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

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Side 8

An oblong is that which has all its

32 . A rhombus is that which has all its sides equal , but its

...

An oblong is that which has all its

**angles**right**angles**, but not all its sides equal .32 . A rhombus is that which has all its sides equal , but its

**angles**are not right**angles**. 33 . A rhomboid is that which has its**opposite**sides equal to one another...

Side 12

... their other

sides are

respectively equal to those of another , the triangles are equal in every respect .

... their other

**angles**shall be equal , each to each , viz . , those to which the equalsides are

**opposite**. Or , If two sides and the contained**angle**of one triangle berespectively equal to those of another , the triangles are equal in every respect .

Side 13

put upon And the other

equal , each to each , viz . , the

to the

put upon And the other

**angles**to which the equal sides are**opposite**, shall beequal , each to each , viz . , the

**angle**ABC to the**angle**DEF , and the**angle**ACBto the

**angle**DFE . Proof . — For if the triangle ABC be applied to ( or placed ... Side 14

And the

of the base ) . ... the one are equal to the = remaining

cach , to which the 2 Arc = cqual sides are

And the

**angle**CBD shall be equal to the anglo BCE (**angles**upon the other sideof the base ) . ... the one are equal to the = remaining

**angles**of the other , cach tocach , to which the 2 Arc = cqual sides are

**opposite**, viz . , the**angle**ACF to the ... Side 15

If two

or are

a triangle having the

If two

**angles**of a triangle be equal to one another , the sides also which subtend ,or are

**opposite**to , the equal**angles**, shall be equal to one another . Let ABC bea triangle having the

**angle**ABC equal to the**angle**ACB . The side AB shall be ...### 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.