## Elements of geometry, based on Euclid, books i-iii |

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Resultat 1-5 av 20

Side 6

Thus , the angle contained by the straight lines AB and BC is ex . pressed either

by

by one line ; which is called the circumference , and is such , that all straight lines

...

Thus , the angle contained by the straight lines AB and BC is ex . pressed either

by

**ABC**or CBA , and the angle contained ... A**circle**is a plane figure containedby one line ; which is called the circumference , and is such , that all straight lines

...

Side 10

From the centre B , at the distance BA , describe the

the point C , in which the

to the points A and B ( Post . 1 ) . Then

From the centre B , at the distance BA , describe the

**circle**ACE ( Post . 3 ) . Fromthe point C , in which the

**circles**cut one another , draw the straight lines CA , CBto the points A and B ( Post . 1 ) . Then

**ABC**shall be an equilateral triangle . Side 12

Because the point A is the centre of the

equal to the angle EDF : - thenThe base BC shall be equal to the base EF ; The

triangle

abbreviation ...

Because the point A is the centre of the

**circle**AE = AD . ... And the angle BACequal to the angle EDF : - thenThe base BC shall be equal to the base EF ; The

triangle

**ABC**shall be Bea equal to the triangle DEF ; * Q . E . F . is anabbreviation ...

Side 20

If it be possible , let the two straight lines

common to · both of them . CONSTRUCTION . ... From the centre C , at the

distance CD , describe the

FG A F & B ...

If it be possible , let the two straight lines

**ABC**, ABD , have the segment ABcommon to · both of them . CONSTRUCTION . ... From the centre C , at the

distance CD , describe the

**circle**EGF , meet ing AB in F and G ( Post . 3 ) . BisectFG A F & B ...

Side 83

Let the two

have the same centre . For , if it be possible , let E be ... Because E is the centre of

the Alb EC = ET

Let the two

**circles ABC**, CDG cut one another in the points B , C . They shall nothave the same centre . For , if it be possible , let E be ... Because E is the centre of

the Alb EC = ET

**circle ABC**, EC is equal to EF ( I . Def . 15 ) . And because E is ...### Hva folk mener - Skriv en omtale

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Elements of Geometry, Based on Euclid, Bøker 1-3 Edward Atkins Ingen forhåndsvisning tilgjengelig - 2016 |

### Vanlige uttrykk og setninger

ABCD angle ABC angle BAC angle BCD angle equal base BC BC is equal bisect centre chord circle ABC circumference coincide common Const CONSTRUCTION cqual describe diagonal diameter difference divided double draw drawn equal to CD equal to twice exterior angle extremities fall figure four given point given rectilineal given straight line gnomon greater impossible join length less Let ABC Let the straight manner meet opposite angles parallel parallelogram pass perpendicular possible produced PROOF PROOF.—Because Proposition proved rectangle contained right angles segment semicircle shown side BC sides square on AC Take taken third touches the circle triangle ABC twice the rectangle unequal whole

### Populære avsnitt

Side 35 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are equal to two right angles.

Side 13 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal. Let ABC be an isosceles triangle, of which the side AB is equal to AC, and let the straight lines AB, AC be produced to D and E.

Side 7 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Side 17 - If two triangles have two sides of the one equal to two sides of the...

Side 51 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.

Side 9 - 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 69 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.

Side 9 - Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another.

Side 32 - Wherefore, if a straight line, &c. QED PROPOSITION XXVIII. THEOREM. If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line ; or make the interior angles upon the same side together equal to two right angles ; the two straight lines shall be parallel to one another.

Side 67 - If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line, which is made up of the half and the part produced.