## 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 3

An acute - angled triangle is that which has three acute angles . Of four - sided figures , XXX . A

An acute - angled triangle is that which has three acute angles . Of four - sided figures , XXX . A

**square**BOOK I. Side 4

A

A

**square**is that which has all its sides equal , and all its angles right angles : XXXI . An oblong is that which has all its angles right angles , but not ... Side 45

To describe a

To describe a

**square**upon a given straight line . Let AB be the given straight line : it is required to describe a**square**upon AB . Side 46

On BC describe the

On BC describe the

**square**BDEC ( 1. 46 ) , and on BA , AC the squares GB , HC ; and through A draw AL parallel to BD or CE , and join AD , FC . Side 47

GB , HC upon BA , AC ; therefore the

GB , HC upon BA , AC ; therefore the

**square**upon the side BC is equal to the squares upon the sides BA , AC . Wherefore , In any right angled triangle fc .### 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.