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

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Resultat 1-5 av 27

Side 14

FA , AC rcTherefore the two sides FA , AC aro , equal to tho two sides GA , AB ,

cach to * each ; And they contain the angle FAG ,

AFC , AGB . : . FC = C3 Therefore the base FC is equal to the base GB ( I . 4 ) ;

And ...

FA , AC rcTherefore the two sides FA , AC aro , equal to tho two sides GA , AB ,

cach to * each ; And they contain the angle FAG ,

**common**to the two trianglesAFC , AGB . : . FC = C3 Therefore the base FC is equal to the base GB ( I . 4 ) ;

And ...

Side 15

CONSTRUCTION . – From AB , the greater , cut off a part DB , Make equal to AC ,

the less ( I . 3 ) . Join DC . Proor . Because in the triangles DBC , ACB , DB is

equal to AC , and BC is

equal ...

CONSTRUCTION . – From AB , the greater , cut off a part DB , Make equal to AC ,

the less ( I . 3 ) . Join DC . Proor . Because in the triangles DBC , ACB , DB is

equal to AC , and BC is

**common**to both , Therefore the two sides DB , BC areequal ...

Side 18

and AF is

equal to the two sides EA , AF , each to each ; And the base DF is equal to the

base EF ( Const . ) ; : : LDAF Therefore the angle DAF is equal to the angle EAF (

I . 8 ) ...

and AF is

**common**to the two triangles DAF , EAF ; The two sides DA , AF areequal to the two sides EA , AF , each to each ; And the base DF is equal to the

base EF ( Const . ) ; : : LDAF Therefore the angle DAF is equal to the angle EAF (

I . 8 ) ...

Side 19

and CD

equal to the two sides BC , CD , each to each ; And the angle ACD is equal to the

angle BCD ( Const . ) ; Therefore the base AD is equal to the base DB ( I . 4 ) .

and CD

**common**to the two triangles ACD , BCD : The two sides AC , CD areequal to the two sides BC , CD , each to each ; And the angle ACD is equal to the

angle BCD ( Const . ) ; Therefore the base AD is equal to the base DB ( I . 4 ) .

Side 20

By help of this problem , it may be demon . strated that Two straight lines cannot

have a

have the segment AB

By help of this problem , it may be demon . strated that Two straight lines cannot

have a

**common**segment . If it be possible , let the two straight lines ABC , ABD ,have the segment AB

**common**to · both of them . CONSTRUCTION . – From the ...### 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.

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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.

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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.