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

### Inni boken

Resultat 6-10 av 17

Side 15

ABC , DBC are two isosceles triangles on the same base and on the same side of

it ; prove that A D bisects the angle BAC . 2 . If two isosceles triangles stand upon

ABC , DBC are two isosceles triangles on the same base and on the same side of

it ; prove that A D bisects the angle BAC . 2 . If two isosceles triangles stand upon

**opposite sides**of the same base , the straight line which joins their vertices will ... Side 16

Let the triangle ABC be taken up , turned round , and put down again with its

to one another , the

...

Let the triangle ABC be taken up , turned round , and put down again with its

**sides**reversed ; let B in its new position be ... If two angles of a triangle be equalto one another , the

**sides**also which subtend ( that is , are**opposite**to ) the equal...

Side 20

Shew that if ADB be on the other side of AB , then AC , AD may be equal to each

other , and likewise BC , BD . 3 . ... with the base EF , but having the vertex A on

the

Shew that if ADB be on the other side of AB , then AC , AD may be equal to each

other , and likewise BC , BD . 3 . ... with the base EF , but having the vertex A on

the

**opposite side**of EF from D ; let A ' EF represent this new position of ABC . Side 26

2 . In a given straight line determine a point which shall be equidistant from two

given points , one in the given line and the other above it . 3 . Two points lie on

...

2 . In a given straight line determine a point which shall be equidistant from two

given points , one in the given line and the other above it . 3 . Two points lie on

**opposite sides**of a given straight line ; find a point in the line equidistant from the...

Side 27

Take any point D on the other side of AB ; with C as centre , and at the distance

CD describe a circle ; let E and F be the ... Find a point in a given straight line

such that the angle formed by joining it to two given points on

the ...

Take any point D on the other side of AB ; with C as centre , and at the distance

CD describe a circle ; let E and F be the ... Find a point in a given straight line

such that the angle formed by joining it to two given points on

**opposite sides**ofthe ...

### 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.