiple of B the ...

If the first be the same multiple of the second, which the

**third**is of the fourth ; andif of the first and

**third**there be taken like multiples, these will be like multiples ofthe second and fourth, each of each. Let A the first be the same multiple of B the ...

Side 109

if the double of the first be greater than the double of the second, the double of

the

second, the double of the first is greater (V. ax. 3.) than the double of the second;

...

if the double of the first be greater than the double of the second, the double of

the

**third**is greater than the double of the fourth; but if the first be greater than thesecond, the double of the first is greater (V. ax. 3.) than the double of the second;

...

Side 184

If two planes cutting one another be each perpendicular to a

common section is peopendicular to the same plane. Let the two planes AB, BC

be each perpendicular to a

of ...

If two planes cutting one another be each perpendicular to a

**third**plane; theircommon section is peopendicular to the same plane. Let the two planes AB, BC

be each perpendicular to a

**third**plane ADC, and let BD be the common sectionof ...

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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...