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

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Resultat 6-10 av 20

Side 14

In BD take any point F ; from AE the

. 3 . ) join FC , GB . Demonstration . In the triangles AFC , AGB , because AF is

equal to AG ( constr . ) , and AC to AB ; ( hyp . ) and the angle A is common to the

...

In BD take any point F ; from AE the

**greater**cut off AG equal to AF the less ; ( prop. 3 . ) join FC , GB . Demonstration . In the triangles AFC , AGB , because AF is

equal to AG ( constr . ) , and AC to AB ; ( hyp . ) and the angle A is common to the

...

Side 17

If AC is not equal to AB , one of them must be

then that AB is the

less ; ( prop . 3 ) join CD . ( post . 1 ) Demonstration . Then in the triangles DBC ,

ACB ...

If AC is not equal to AB , one of them must be

**greater**than the other ; supposethen that AB is the

**greater**, and from BA the**greater**cut off BD equal to CA theless ; ( prop . 3 ) join CD . ( post . 1 ) Demonstration . Then in the triangles DBC ,

ACB ...

Side 18

9 ) therefore the angle ADC is also

is the angle BDC

side BD is equal to the side BC , therefore the angle BDC is equal to the angle ...

9 ) therefore the angle ADC is also

**greater**than the angle BCD ; much more thenis the angle BDC

**greater**than the angle BCD . But since in the triangle BDC , theside BD is equal to the side BC , therefore the angle BDC is equal to the angle ...

Side 19

5 ) but the angle ECD is

FDC is also

to ...

5 ) but the angle ECD is

**greater**than the angle BCD , ( ax . 9 ) therefore the angleFDC is also

**greater**than the angle BCD ; much more then is the angle BDC**greater**than the angle BCD . But since in the triangle BCD , the side BD is equalto ...

Side 26

1 ) the less equal to the

cannot have a common segment . Exercises . 1 . Draw a straight line any point of

which shall be equidistant from the extremities of a given straight line . 2 .

1 ) the less equal to the

**greater**, which is impossible . Therefore two straight linescannot have a common segment . Exercises . 1 . Draw a straight line any point of

which shall be equidistant from the extremities of a given straight line . 2 .

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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.