## The Elements of Euclid |

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Resultat 1-5 av 17

Side 25

... each to each, to which the equal sides are opposite; therefore the angle GCB is

equal to the angle DFE; but DFE is, by the hypothesis, equal to the angle BCA;

wherefore also the angle BCG is equal to the angle BCA, the

... each to each, to which the equal sides are opposite; therefore the angle GCB is

equal to the angle DFE; but DFE is, by the hypothesis, equal to the angle BCA;

wherefore also the angle BCG is equal to the angle BCA, the

**less**to the greater, ... Side 36

to two right angles: wherefore the angles BHF, HFE are

: but straight lines which with another straight line make the interior angles upon

the same side

to two right angles: wherefore the angles BHF, HFE are

**less**than two right angles: but straight lines which with another straight line make the interior angles upon

the same side

**less**than two right angles, do meet (12. Ax.) if produced far ... Side 73

In a circle, the angle in a semicircle is a right angle; but the angle in a segment

greater than a semicircle is

...

In a circle, the angle in a semicircle is a right angle; but the angle in a segment

greater than a semicircle is

**less**than a right angle; and the angle in a segment**less**than a semicircle is greater than a right angle. Let ABCD be a circle, of which...

Side 107

greater than B. | Next, let C have a greater ratio to C | F B that it has to A.; B is

than A : for there is some multiple F of C, and some equimultiples E and D of B

and A such, that F is greater than E, but | it is not greater than D : E therefore B is

...

greater than B. | Next, let C have a greater ratio to C | F B that it has to A.; B is

**less**than A : for there is some multiple F of C, and some equimultiples E and D of B

and A such, that F is greater than E, but | it is not greater than D : E therefore B is

...

Side 169

But BAC is not

either of them, is greater than the other. Wherefore, if a solid angle, &c. Q. E. D.

PROP. XXI. THEOR. EveRy solid angle is contained by plane angles which

together ...

But BAC is not

**less**than either of the angles DAB, BAC: therefore BAC, witheither of them, is greater than the other. Wherefore, if a solid angle, &c. Q. E. D.

PROP. XXI. THEOR. EveRy solid angle is contained by plane angles which

together ...

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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.