## The Elements of Euclid |

### Inni boken

Resultat 1-5 av 6

Side 36

To describe a o equal to a given retilineal figure, and having an angle equal to a

given rectilineal angle.” Let ABCD be the given

rectilineal angle. It is required to describe a parallelogram equal to ABCD, and ...

To describe a o equal to a given retilineal figure, and having an angle equal to a

given rectilineal angle.” Let ABCD be the given

**rectilineal figure**, and E the givenrectilineal angle. It is required to describe a parallelogram equal to ABCD, and ...

Side 80

D E FINITION S. I. A

the figure in which it is inscribed, each --—, upon each.* | II. t In like manner, a

figure is ...

D E FINITION S. I. A

**RECTILINEAL figure**is said to be inscribed in another**rectilineal figure**, when all the angles of the inscribed figure are upon the sides ofthe figure in which it is inscribed, each --—, upon each.* | II. t In like manner, a

figure is ...

Side 141

Therefore, universally, similar

duplicate ratio of their homologous sides. CoR. 2. And if to AB, FG, two of the

homologous sides, a third proportional M be taken AB has (10, def 5,) to M the

duplicate ...

Therefore, universally, similar

**rectilineal figures**are to one another in theduplicate ratio of their homologous sides. CoR. 2. And if to AB, FG, two of the

homologous sides, a third proportional M be taken AB has (10, def 5,) to M the

duplicate ...

Side 144

6.): for the same reason, the parallelogram ABCD is similar to the parallelogram

FHCK. Wherefore each of the parallelograms GE, KH is similar to DB ; but

to one ...

6.): for the same reason, the parallelogram ABCD is similar to the parallelogram

FHCK. Wherefore each of the parallelograms GE, KH is similar to DB ; but

**rectilineal figures**which are similar to the same**rectilineal figure**are also similarto one ...

Side 266

PROP. XXV. B. VI. It is very evident that the demonstration which Euclid had

given of this proposition has been vitiated by some unskilful hand: for, after this

editor had demonstrated that “as the

KGH, ...

PROP. XXV. B. VI. It is very evident that the demonstration which Euclid had

given of this proposition has been vitiated by some unskilful hand: for, after this

editor had demonstrated that “as the

**rectilineal figure**ABC is to the rectilinealKGH, ...

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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.