## Euclid, book i., propositions i. to xxvi., with exercises and alternative proofs [by T. Dalton]. |

### Inni boken

Side 5

A plane angle is the inclination of two lines to each other in a plane which meet

together , but are not in the same straight line . 22 . An obtuse angle is an angle

.

A plane angle is the inclination of two lines to each other in a plane which meet

together , but are not in the same straight line . 22 . An obtuse angle is an angle

**greater**than a right angle . 23 . An acute angle is an angle less than a right angle.

Side 7

Things which are halves of the same thing are equal to one another . 8 .

Magnitudes which coincide with one another , that is which exactly fill the same

space , are equal to one another . 9 . The whole is

straight ...

Things which are halves of the same thing are equal to one another . 8 .

Magnitudes which coincide with one another , that is which exactly fill the same

space , are equal to one another . 9 . The whole is

**greater**than its part . 10 . Twostraight ...

Side 8

From the

part equal to the less . 3 . Given two straight lines terminated in the same point ,

one of them finite , the second of unlimited length ; shew how to cut off from the ...

From the

**greater**of two given straight lines terminated at the same point cut off apart equal to the less . 3 . Given two straight lines terminated in the same point ,

one of them finite , the second of unlimited length ; shew how to cut off from the ...

Side 10

From the

AB and CD be the two given straight lines , of which AB is the

required to cut off from AB the

Construction .

From the

**greater**of two given straight lines to cut off a part equal to the less . LetAB and CD be the two given straight lines , of which AB is the

**greater**; it isrequired to cut off from AB the

**greater**, a part equal to OD the less . BConstruction .

Side 11

1 ) Wherefore from AB the

equal to CD the less . Q . E . F . Exercises . 1 . On the

describe an isosceles triangle , each of whose sides shall be equal to the less .

1 ) Wherefore from AB the

**greater**of two straight lines , a part AF has been cut offequal to CD the less . Q . E . F . Exercises . 1 . On the

**greater**of two straight linesdescribe an isosceles triangle , each of whose sides shall be equal to the less .

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Euclid, Book I., Propositions I. to XXVI., with Exercises and Alternative ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |

### Vanlige uttrykk og setninger

AC is equal ACD is greater angle ABC angle ACB angle BAC angle BCD angle contained angle DEF angle DFE angle EDF angle equal base BC bisects the angle centre circle circumference coincide common constr Construction Demonstration distance Divide draw a straight drawn equal angles equal sides equal to CD equidistant equilateral triangle Euclid exterior angle extremities figure Find a point four given point given straight line greater impossible intersect isosceles triangle join length less Let ABC likewise meet middle point namely opposite sides placed plane position PROBLEM produced proof prop PROPOSITION Prove Q.E.D. Exercises quadrilateral remainder respects right angles shew shewn side AC sides equal stands straight line drawn taken terminated THEOREM thing triangle ABC triangle DEF triangles be equal unequal whole

### Populære avsnitt

Side 39 - IF two triangles have two sides of the one equal to two sides of the...

Side 25 - To draw a straight line at right angles to a given straight line, from a given point in the same.

Side 4 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.

Side 7 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...

Side 7 - Notions 1. Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one another.

Side 36 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.

Side 37 - ... shall be equal to three given straight lines, but any two whatever of these must be greater than the third.

Side 18 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of' the base, equal to one another, and likewise those which are terminated in the other extremity.

Side 29 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line. At the point B in the straight line AB, let the two straight lines...

Side 3 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.