## The Elements of Euclid |

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Resultat 1-5 av 7

Side 140

has to the

side FG. Join BE, EC, GL, LH: and because the

...

has to the

**polygon**FGHKL the duplicate ratio of that which the side AB has to theside FG. Join BE, EC, GL, LH: and because the

**polygon**ABCDE is similar to the**polygon**FGHKL, the angle BAE is equal to the angle GFL (1. def. 6), and BA is to...

Side 170

But all the angles at the bases of the triangles are greater than all the angles of

the

triangles, viz. those at the vertex, which contain the solid angle at A, are less than

four ...

But all the angles at the bases of the triangles are greater than all the angles of

the

**polygon**, as has been proved. Wherefore, the remaining angles of thetriangles, viz. those at the vertex, which contain the solid angle at A, are less than

four ...

Side 201

SIMILAR

diameters. ... Join BE, AM, GL, FN : and because the

the

SIMILAR

**polygons**inscribed in circles are to one another as the squares of theirdiameters. ... Join BE, AM, GL, FN : and because the

**polygon**ABCDE is similar tothe

**polygon**FGHKL, and similar**polygons**are divided into similar triangles: the ... Side 203

Let then the segments EK, KF, FL, LG, GM, MH, HN, NE, be those that remain and

are together less than the excess of the circle EFGH above S : therefore the rest

of the circle, viz. the

Let then the segments EK, KF, FL, LG, GM, MH, HN, NE, be those that remain and

are together less than the excess of the circle EFGH above S : therefore the rest

of the circle, viz. the

**polygon**EKFLGMHN, is greater than the space S. Describe ... Side 217

than the solid Z: let these be the segments upon EO, OF, FP, PG, GR, RH, HS, SE

: therefore the remainder of the cone, viz. the pyramid of which the base is the

...

than the solid Z: let these be the segments upon EO, OF, FP, PG, GR, RH, HS, SE

: therefore the remainder of the cone, viz. the pyramid of which the base is the

**polygon**EOFPGRHS, and its vertex the same with that of the cone, is greater than...

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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1834 |

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.