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

### Inni boken

Resultat 1-5 av 12

Side 7

A

circumference which it cuts off . 20 . Rectilineal figures are those which are

contained by straight lines . 21 . Trilateral figures , or triangles , by three straight

lines .

A

**segment**of a circle is the figure contained by a straight line and the part of thecircumference which it cuts off . 20 . Rectilineal figures are those which are

contained by straight lines . 21 . Trilateral figures , or triangles , by three straight

lines .

Side 20

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

have a common

have the

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 ... Side 78

A

circumference which it cuts off . 7 . The angle of a

contained by the straight line and the circumference . 8 . An angle in a

the anglo ...

A

**segment**of a circle is the figure contained by a straight line and thecircumference which it cuts off . 7 . The angle of a

**segment**is that which iscontained by the straight line and the circumference . 8 . An angle in a

**segment**isthe anglo ...

Side 98

The angles in the same

be a circle , and BAD , BED angles in the same

, BED shall be equal to one another . CASE 1 . – First , let the

...

The angles in the same

**segment**of a circle are equal to one another . Let ABCDbe a circle , and BAD , BED angles in the same

**segment**BAED . The angles BAD, BED shall be equal to one another . CASE 1 . – First , let the

**segment**BAED be...

Side 99

Next , let the

. — Draw AF to the centre , and produce it to C , and join CE . PROOF . — Then

the

Next , let the

**segment**BAED | be not greater than a semicircle . CONSTRUCTION. — Draw AF to the centre , and produce it to C , and join CE . PROOF . — Then

the

**segment**BADC is greater than a semicircle , and therefore the angles BAC ...### 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.