## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illus., and an Appendix in Five Books |

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Resultat 1-5 av 5

Side 21

If one side of a triangle be

the interior remote angles. Let ABC be a triangle, and let its side BC be

to D; the exterior angle ACD is greater than either of the interior remote angles ...

If one side of a triangle be

**produced**, the exterior angle is greater than either ofthe interior remote angles. Let ABC be a triangle, and let its side BC be

**produced**to D; the exterior angle ACD is greater than either of the interior remote angles ...

Side 52

If a straight line be bisected, and

by the whole line thus

square of half the line bisected, is equal to the square of the straight line which is

...

If a straight line be bisected, and

**produced**to any point; the rectangle containedby the whole line thus

**produced**, and the part of it**produced**, together with thesquare of half the line bisected, is equal to the square of the straight line which is

...

Side 55

or DB2+2AC.CD= AC*-HCD* : also (II. 4.) AD 9–AC*-ī-CD4+2AC.CD. Add these

equals together, and from the sums take 2AC.CD; then AD 9-1-DB2=2AC2-

H2CD2. PROP. X. THEOR. If a straight line be bisected, and

point, the ...

or DB2+2AC.CD= AC*-HCD* : also (II. 4.) AD 9–AC*-ī-CD4+2AC.CD. Add these

equals together, and from the sums take 2AC.CD; then AD 9-1-DB2=2AC2-

H2CD2. PROP. X. THEOR. If a straight line be bisected, and

**produced**to anypoint, the ...

Side 164

To

being described on the

described on the whole line

To

**produce**a given straight line so that a parallelogram similar to a given onebeing described on the

**produced**part, another parallelogram of equal altitudedescribed on the whole line

**produced**, may be equal to a given rectilineal figure ... Side 183

First, let them be

is in the plane AB, K is in A.B. For the same reason, K is also in CD: wherefore

the planes AB, CD I' th

First, let them be

**produced**towards FH, and meet in the point K. Then, since EFKis in the plane AB, K is in A.B. For the same reason, K is also in CD: wherefore

the planes AB, CD I' th

**produced**meet one another; but they do not meet, since ...### Hva folk mener - Skriv en omtale

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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Ingen forhåndsvisning tilgjengelig - 2016 |

### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol segments semicircle sides similar similar triangles solid angles square of AC straight lines drawn tangent THEOR third triangle ABC triplicate ratio vertex vertical angle wherefore

### Populære avsnitt

Side 94 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Side 53 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.

Side 143 - 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 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.

Side 57 - 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 on the other part.

Side 138 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...

Side 43 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.

Side 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 40 - 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 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...