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

### Inni boken

Resultat 1-5 av 7

Side 15

3 ) also it has been

CGB , the two sides BF , FC are equal to the two sides CG , GB , each to each ,

and the included angle BFC has been

3 ) also it has been

**shewn**that FC is equal to GB : hence in the triangles BFC ,CGB , the two sides BF , FC are equal to the two sides CG , GB , each to each ,

and the included angle BFC has been

**shewn**equal to the included angle CGB ... Side 26

By the help of this problem , it may be

common segment . For if it be possible let the straight lines GHK , GHL have a

segment GH common to them . HK From H draw HM at right angles to GH .

By the help of this problem , it may be

**shewn**that two straight lines cannot have acommon segment . For if it be possible let the straight lines GHK , GHL have a

segment GH common to them . HK From H draw HM at right angles to GH .

Side 29

In the same way it may be

line with BC ; therefore BD is in the same straight line with BC . Q . E . D . .

Exercises . 1 . How would this proof be affected if BE were drawn on the other

side of ...

In the same way it may be

**shewn**that no other line but BD is in the same straightline with BC ; therefore BD is in the same straight line with BC . Q . E . D . .

Exercises . 1 . How would this proof be affected if BE were drawn on the other

side of ...

Side 30

3 ) Similarly it may be

. D . Exercises . 1 . Write out the proof that the angle A ED is equal to the angle

BEC . 2 . If two straight lines bisect each other , the straight lines joining their ...

3 ) Similarly it may be

**shewn**that the angle AED is equal to the angle BEC . Q . E. D . Exercises . 1 . Write out the proof that the angle A ED is equal to the angle

BEC . 2 . If two straight lines bisect each other , the straight lines joining their ...

Side 31

4 ) but the angle ECD is greater than the angle ECF , ( ax . 9 ) therefore the angle

ECD is also greater that the angle EAB , that is , the angle ACD is greater than

the angle CAB . Similarly , if AC be produced to G , it may be

angle ...

4 ) but the angle ECD is greater than the angle ECF , ( ax . 9 ) therefore the angle

ECD is also greater that the angle EAB , that is , the angle ACD is greater than

the angle CAB . Similarly , if AC be produced to G , it may be

**shewn**that theangle ...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

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.