## The Elements of Euclid, the parts read in the University of Cambridge [book 1-6 and parts of book 11,12] with geometrical problems, by J.W. Colenso |

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Side 79

If two points be taken in the diameter of a circle equally distant from the centre , the sum of the squares of two lines drawn from these points to any point in the

If two points be taken in the diameter of a circle equally distant from the centre , the sum of the squares of two lines drawn from these points to any point in the

**circumference**will be constant . 47. The hypothenuse AB of a right ... Side 80

EQUAL circles are those of which the diameters are equal , or from the centres of which the straight lines to the

EQUAL circles are those of which the diameters are equal , or from the centres of which the straight lines to the

**circumferences**are equal . This is not a definition , but a theorem , the truth of which is evident ; for , if the circles ... Side 81

And an angle is said to insist or stand upon the

And an angle is said to insist or stand upon the

**circumference**intercepted between the straight lines that contain the angle . X. A sector of a circle is the figure contained by two straight lines drawn from the centre , and the ... Side 82

If any two points be taken in the

If any two points be taken in the

**circumference**of a circle , the straight line which joins them shall fall within the circle . Let ABC be a circle , and A , B any two points in the**circumference**: the straight line drawn from A to B ... Side 83

... greater — which is absurd ; therefore the straight line drawn from A to B does not fall without the circle : And , in like manner , it may be demonstrated that it does not fall upon the

... greater — which is absurd ; therefore the straight line drawn from A to B does not fall without the circle : And , in like manner , it may be demonstrated that it does not fall upon the

**circumference**; therefore it falls within it .### Hva folk mener - Skriv en omtale

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The Elements of Euclid, the Parts Read in the University of Cambridge [Book ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |

### Vanlige uttrykk og setninger

ABCD angle ABC angle ACB angle BAC base base BC BC is equal bisected centre chord circle circle ABC circumference common described diameter difference divided double draw drawn equal equal angles equiangular equimultiples extremities fall figure fore four fourth given circle given line given point given straight line greater half inscribed intersection join less Let ABC lines be drawn lines drawn magnitudes manner meet multiple opposite sides parallel parallelogram pass perpendicular plane polygon PROB produced PROP proportionals Q.E.D. PROP rectangle rectangle contained rectilineal figure right angles segment semicircle shew shewn sides similar square square of AC straight lines &c Take taken THEOR third touches the circle triangle ABC Wherefore whole

### Populære avsnitt

Side 42 - 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 4 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 33 - F, which is the common vertex of the triangles: that is », together with four right angles. Therefore all the angles of the figure, together with four right angles are equal to twice as many right angles as the figure has sides.

Side 62 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.

Side 22 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.

Side 58 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.

Side 146 - ... may be demonstrated from what has been said of the pentagon : and likewise a circle may be inscribed in a given equilateral and equiangular hexagon, and circumscribed about it, by a method like to that used for the pentagon.

Side 194 - 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 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16.

Side 69 - 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 of the other part.