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

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Resultat 1-5 av 25

Side 9

The

11 . All right angles are equal to one another . 12 . If a straight line meet two

straight lines , so as to make the two interior angles on the same side of it taken ...

The

**whole**is greater than its part . 10 . Two straight lines cannot inclose a space .11 . All right angles are equal to one another . 12 . If a straight line meet two

straight lines , so as to make the two interior angles on the same side of it taken ...

Side 13

Therefore the

, and is equal to it ( Ax . 8 ) . = A DEF . And the other angles of the one coincide

with the remain - 6 ABC = ing angles of the other , and are equal to them , viz .

Therefore the

**whole**triangle ABC coincides with the**whole**: : A ABC triangle DEF, and is equal to it ( Ax . 8 ) . = A DEF . And the other angles of the one coincide

with the remain - 6 ABC = ing angles of the other , and are equal to them , viz .

Side 14

And because the

, are equal ( Hyp . ) , BF = CG . The remainder BF is equal to the remainder CG (

Ax . 3 ) . And FC was proved to be equal to GB ; Therefore the two sides DF , FC ...

And because the

**whole**AF is equal to the**whole**AG , of which the parts AB , A . C, are equal ( Hyp . ) , BF = CG . The remainder BF is equal to the remainder CG (

Ax . 3 ) . And FC was proved to be equal to GB ; Therefore the two sides DF , FC ...

Side 38

But the angle ACÈ was shown to be equal to the angle BAC ; : : 4 ACD Therefore

the

angles BAC , ABC ( Ax . 2 ) . Adil To each of these equals add the angle ACB .

But the angle ACÈ was shown to be equal to the angle BAC ; : : 4 ACD Therefore

the

**whole**exterior angle ACD is equal to the 7 ADC . two interior and oppositeangles BAC , ABC ( Ax . 2 ) . Adil To each of these equals add the angle ACB .

Side 40

CDB , And because the angle ABC is equal to the angle BCD , and the angle

CBD to the angle ACB , Therefore the

ACD , il BD . angle ACD ( Ax . 2 ) . And the angle BAC has been shown to be

equal ...

CDB , And because the angle ABC is equal to the angle BCD , and the angle

CBD to the angle ACB , Therefore the

**whole**angle ABD is equal to the**whole**ELACD , il BD . angle ACD ( Ax . 2 ) . And the angle BAC has been shown to be

equal ...

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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.

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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.

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.