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

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Resultat 1-5 av 11

Side 8

Let AB be the given straight line ; it is required to describe an equilateral

on AB . ... 1 ) Then shall ABC be an equilateral

Because A is the centre of the circle BCD , therefore AB is equal to AC . (

Let AB be the given straight line ; it is required to describe an equilateral

**triangle**on AB . ... 1 ) Then shall ABC be an equilateral

**triangle**. Demonstration .Because A is the centre of the circle BCD , therefore AB is equal to AC . (

**def**. Side 9

1 ) Upon AB describe the equilateral

of these , DB , DA ( being sides of an equilateral

, therefore the remainder BG is equal to the remainder AL . ( ax . 3 ) Now AL and

...

1 ) Upon AB describe the equilateral

**triangle**ABD . ( prop . ... (**def**. 11 ) but partsof these , DB , DA ( being sides of an equilateral

**triangle**) are equal to each other, therefore the remainder BG is equal to the remainder AL . ( ax . 3 ) Now AL and

...

Side 11

(

them equal to AE , and therefore AF and CD are ... On the greater of two straight

lines describe an isosceles

less .

(

**def**. 11 ) But CD is equal to AE ; ( const . ) therefore AF and CD are each ofthem equal to AE , and therefore AF and CD are ... On the greater of two straight

lines describe an isosceles

**triangle**, each of whose sides shall be equal to theless .

Side 12

Let ABC , DEF be two triangles , in which the side AB is equal to the side DE ,

and the side AC equal to the side DF ... then shall the base BC be equal to the

base EF , and the triangle ABC to the

to ...

Let ABC , DEF be two triangles , in which the side AB is equal to the side DE ,

and the side AC equal to the side DF ... then shall the base BC be equal to the

base EF , and the triangle ABC to the

**triangle DEF**, and the other angles , eachto ...

Side 20

Let ABC ,

EF ; then shall the

Conceive the

Let ABC ,

**DEF**be two**triangles**, in which AB is equal to DE , AC to DF , and BC toEF ; then shall the

**triangles**ABC ,**DEF**be equal in all respects . Construction .Conceive the

**triangle**ABC to be placed so that the base BC coincides with the ...### Hva folk mener - Skriv en omtale

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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.