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

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Side 55

The area of a trapezium having two parallel sides is equal to half the

trapezium , and the sum of the parallel sides . 36 . The area of any trapezium is

half the ...

The area of a trapezium having two parallel sides is equal to half the

**rectangle****contained**by the perpendicular distance between the parallel sides of thetrapezium , and the sum of the parallel sides . 36 . The area of any trapezium is

half the ...

Side 56

The area of any trapezium is half the

of the trapezium , and the sum of the perpendiculars let fall upon it from the

opposite angles . 37 . If the middle points of the sides of a triangle be joined , the

...

The area of any trapezium is half the

**rectangle contained**by one of the diagonalsof the trapezium , and the sum of the perpendiculars let fall upon it from the

opposite angles . 37 . If the middle points of the sides of a triangle be joined , the

...

Side 58

A

of the straight lines which

parallelogram , the figure which is composed of either of the parallelograms

about a diameter ...

A

**rectangle**, or right - angled parallelogram , is said to be**contained**by any twoof the straight lines which

**contain**one of the right angles . 2 . In anyparallelogram , the figure which is composed of either of the parallelograms

about a diameter ...

Side 59

If there be two straight lines , one of which is divided into any number of parts ,

the

and BC ...

If there be two straight lines , one of which is divided into any number of parts ,

the

**rectangle contained**by the two straight lines is equal to the**rectangles****contained**by the undivided line , and the several parts of the divided line . Let Aand BC ...

Side 60

AB · BC The

the Therefore the square on AB is equal to the rectangles AF parts AF + and CE .

AB · BC The

**rectangle contained**by AB and BC , together with the AB : .**rectangle****contained**by AB and AC , shall be equal ... But AE is the square on AB ; ABP isthe Therefore the square on AB is equal to the rectangles AF parts AF + and CE .

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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.