## The Elements of Euclid |

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Resultat 1-5 av 11

Side 38

upon the side subtending the right angle, is equal to the squares

the sides which contain the right angle. Let ABC be a right angled triangle,

having the right angle BAC; the square

the ...

upon the side subtending the right angle, is equal to the squares

**described**uponthe sides which contain the right angle. Let ABC be a right angled triangle,

having the right angle BAC; the square

**described**upon the side BC is equal tothe ...

Side 86

To

of the third angle. ... that the rectangle AB, BC be equal to the square of CA; and

from the centre A, at the distance AB,

.) ...

To

**describe**an isosceles triangle, having each of the angles at the base doubleof the third angle. ... that the rectangle AB, BC be equal to the square of CA; and

from the centre A, at the distance AB,

**describe**the circle BDE, in which place (1. 4.) ...

Side 89

... the five angles GHK, HKL, KLM, LMG, MGH being equal to one another, the

pentagon GHKLM is equiangular: and it is equilateral, as was demonstrated; and

it is

... the five angles GHK, HKL, KLM, LMG, MGH being equal to one another, the

pentagon GHKLM is equiangular: and it is equilateral, as was demonstrated; and

it is

**described**about the circle ABCDE. Which was to be done. PROP. XIII. PROB. Side 90

Let ABCDE be the given equilateral and equiangular pentagon; it is required to

FD, FE are equal to one another; and the circle

...

Let ABCDE be the given equilateral and equiangular pentagon; it is required to

**describe**a circle about it. ... FC or FD: therefore the five straight lines FA, FB, FC,FD, FE are equal to one another; and the circle

**described**from the centre F, at the...

Side 150

Let ABC be a right angled triangle, having the right angle BAC; the rectilineal

figure

upon BA, AC. Draw the perpendicular AD; therefore, because in the right angled

...

Let ABC be a right angled triangle, having the right angle BAC; the rectilineal

figure

**described**upon BC is equal to the similar and similarly**described**figuresupon BA, AC. Draw the perpendicular AD; therefore, because in the right angled

...

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The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Robert Simson Ingen forhåndsvisning tilgjengelig - 2017 |

The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Robert Simson Ingen forhåndsvisning tilgjengelig - 2017 |

### Vanlige uttrykk og setninger

altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gles gnomon join less Let ABC meet multiple parallel parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third three plane angles triangle ABC triplicate ratio vertex wherefore

### Populære avsnitt

Side 45 - Ir a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Side 41 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Side 54 - Ir 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 shall fall within the circle.

Side 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.

Side 10 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line: it is required to draw from the point A a straight line equal to BC.

Side 8 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 256 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.

Side 129 - 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 23 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...

Side 20 - ANY two angles of a triangle are together less than two right angles.