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

### Inni boken

Resultat 1-5 av 7

Side 3

A plane rectilineal angle is the inclination of two straight lines to one another ,

which

expressed by three letters , the middle one of which must be the letter at the point

...

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 . An angle is generallyexpressed by three letters , the middle one of which must be the letter at the point

...

Side 5

Parallel straight lines are such as are in the same plane , and which being

produced ever so far both ways do not

) are placed by Euclid with the above , but they do not occur in the Propositions of

the ...

Parallel straight lines are such as are in the same plane , and which being

produced ever so far both ways do not

**meet**. The remaining Definitions ( 21 to 35) are placed by Euclid with the above , but they do not occur in the Propositions of

the ...

Side 7

If a straight line

the same side of it , taken together , less than two right angles , these two straight

lines being continually produced shall at length

If a straight line

**meet**two straight lines so as to make the two interior angles onthe same side of it , taken together , less than two right angles , these two straight

lines being continually produced shall at length

**meet**on that side on which are ... Side 9

3 ) and let G be the point where it

the distance DG , describe the circle GLK , ( post . 3 ) and let L be the point where

it

3 ) and let G be the point where it

**meets**the straight line DF . With D as centre , atthe distance DG , describe the circle GLK , ( post . 3 ) and let L be the point where

it

**meets**the straight line DE . Then shall AL be equal to BC . Demonstration . Side 29

Then because AB

are together equal to two right angles ; ( prop . 13 ) but the angles ABC , ABD are

together equal to two right angles ; ( hyp . ) therefore ABC , ABE together are ...

Then because AB

**meets**the straight line CBE , therefore the angles ABC , ABEare together equal to two right angles ; ( prop . 13 ) but the angles ABC , ABD are

together equal to two right angles ; ( hyp . ) therefore ABC , ABE together are ...

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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.