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

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Resultat 1-5 av 7

Side 105

In equal circles , equal

and the less equal to the less . Let ABC , DEF be equal circles , and BC , EF

equal

...

In equal circles , equal

**chords**cut off equal arcs , the greater equal to the greater ,and the less equal to the less . Let ABC , DEF be equal circles , and BC , EF

equal

**chords**in them , which cut off the two greater arcs BAC , EDF , and the two...

Side 106

In equal circles equal arcs are subtended by equal

equal circles , and let BGC , EHF be cqual arcs in them , and join BC , EF . The

the ...

In equal circles equal arcs are subtended by equal

**chords**. Let ABC , DEF beequal circles , and let BGC , EHF be cqual arcs in them , and join BC , EF . The

**chord**BC shall be equal to the**chord**EF . Take K CONSTRUCTION . - Take K , L ,the ...

Side 107

But equal

equal to the less ( III . 28 ) ; And each of the arcs AD , DB is less than a semicircle

, because DC , if produced , is a diameter ( III . 1 , cor . ) ; Therefore the arc AD ...

But equal

**chords**cut off equal arcs , the greater equal to the greater , and the lessequal to the less ( III . 28 ) ; And each of the arcs AD , DB is less than a semicircle

, because DC , if produced , is a diameter ( III . 1 , cor . ) ; Therefore the arc AD ...

Side 108

The angles contained by a tangent to a circle and a

contact are equal to the angles in the alternate segments of the circle . Let EF be

a tangent to the circle ABCD , and BD a

The angles contained by a tangent to a circle and a

**chord**drawn from the point ofcontact are equal to the angles in the alternate segments of the circle . Let EF be

a tangent to the circle ABCD , and BD a

**chord**drawn from the point of contact B ... Side 117

Show that the centre of a circle may be found by drawing per . pendiculars from

the middle points of any two

circle , straight lines be drawn to the extremities of a parallel

of ...

Show that the centre of a circle may be found by drawing per . pendiculars from

the middle points of any two

**chords**. 4 . ... If , from any point in the diameter of acircle , straight lines be drawn to the extremities of a parallel

**chord**, the squaresof ...

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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.